Gpr161 null mice. We found that embryos with Pax3 lineage-specific deletion of Gpr161 presented with tectal hypertrophy , cranial vault and facial bone hypoplasia , vertebral abnormalities (somite) and the closed form of spina bifida . In particular, the closed form of spina bifida was partly due to reduced Pax3 and Cdx4 gene expression in the posterior dorsal neural tubes of Gpr161 mutant embryos with decreased Wnt signaling, whereas Shh signaling was increased. We describe a previously unreported role for Gpr161 in the development of posterior neural tubes and confirm its role in cranial neural crest- and somite-derived skeletogenesis and midbrain morphogenesis in mice.Sonic hedgehog (Shh) signaling is the morphogen signaling that regulates embryonic craniofacial and neural tube development. G protein-coupled receptor 161 (Gpr161) is a negative regulator of Shh signaling, and its inactivation in mice results in embryo lethality associated with craniofacial defects and neural tube defects. However, the structural defects of later embryonic stages and cell lineages underlying abnormalities have not been well characterized due to the limited lifespan of  Summary: Using Gpr161 conditional knockout mice with Pax3-Cre as a model for closed spina bifida, this study highlights the involvement of Gpr161, Pax3 and Wnt/β-catenin signaling in spinal neural tube development. The embryonic neural tube is the precursor of the brain and spinal cord, and its development involves highly coordinated multiple cellular processes and signaling events . The faiSmo) (Sufu)  , bone morphogenetic protein (BMP) and canonical Wnt/β-catenin signaling, plays a critical role in tissue patterning and organ morphogenesis during embryonic development . Shh andSmo) , suppres) (Sufu) , and pro Prkaca) , are assPax3 mutant mice with NTDs, including Splotch mice with mutant alleles of Pax3, such as Sp  10.5, and they present with cranial defects and posterior NTDs with full penetrance, along with facial and limb bud defects. Gpr161 hypomorphic mutant mice displayed spinal NTDs and cataracts  mice with various Cre lines, including Wnt1-Cre, Nestin-Cre, GFAP-Cre and Prx1-Cre, showed Gpr161 depletion-mediated developmental defects at later embryonic stages, including intramembranous/endochondral skeletal defects  is a bona fide negative regulator of Shh signaling in multiple developmental and cellular contexts . It is pataracts . Additio defects , facial  defects , forebra defects , ventric defects  and limb defects , which p with SB  and thos with SB . HoweverGpr161 cKO mice with Pax3-Cre. We identified that f/f;Pax3-CreGpr161 (hereafter Gpr161 cKO) mice presented with craniofacial defects, cranial vault/facial and vertebral skeletal defects, and spinal neural tube malformations. In addition, we observed that Pax3 gene expression was downregulated partly via inhibition of Wnt/β-catenin signaling in the dorsal spinal neural tubes of Gpr161 cKO mice, which suggests a molecular mechanism for Gpr161-mediated spinal neural tube development in mice.In this study, we investigated the role of Gpr161 in the cranial neural crest and dorsal neural progenitor lineages during mouse embryonic development, using Gpr161 mutant mice present with craniofacial malformations during mouse embryonic development (Gpr161 knockout (KO) embryos presented with delayed posterior neuropore closure  mice did express low frequency (∼4.55%) of phenotypic malformations  mice at a very low frequency  fetuses showed both craniofacial defects and spinal neural tube malformations (Gpr161 cKO mice with Wnt1-Cre in our previous study (Gpr161 cKO fetuses (Gpr161 cKO fetuses at E17.5 or E18.5: some fetuses showed skin covered without a protrusive sac at the lumbar regions (4/5), whereas one affected fetus showed a skin-covered lesion with a protrusive sac at the same region (1/5)  . Of noteGpr161 cKO fetuses   was also reduced. More intriguingly, spinal columns and ribs were substantially misaligned and disorganized along the entire vertebral column from the cervical to sacral regions, and the neural canal was widened in Gpr161 cKO fetuses at E17.5  , we perfat E17.5 . The verertebrae . To confertebrae , demonstGpr161 cKO fetuses with Wnt1-Cre, which phenocopied the craniofacial phenotypes of Gpr161 cKO fetuses with Pax3-Cre. In the present study, we rigorously pursued the molecular basis of the spinal neural tube malformations in Gpr161 cKO mice, which is the distinguishing phenotypic malformation observed in Gpr161 cKO mice with Pax3-Cre. First, we determined Ptch1 expression in Gpr161 cKO embryos via whole-mount in situ hybridization to check Shh signaling activity , another indicator of canonical Wnt signaling activity, in the posterior region of Gpr161 cKO embryos, whereas the total β-catenin level had not changed  staining in the mesencephalic progenitors in Gpr161 cKO fetuses at E13.5  opening (only less than 5% embryos) right after neurulation (at E10.5) and the histological analysis of the spinal neural tube of Gpr161 cKO fetuses  during somitogenesis, providing an alternative regulatory mechanism of Gpr161-mediated Pax3 gene regulation via Shh signaling.A previous report revealed that the transcriptional regulation of  closure , which lGpr161 cKO mice, we failed to observe any proliferation changes in the spinal neuroepithelium of Gpr161 cKO fetuses  and closed (cKO) SB, our study provides a research model to study the differential molecular profiles between open and closed SB and the potential genetic implication of GPR161 in human closed SB, which has been rarely studied, beyond its implication in open SB that we previously reported  and KO (−/−Gpr161) mice were graciously provided by Dr Saikat Mukhopadhyay  and detailed information concerning the generation of transgenic lines has been previously reported (Pax3-Cre (#005549) and Tcf/Lef1;H2BB-EGFP (#013752) were purchased from Jackson Laboratory. The genotypes of the mice and embryos/fetuses were determined by PCR-based genotyping.All mice were maintained according to the guidelines approved by the Institutional Animal Care and Use Committee (IACUC) of The University of Texas at Austin. reported . The train situ hybridization, paraffin-embedded embryos were sectioned at 10 µm thickness, deparaffinized, and the slides were visualized using an Olympus SZX2-ILLT microscope . The EGFP- and DAPI-positive cells in the neuroepithelium of neural tubes were counted with ImageJ/Fiji software .Embryos were collected at E10.5 from timed matings and processed for cryo-sectioning. To this end, the embryos from different litters were fixed, incubated in 30% sucrose solution at 4°C until they were submerged, and mounted into optimal cutting temperature (OCT) solution. OCT-embedded embryos were cryo-sectioned using a Cryotome (Thermo Fisher Scientific) with 10 µm thickness for immunostaining. The frozen sections were incubated with blocking buffer (10% goat serum in PBS) followed by washing with PBS. Subsequently, they were incubated with Alexa Fluor 488-conjugated anti-GFP antibody  in blocking buffer and then with DAPI (1 µg/ml) prior to mounting. Images were captured using a Nikon Ti2E/CSU-W1 spinning-disc confocal microscope. For whole-mount f/fGpr161 and f/+;Pax3-Cre/+.Gpr161 Collected fetuses were fixed, paraffin embedded and sectioned with 4 μm thickness. The paraffin-embedded sections were deparaffinized, dehydrated, antigen-retrieved, blocked , and incubated with primary antibody  overnight at 4°C. After washing, sections were incubated with horseradish peroxidase (HRP) polymer conjugate  and 3,3′-diaminobenzidine . The sections were counterstained with Hematoxylin (Thermo Fisher Scientific). Images were captured using an All-In-One Fluorescence microscope (Keyence) using a 2× and 20× objective. The images were analyzed with ImageJ/Fiji software.Fetuses were harvested at E13.5 from timed matings between f/fGpr161 and f/+;Pax3-Cre/+Gpr161 or between Gpr161 heterozygotes (+/−Gpr161). The collected embryos were fixed and dehydrated with methanol and were then pooled based on their genotypes for further analysis. Whole-mount in situ hybridization was performed according to standard protocols (Pax3 and Axin2 were obtained from Lee Niswander (University of Colorado), Sox10 from Yoshihiro Komatsu , and Ptch1 from Steven Vokes (The University of Texas at Austin). The DNA template for RNA probes targeting Cdx4 were generated . Images were captured with the Olympus SZX2-ILLT microscope.Embryos were collected at E10.5 from timed matings either between rotocols . The cDNenerated  based onf/fGpr161 and f/+;Pax3-Cre/+Gpr161 mice. The posterior part of embryos from different litters was collected by cutting at the level of hindlimb buds and was lysed with radioimmunoprecipitation assay (RIPA) buffer . The lysates were used for western blotting with anti-ABC , anti-β-catenin  and anti-GAPDH  antibodies, and then with 1RDye 800CW goat anti-rabbit IgG (LiCOR). The images were captured using an Odyssey imaging system (LI-COR). The band intensity was quantified with ImageJ software.Embryos were harvested at E10.5 from timed matings between 2O and 90% ethanol) for 3 days at 37°C. After washing, samples were kept in 1% KOH for 48 h. For long-term storage, specimens were serially transferred into 20%, 50% and 80% glycerol solutions and were ultimately maintained in 100% glycerol. The images were captured with the Olympus SZX2-ILLT microscope.Skeletal staining was performed using a modified Alcian Blue/Alizarin Red staining procedure . BrieflyE17.5 fetuses collected from different litters were fixed with 10% formalin, followed by fixation with 70% ethanol. Specimens were scanned at the University of Texas High-Resolution X-ray Computed Tomography Facility using the flat panel detector on a Zeiss Xradia 620 Versa microscope. The X-ray source was set to 70 kV and 8.5 W with no filter. A total of 2001 0.1 s projections were acquired over ±180° of rotation with no frame averaging. A source-object distance of 18.0 mm and a detector-object distance of 251.7 mm resulted in 9.98 μm resolution.10.1242/dmm.050277_sup1Supplementary informationClick here for additional data file.


What is the performance of large language models on neurology board–style examinations?In this cross-sectional study, a newer version of the large language model significantly outperformed the mean human score when given questions from a question bank approved by the American Board of Psychiatry and Neurology, answering 85.0% of questions correctly compared with the mean human score of 73.8%, while the older model scored below the human average (66.8%). Both models used confident or very confident language, even when incorrect.These findings suggest that with further refinements, large language models could have significant applications in clinical neurology. This cross-sectional study assesses the performance of large language models (LLMs) on neurology board–style examinations. Recent advancements in large language models (LLMs) have shown potential in a wide array of applications, including health care. While LLMs showed heterogeneous results across specialized medical board examinations, the performance of these models in neurology board examinations remains unexplored.To assess the performance of LLMs on neurology board–style examinations.This cross-sectional study was conducted between May 17 and May 31, 2023. The evaluation utilized a question bank approved by the American Board of Psychiatry and Neurology and was validated with a small question cohort by the European Board for Neurology. All questions were categorized into lower-order  and higher-order  questions based on the Bloom taxonomy for learning and assessment. Performance by LLM ChatGPT versions 3.5 (LLM 1) and 4 (LLM 2) was assessed in relation to overall scores, question type, and topics, along with the confidence level and reproducibility of answers.Overall percentage scores of 2 LLMs.LLM 2 significantly outperformed LLM 1 by correctly answering 1662 of 1956 questions (85.0%) vs 1306 questions (66.8%) for LLM 1. Notably, LLM 2’s performance was greater than the mean human score of 73.8%, effectively achieving near-passing and passing grades in the neurology board examination. LLM 2 outperformed human users in behavioral, cognitive, and psychological–related questions and demonstrated superior performance to LLM 1 in 6 categories. Both LLMs performed better on lower-order than higher-order questions, with LLM 2 excelling in both lower-order and higher-order questions. Both models consistently used confident language, even when providing incorrect answers. Reproducible answers of both LLMs were associated with a higher percentage of correct answers than inconsistent answers.Despite the absence of neurology-specific training, LLM 2 demonstrated commendable performance, whereas LLM 1 performed slightly below the human average. While higher-order cognitive tasks were more challenging for both models, LLM 2’s results were equivalent to passing grades in specialized neurology examinations. These findings suggest that LLMs could have significant applications in clinical neurology and health care with further refinements. The recent emergence of powerful transformer-based artificial intelligence models4 provides a new avenue for exploring their implications in the field of neurology. These LLMs undergo training using expansive data sets, encompassing more than 45 terabytes of information. This rigorous training process equips them to recognize patterns and associations among words, which, in turn, empowers them to produce responses that are both contextually accurate and logically consistent.5 While the newer model performed better in a variety of examinations,5 the older model remains faster in processing tasks. The application of these models in specialized medical examinations has been tested to some extent. The older model showed near-pass performance in the United States Medical Licensing Examination (USMLE),7 while it failed to pass the ophthalmology board examination.8 Two recent reports showed slightly deviating results on neurosurgery board–style examinations, with 1 report claiming a near-pass with the older model and the other showing an approximately 10% lower performance. The older model achieved a near-pass in radiology board–like examinations,9 while the new model successfully passed neurosurgery board–like examinations.10 In contrast, neurology board–like examinations present a different set of challenges. Compared with radiology, ophthalmology, or neurosurgery, the questions in neurology board examinations often present complex narratives with subtle diagnostic clues that require a nuanced understanding of neuroanatomy, neuropathology, and neurophysiology. The candidate is expected to navigate through these complex narratives, extracting relevant data, and synthesizing this information into a coherent diagnostic hypothesis and subsequent therapeutic decisions. Written board examinations, designed to test a broad range of neurology topics, are common in the United States, Canada, and Europe. These examinations typically use multiple-choice questions, a format also adopted in the United States by the American Board of Psychiatry and Neurology (ABPN)11 and in Europe by the European Board of Neurology (UEMS-EBN).12Deep learning algorithms have been investigated in neurology for a variety of tasks, such as neurologic diagnosis, prognosis, and treatment.In this cross-sectional study, our objective was to evaluate the performance of these 2 models in comparison with human performance in neurology board–like written examinations. We used the context of neurology board–like written examinations as a representative example to scrutinize the complex reasoning abilities and the capacity of LLMs to navigate intricate medical cases, thereby illuminating their potential in more sophisticated, real-world clinical applications. Our ultimate aim was not only to determine their accuracy and reliability in this specialized context but also to characterize their strengths and limitations. As LLMs continue to evolve, understanding their potential contributions and challenges in medical examinations could pave the way for future applications in neurology and neurology education.STROBE) reporting guideline for observational studies. This exploratory prospective study was performed from May 17 to May 31, 2023.This study did not involve human participants or patient data, so it was exempt from institutional review board approval. This report follows the Strengthening the Reporting of Observational Studies in Epidemiology  and GPT-4 (LLM 2). Questions including videos or images as well as questions that were based on preceding questions were excluded in this study . This question bank is approved by the ABPN as part of a self-assessment program and can be used as a tool for certified medical education.13 Questions were in single best answer, multiple-choice format with 3, 4, or 5 distractors and 1 correct answer. To validate the results from this question bank, open-book sample questions from 2022 from the European Board of Neurology were used (19 questions). These questions are either behind a paywall (in the case of the question bank) or published after 2021 and therefore out-of-training data for both LLMs. Memorization analyses15 were performed to exclude the possibility that test questions were in-training data for the models , LLM 1 did so in 87.0% of cases (348 of 400 questions). Question length was assessed by counting the characters of the question.Questions were then classified by type using principles of the Bloom taxonomy for learning and assessment as testing either lower-order  or higher-order  thinking.The questions can be further categorized according to 26 topics in the field of neurology that are listed in the 5 At the time of this study, we did not have access to other powerful closed-source models.19 LLM 1 and LLM 2 were pretrained on more than 45 terabytes of text data, including a substantial portion of internet websites, books, and articles. The investigators did not perform any additional neurology-specific fine-tuning of the model. In this study, we used server-contained language models that were trained up to September 2021. The used models do not have the ability to search the internet or external databases.LLM 1 and 2 were used via the application programming interface (API). These are 2 commonly used LLMs.Each multiple-choice stem along with its answer choices was provided to the models via its API together with the following prompt:“You are a medical doctor and are taking the neurology board exam. The board exam consists of multiple choice questions.All output that you give must be in JSON format.- Return the answer letter- Give an explanation- Rate your own confidence in your answer based on a Likert scale that has the following grades: 1 = no confidence [stating it does not know]; 2 = little confidence ; 3 = some confidence; 4 = confidence ; 5 = high confidence [stating answer and explanation without doubt])- Classify the question into the following two categories: 1. lower order questions that probe remembering and basic understanding, and 2. higher order question where knowledge needs to be applied, analysis capabilities are examined, or evaluation is needed. (return “Higher” or “Lower”)- Rate the confidence of your classification into these categories based on the Likert scale that has the following grades1 = no confidence [stating it does not know]; 2 = little confidence ; 3 = some confidence; 4 = confidence ; 5 = high confidence [stating answer and explanation without doubt])Your output must look like the following:{”answerletter”:…,”reasoning”:…,”confidence_answer_likert”:…,”classification”:…,” confidence_classification_likert”:…”All answer choices and responses were recorded. A passing score was considered 70% or higher on this neurology board–style examination without images to approximate the written examination from the ABPN and the EBN. The question bank uses 70% as passing threshold to gain credits for certified medical education (CME) points. The Royal College examination in Canada considers 70% or greater on all written components a passing score. There, questions undergo psychometric validation, with removal of questions found not discriminatory or too difficult, which was not performed. The ABPN and EBN examinations use criterion-referenced scoring, which was not used.20 and the percentage of each question was recorded. Then, answers with high reproducibility  were compared with answers without high reproducibility.For the reproducibility analyses, 100 questions were answered by both models with 50 independent queries probing the principle of self-consistency21 The source of these embeddings is the model parameters or weights, which are used to code and decode the texts for input and output. A dimensionality reduction of the embeddings was performed with a t-distributed stochastic neighbor embedding (tSNE) analysis,22 and clusters were subsequently examined. Similarity between question and answer embeddings was compared calculating cosine similarity.For the high-dimensional analysis of question representations, the embeddings of these questions were analyzed. These numeric vector representations encompass the semantic and contextual essence of the tokens  processed by the model.2 test). We also executed a subgroup analysis for various subclasses of higher-order thinking questions and the 26 topics, in which we utilized the χ2 test for multiple comparisons with a Bonferroni correction. Given that the models had a probabilistic chance of correctly answering each question, we utilized a guessing correction formula23 to glean further understanding: it is computed by subtracting the ratio of the number of incorrect responses to the total number of choices minus one from the number of correct responses: ncorrect − (nwrong / ) (P = .02).To identify any topic-specific strengths or weaknesses displayed by each model, we analyzed their performance in topics that contained more than 50 questions. Notably, LLM 1 did not display any significant performance variation across topics. In contrast, LLM 2 showed significantly enhanced performance in answering questions related to behavioral, cognitive and psychological categories (433 of 482 [89.8%]) compared with its performance on questions concerning epilepsy and seizures (39 of 55 [70.9%]) . Incorrect LLM 2 and LLM 1 answers were all subjectively assessed by the models as expressing confidence or high confidence  . Self-assessment of confidence expressed by LLM 1 and LLM 2 in their answers showed a small difference between incorrect and correct responses , potentially indicating another marker of confidence of LLMs that might be leveraged to filter out invalid responses. The same observation was made with LLM 2, with 78 of 96 correct answers (81.3%) in those with high reproducibility vs 1 of 4 (25.0%) in answers with low reproducibility (P = .04).Reproducibility analyses revealed that highly reproducible answers were more likely to be answered correctly than inconsistent answers by LLM 1  , indicating that the distance between question and answer did not significantly affect the models’ answer choice.To investigate whether the models use the similarity of question and answers in the multidimensional embedding space to select their answer, similarity between the question embedding and each answer embeddings was compared. It was found that in 28.3% of questions (476 of 1681), the correct answer was the closest in the multidimensional embedding space. Accordingly, the LLMs labeled the most similar answer as correct in more than 30% of cases (LLM 2: 513 of 1681 [30.5%]; 26 Despite being extensively pretrained on vast data sets and offering promising possibilities within the health care sector, their specific application in neurology remains relatively uncharted territory. The efficacy of these models in handling specialized neurology knowledge also remained indeterminate until this study.The notable progress achieved by the 2 LLMs studied has substantially enhanced the potential of these models across a wide range of applications.This exploratory research revealed LLM 2’s proficiency in completing a neurology board–like examination, a task LLM 1 was unable to accomplish. This finding underscores the rapid and significant evolution of LLMs. Our results suggest that LLM 2 would be able to pass a neurology board–like examination, whereas LLM 1’s performance falls short of passing such a specialized examination.16 In comparison with its performance on the USMLE Step Examinations,28 where it did not exceed a 65% accuracy, LLM 1 scored surprisingly well in this more specialized examination.Despite their strengths, both models demonstrated weaker performance in tasks requiring higher-order thinking compared with questions requiring only lower-order thinking.29 It is important to note that the models have been changing over time.30 Therefore, for models to be reliably used in the medical context, it would be important to use models that remain stable and are continuously tested when updated.As these models are trained to identify patterns and relationships among words in their training data, they can struggle in situations requiring a deeper understanding of context or specialized technical language. This limitation is crucial for neurologists to bear in mind, particularly with LLMs now being incorporated into popular search engines and readily accessible to the public.32 and originates from the training objective of these models, which is to predict the most likely sequence of words following an input. This characteristic, coupled with the model’s inclination to generate plausible, convincing, and human-like responses, can potentially mislead individuals relying solely on it for information.34 However, the model was able to partially differentiate its own confidence level, as there were slight but important differences between correct and incorrect answers, although the values on the Likert scale predominantly are between confident and highly confident. Furthermore, we identified that reproducible answers are correlated with correctness and might serve as an intrinsic, surrogate marker of confidence defined by the output of the LLM.Interestingly, both models exhibited confident language when answering questions, even when their responses were incorrect. This trait is a recognized limitation of LLMsThis study has some limitations. The questions used were not official ABPN or EBN board examination questions due to their confidential and regulated nature. Additionally, image-based questions were not included because LLM 1 and versions of LLM 2 at the time of the study were not equipped to process these. Furthermore, the passing grade was an approximation based on the threshold by the ABPN for approving of points for CME. The limited number of questions in each subgroup in this exploratory study also reduced the power of subgroup analyses. We only included these 2 models in this assessment as other similarly powerful closed-source models were not available to us at the time of this study. The absence of significant differences between the 2 models in the EBN question bank should be considered in the context of limited number of questions in this cohort.In addition, the level of education of the human scorers is not exactly known and should be considered when interpreting comparisons between the models and the users scores. Additionally, human scores could be overestimated due to users that repeat question banks for practice. Therefore, it is important to also consider the absolute scores from the models.35 LLM 2 passed a neurology board–style examination after exclusion of video and image questions. As deep learning architectures are continuously refined for computer vision and medical imaging,37 this image-processing limitation may be addressed in future models, potentially including the upcoming multimodal input functionalities of LLM 2. Despite performing admirably on questions assessing basic knowledge and understanding, the model showed slightly lower performance on higher-order thinking questions. Consequently, neurologists should be aware of these limitations, including the models’ tendency to phrase inaccurate responses confidently, and should be cautious regarding its usage in practice or education. With the anticipated advancements in LLMs, neurologists and experts of other clinical disciplines will need to comprehend their performance, reliability, and applications within neurology better. Investigating the potential applications of LLMs that have been fine-tuned specifically for neurology represents a compelling direction for future research.In conclusion, this study underscored the vast potential of LLMs, particularly in neurology, even without neurology-specific pretraining. Potential applications in clinical settings include documentation and decision-making support systems as well as educational tools.


Shallow, CNOT-efficientquantum circuits are crucial for performingaccurate computational chemistry simulations on current noisy quantumhardware. Here, we explore the usefulness of noniterative energy corrections,based on the method of moments of coupled-cluster theory, for acceleratingconvergence toward full configuration interaction. Our preliminarynumerical results relying on iteratively constructed ansätzesuggest that chemically accurate energies can be obtained with substantiallymore compact circuits, implying enhanced resilience to gate and decoherencenoise. Such schemesrequire much shallower circuits than pure quantum algorithms, e.g.,quantum phase estimation,20 substantially reducing the computationalcost and sensitivity to gate and decoherence noise.The first electronic structurecalculation on quantum hardware was reported more than 10 years ago.t = is a vector of parameters, |Φ⟩ is a reference state thatcan be easily realized on the quantum device, andT)((t)⟩. UT). In this case, the UμT)((tμ) unitaries have the formμ is a genericfermionic anti-Hermitian operator. In the language of second quantizationand in the case of an n-body operator, κμ is defined asap (ap ≡ ap†) is the annihilation (creation)operatoracting on spinorbital ϕp and indices i1, i2, ... or i, j, ...  label spinorbitals occupied (unoccupied) in |Φ⟩.Although starting from a fermionic UCC unitary and translating itto the qubit space is a natural choice for the study of electronicstructure problems, it generally leads to circuits containing a substantialnumber of CNOT gates. This is particularly problematic, since currenthardware implementations of two-qubit gates, such as CNOTs, are typically∼10 times noisier than their one-qubit analogs. More CNOT-efficientansätze are obtained, for example, by directly building UCCin the qubit space47 or employing the fermionic-excitation-based (FEB) circuits and theirqubit (QEB) counterparts.50 Approximateimplementations of the FEB and QEB circuits have recently been explored,resulting in single- and two-qubit gate counts that scale linearlywith the excitation rank.51To pavethe way toward practical and robust computations on actualquantum devices, various schemes have been devised to reduce the circuitdepth of hybrid quantum–classical algorithms even further.In the case of ansatz-dependent approaches, which are of particularimportance to this work, the construction of compact, yet sufficientlyexpressive, trial states is crucial. In general, the trial state isexpressed as24 by Ryabinkinet al.52 By considering various low-orderperturbative corrections to the iQCC energies, they were able to achievea given level of accuracy with a smaller number of iQCC iterations.Anotherpromising approach for reducing quantum resource requirementsthat has received relatively little attention is the use of noniterativeenergy corrections. Such schemes, in conjunction with iterativelyconstructed ansätze, have the potential to accelerate convergencetoward the exact, full configuration interaction (FCI), solution,thus decreasing the depth of the underlying quantum circuits. Thisavenue was initially explored in the context of the iterative qubitcoupled cluster (iQCC) approach66 in accelerating the convergence to FCI of adaptive schemes. Correctionsbased on the MMCC framework have several desirable properties. Unlikenoniterative corrections based on many-body perturbation theory arguments,76 which generally fail when nondynamical correlations become substantial,MMCC-type corrections are robust in the presence of quasi-degeneraciesencountered in typical problems of chemical interest, such as singlebond breaking and biradicals. In its exact form, the MMCC frameworkprovides the noniterative correction to the energy of an approximateCC method needed to recover the FCI energy. Although in practice onecomputes an approximate MMCC correction, improving its quality byincorporating higher-rank moments is straightforward, albeit computationallydemanding on a classical machine. Nevertheless, in the case of a unitaryansatz, the necessary ingredients to compute such corrections canbe efficiently calculated on a quantum computer (vide infra). Furthermore,UCC-based approaches provide upper bounds to the FCI energy, renderingthem immune to the catastrophic failures plaguing traditional single-referenceCC methods in the presence of strong correlations, and excellent startingpoints for noniterative corrections  equationsalso ref  for the 21 and selected PQE (SPQE)11 approaches, which are based on iteratively constructedansätze optimized with VQE and PQE, respectively. Recall thatin the VQE and PQE schemes, the energy ET)( = UT)†(HUT) to the ansatz. In the case of VQE,the energy gradientsμ⟩ ≡κμ |Φ⟩) of the connected clusterform of the Schrödinger equation with the UCC ansatz, P) and thoseexcluded (Q), then for VQE the optimization is performedvariationally, which translates into enforcing the condition gp = 0 ∀ κp ∈ P. In the PQEcase, a similar condition is imposed for the residuals (rp = 0 ∀ κp ∈ P). As shown in ref rμ(T) are the residuals or moments of the UCC equations80 and EμT) generalization82 to the language of UCC .In the numerator of the CCcorrection appears the product of moments of CC equations correspondingto the right and left CC states. Recall that traditional CC theoryis non-Hermitian and as such the CC similarity-transformed Hamiltonianhas distinct right and left eigenvectors. Since the UCC similarity-transformedHamiltonian is Hermitian, in the translation process, the left-statemoment is replaced by the complex conjugate of the right moment. Froman alternative point of view, Next, we move on with the discussionof the noniterative corrections.Here, we consider two families of noniterative MMCC-type corrections.The first one has the formof view, μ⟩ forwhich rμ(T) ≠0, namely, |Φμ⟩ ∈ Q for PQE and |Φμ⟩ ∈ P ⊕Q in the case of VQE. For example,in a UCCSD calculation relying on PQE optimization (UCCSD-PQE), theoptimum parameters are obtained by imposing the residual conditionsIa (UCCSD-PQE)moment correction runs over all triply, quadruply, etc. excited Slaterdeterminants . Alternatively, in a VQE-based UCCSD (UCCSD-VQE)computation, the parameter optimization is performed variationally,i.e., by enforcingIa(UCCSD-VQE) noniterative correctioninvolves all UCCSD-VQE moments, including those corresponding to singlesand doubles. In this case, the appropriate schemes are based on thegeneralized MMCC formalism that was introduced in the context of extendedcoupled cluster theory.57In ourcurrent implementation,the summation appearing in rμ(SPQE) residualsare already available, since they are generated for the selectionof new operators. This is analogous to how perturbative energy correctionsare evaluated in selected configuration interaction (CI) techniques,such as the CI method using perturbative selection made iteratively,90 adaptive CI,92 and adaptive sampling CI,93 to mention a few. In the case of ADAPT-VQE simulations,the residuals need to be evaluated, but this can be efficiently accomplishedby repeated measurements of the residual vector, as discussed above.Furthermore, both SPQE and ADAPT-VQE have access to the ET), we replace the similarity-transformed Hamiltonian in EμT), is more drastic,replacing the entire denominator appearing in μ ≡Δi1 ··· ina1 ··· an = ϵi1 + ···+ ϵin – ϵa1 – ϵan, with ϵp denoting the Hartree–Fock energy of spinorbitalϕp. Note that unlike Supporting Information for the proof and underlyingconditions for the size consistency of Next, weconsider the computational burden associated with theevaluation of 55 namely,(ext)⟩ is thewavefunction froman external source and serves as an approximation to the FCI wavefunction.If |Ψ(ext)⟩ ≡ |Ψ(FCI)⟩, then ET)( + δII(T) = E(FCI). In this regard, 106 The derivation of this noniterative correction can be found in theAppendix of Peng and Kowalski.77 As wasthe case with μ⟩ forwhich rμ(T) ≠0. An intriguing aspect of this noniterative correction is its flexibilityregarding the external state. One has the possibility of utilizingany quantum algorithm that can produce an approximate eigenstate ofthe Hamiltonian and combining it with any ansatz-dependent schemewith the intention of improving the results of both.The second familyof noniterative corrections we consider is basedon the one defining the original renormalized and completely renormalizedCC approaches,Beforewe proceed with the discussion of our numerical simulations,we would like to comment on the orbital invariance of the moment energycorrections introduced in our work. The use of Epstein–Nesbet-likedenominators in 6 linear chain, as described by the minimum STO-6G basis.107 In these preliminary calculations, we consideredthree representative points along the potential energy curve, characterizedby the distances between neighboring H atoms of RH–H = 1.0, 2.0, and 3.0 Å, corresponding tothe equilibrium, recoupling, and strongly correlated regions of thepotential, respectively. The underlying quantum algorithms used togauge the performance of the δI(T) corrections, 51 Inbenchmarking the δII(T) correction,the trial state was obtained with VQE using a UCCSD ansatz. As a proofof principle, the external states were initially taken to be UCCGSDand UCCSDTQPH, optimized with VQE and PQE, respectively. Both UCCGSDand UCCSDTQPH are exact in the case of H6/STO-6G, and theδII(UCCSD) correction to the UCCSD energies reproducedthe FCI result with microhartree or better accuracy. In the productionrun, the external states were those extracted at every macro-iterationof QEB-ADAPT-VQE simulations. This approach shares the same philosophywith the externally corrected CCSD methods based on FCI quantum MonteCarlo104 and selected CI wavefunctions106  scheme based on FCI quantum Monte Carlo108 and its selected CI counterpart109).To assess the ability of the noniterative,MMCC-type, energy correctionsexplored in this study to accelerate convergence toward FCI and reducethe resources used by the underlying quantum algorithms, we performednumerical simulations of the symmetric dissociation of the H–2Eh. The PQE micro-iteration threshold was set to 10–5Eh, while the direct inversion of theiterative subspace112 was utilized to accelerate convergence.Although in typical SPQE runs, multiple operators are added to theansatz per macro-iteration, here we followed the ADAPT-VQE paradigmand added operators sequentially. This allowed us to properly examinethe ability of the noniterative corrections to accelerate convergenceof SPQE toward FCI. The ADAPT-VQE simulations relied on a pool ofgeneralized singles and doubles114 and macro-and micro-iteration thresholds of 10–3Eh and 10–5Eh, respectively. All numerical simulations reported in this work havebeen performed using QForte,115 a state-vectoremulator developed by our group. The noniterative energy correctionsexplored in this study have been implemented in a local version ofQForte. All computations used restricted Hartree–Fock references,with the one- and two-electron integrals obtained from Psi4.116All SPQE simulations used a full operator pool and macro-iterationthreshold of 10xI ≡ FEB-SPQE+δxI, with x = a, b, c. A quick inspection of Eh more rapidly than the underlyingFEB-SPQE approach. Their performance is particularly impressive inthe weakly and moderately correlated regions, requiring as much as∼45 and ∼20% fewer parameters than FEB-SPQE. This emphasizesthe exceptional ability of such noniterative corrections to recoverdynamical correlation effects. The decrease in the number of parametersis accompanied by similarly remarkable reductions in the CNOT countsof the corresponding ansatz circuits, as illustrated in the bottompanels of Ic scheme that relies on the standard Møller–Plessetdenominator has the least favorable performance. With the exceptionof the very early stages of the FEB-SPQE simulations, FEB-SPQEIb faithfully reproduces the results of its FEB-SPQEIa parent. This remains true even near the dissociation threshold ofH6, represented by the geometry characterized by RH–H = 3.0 Å. This implies that thesize inconsistency introduced in the denominator of 6. As a result, in the subsequent benchmarks,we will be focusing on the δIb correction, sinceit not only provides results similar to the more complete δIa scheme, but is also more computationally efficient (videsupra).We begin the discussion of our numericalresults by examining theability of the noniterative, MMCC-type, energy corrections definedin Ib noniterative correction with aFEB-SPQE. Asalready mentioned above, the recently introduced aFEB circuits areapproximate implementations of the CNOT-efficient FEB ones that requirea number of CNOT gates that scales linearly with the excitation rankof a given operator.51 Furthermore, althoughthe aFEB approximation breaks the particle number N and total spin projection Sz symmetries, it has been demonstrated that aFEB-SPQE is characterizedby an essentially negligible symmetry contamination and a faithfulreproduction of the parent FEB-SPQE energetics. As might have beenanticipated, the same is true when we examine the energies resultingfrom their δIb-corrected counterparts. Indeed, asshown in Figure S1 of the Supporting Information,the aFEB-SPQEIb data are practically indistinguishablefrom those obtained with FEB-SPQEIb. This is even truein the recoupling region, characterized by RH–H = 2.0 Å, where the largest deviation, on theorder of 0.1 mEh, is observed. At thispoint, it is worth mentioning that due to the symmetry breaking introducedby the aFEB quantum circuits, aFEB-SPQE has nonzero moments correspondingto Slater determinants with N ≠ 6 and/or Sz ≠ 0 for the groundelectronic state of H6. In principle, one could incorporatesuch Fock-space moments into the MMCC-type noniterative correctionsto improve the quality of the results even further. However, sincethe contribution of the symmetry contaminants to the aFEB-SPQE wavefunctionis negligible,51 we did not consider sucha generalized correction.In an effort to reduce the circuit depth even further,we combinethe δIb noniterativecorrection in the context of ADAPT-VQE (QEB-ADAPT-VQEIb) and compare the results with those of aFEB-SPQEIb. Whenexamining the errors with respect to FCI, we observe that, in general,the QEB-ADAPT-VQEIb approach offers a major improvementover the underlying QEB-ADAPT-VQE energetics (top panels of Ib to recover the FCI data within 1.0 mEh faster than the underlying QEB-ADAPT-VQE approach, resultingin substantial savings in terms of CNOTs (see the bottom panels of 6. In this case, QEB-ADAPT-VQE is characterized bya very slow convergence to FCI, most likely due to the presence ofa local energy minimum. For QEB-ADAPT-VQEIb, this manifestsitself as a plateau in the corresponding energies. The fact that afterabout 120 parameters the QEB-ADAPT-VQE and QEB-ADAPT-VQEIb results practically coincide, i.e., the QEB-ADAPT-VQE moments areclose to zero, further corroborates to the fact that the QEB-ADAPT-VQEwavefunction closely resembles that of an exact excited electronicstate. Eventually, both QEB-ADAPT-VQE and QEB-ADAPT-VQEIb achieve chemical accuracy at the same time, requiring about 80%of the number of parameters of FCI.Next, we examine the usefulness ofthe δIb is characterized by a faster convergence to FCI than QEB-ADAPT-VQEIb does not necessarily guarantee that it does so with fewernumber of CNOTs. As demonstrated in the bottom panels of 6, characterized by the RH–H values of 1.0, 2.0, and 3.0 Å, QEB-ADAPT-VQEIb attains chemical accuracy with the same, less, and moreCNOTs, respectively, than when aFEB-SPQEIb does.Moving on to the comparison of the ADAPT-VQE andSPQE approaches,a quick inspection of the top panels of II MMCC-typecorrection, given by II scheme in which we corrected the VQE UCCSD energiesusing the wavefunctions resulting from each macro-iteration definingthe QEB-ADAPT-VQE simulations. The reason that we opted to use QEB-ADAPT-VQEas the external source of the wavefunction rather than aFEB-SPQE isthat, for the same number of parameters, the former generates themost CNOT-efficient circuits. In II method and the underlying QEB-ADAPT-VQE approach.As depicted in II consistentlyoutperforms both UCCSD and QEB-ADAPT-VQE. As far as the number ofCNOTs needed to achieve chemical accuracy is concerned, which of theUCCSD and QEB-ADAPT-VQE requires the deepest circuit depends on thestrength of the correlation effects. Based on our numerical resultsfor H6, in the weakly and strongly correlated regions,where UCCSDII recovers the FCI energies within 1.0 mEh rather quickly, UCCSD is the bottleneck interms of CNOT count. The situation changes when we examine the recouplingregion, in which case QEB-ADAPT-VQE defines the overall CNOT cost.In comparing the UCCSDII and QEB-ADAPT-VQEIb approaches among themselves, we observe that UCCSDII ischaracterized by a more rapid convergence to FCI. This can be mostlyattributed to the fact that UCCSD offers a good starting point forthe MMCC-type correction, especially so during the early stages ofthe simulation.Now we turn our attention to the δ6 linear chain are very encouraging. All of the examined correctionsaccelerated the convergence to FCI of the underlying quantum algorithms,resulting in substantial savings in terms of CNOT gates. The performanceof the aFEB-SPQEIb, QEB-ADAPT-VQEIb, and UCCSDII is particularly promising. We point out that the correctionsstudied in this work are applicable even when the trial state is notof the UCC form, opening the possibility to improve hardware-efficientansätze and other trial states that are not expressible viathe UCC form. In the future, we will explore the flexibility of theδII correction, combining different types of trialand external wavefunctions.In this work, we explored theusefulness of moment expansions,used in the past to define the renormalized and completely renormalizedCC approaches, to construct noniterative corrections to the energiesobtained with hybrid quantum–classical algorithms employinga UCC ansatz. In an attempt to minimize the circuit depth, we combinedthe noniterative energy corrections with iteratively constructed ansätzeand CNOT-efficient implementations of quantum circuits. Our preliminarynumerical results for three representative geometries along the potentialenergy curve characterizing the symmetric dissociation of the H6/cc-pVDZ system, onecan perform a VQE/PQE simulation on a minimal, valence active spaceto capture static correlations. Subsequently, a moment energy correction,based on determinants outside of the active space, can be used toestimate dynamical correlations. A similar approach has already beenproposed in the context of perturbative energy corrections for iQCC.52Another aspect worth examining isthe capability of our noniterativecorrections to enable simulations using larger-than-minimum basissets. Taking the example of the H122 we plan to investigate this aspect as well.Finally, inspired by the success of MMCC-typecorrections for excitedelectronic states,


In this paper, novel humidity sensors based on montmorillonite, kaolinite, and composite films coated on micro-cantilevers were prepared to measure the relative humidity (RH) values by the deflection of a micro-cantilever (MC) at room temperature. The humidity-sensing properties, such as response and recovery, sensitivity, repeatability, humidity hysteresis, and long-term stability, were investigated in the range of working humidity (10–80% RH). The humidity response in the close humidity range of 10% RH to 80% RH revealed a linear increase in water absorption of montmorillonite, kaolinite, and montmorillonite/kaolinite mixed dispersant (1:1) as a function of RH with linear correlation factors between the humidity change and deflection estimated to be 0.994, 0.991, and 0.946, respectively. Montmorillonite’s sensitivity was better than kaolinite’s, with the mixed-clay mineral film’s response falling somewhere in between. This research provides a feasible and effective approach to constructing high-performance MC humidity sensors that can be operated at room temperature based on clay minerals. Humidity sensors are increasingly required in many sectors depending on their detection accuracy, detection range, application conditions, and size scale as the performance requirements for current instruments continue to change. The most prevalent types of humidity sensors are thermal, resistive , and capFunctional materials, such as silicon carbide , tungsteHerein, novel micro-cantilever humidity sensors were developed based on clay minerals films as humidity-sensing materials. The absorption of water molecules by the clay mineral coating resulted in the cantilever producing an offset reflecting the relative humidity of the surrounding air. The performances of sensors coated by montmorillonite, kaolinite, and their mixture (1:1) in terms of stability, repeatability, wet hysteresis, and associated humidity response sensitivity were thoroughly examined. The experimental findings revealed relevant low-cost, environmentally friendly, and versatile humidity sensors with good measurement reproducibility.The kaolinite and montmorillonite were purchased from Pioneer Nano, Nanjing, China. The micro-cantilever  was obtained from Micromotive, Germany. To facilitate the presentation, “M” and “K” stand for montmorillonite and kaolinite, respectively. The letter “MK” denotes a 1:1 mixture of the two minerals.The process consisted of dispersing 100 mg of montmorillonite powder and 100 mg of kaolinite powder in 4 mL of deionized water to form a montmorillonite solution and a kaolinite solution at concentrations of 25 mg/mL. Following that, 50 mg of montmorillonite powder and 50 mg of kaolinite powder were then dispersed in 4 mL of water by sonication for 6 h to yield a homogeneous montmorillonite/kaolinite composite-clay mineral dispersion (25 mg/mL) with a 1:1 mass ratio of montmorillonite to kaolinite. Trace amounts of prepared montmorillonite, kaolinite, and 1:1 mixed-clay mineral dispersion were taken, and a simple coating method was used in this experiment, where a clay mineral layer with a film thickness of about 1 µm was applied to the sensor under a microscope using the surface tension of the droplets. Three MC humidity sensors  were prepared, followed by natural air-drying at room temperature (25 °C) for 24 h.l) of the free end of the MC, and the length (L) of the optical path from the laser at the free end of the beam to the PSD can be determined. The PSD measures the deflection changes of the MC and transmits the test data captured by the data acquisition (DAQ) system to the computer data-processing software for processing to complete the testing and recording of the sensor. Using the change (ΔS) of the spot displacement on the PSD, the relationship between the above parameters and the deflection (ΔZ) of the MC can be obtained by arithmetic:The optical lever MC relative humidity sensor experimental setup consisted of three parts: (i) wet temperature monitoring, (ii) humidity regulation, and (iii) sensor testing . The MC 2) and N2 flowing through deionised (DI) water, 10% RH was employed as the reference humidity level, and five test humidity points were selected sequentially from the relative humidity range of 10% RH to 80% RH  in the chamber. The experiment was performed at room temperature (25 °C). Temperature and humidity recorders were used to measure the temperature range (−40–80 °C), relative humidity range (0–100% RH), and error (3% RH). The humidity level in the chamber was then raised to the desired level. After achieving the humidity point and a stable sensor, the sensor deflection at the humidity point was recorded.After placing prepared sensors inside the humidity-controlled chamber, adjusting the humidity of the chamber by controlling the ratio of dry nitrogen  was used to analyze the crystal structure of clay powders. The samples were tested in a dry state. Powder X-ray diffraction (XRD) experiments were performed between 5° and 80° (2θ).The morphology features of sensitive films were observed using a scanning electron microscope . Fourier transform infrared (FTIR) spectroscopy was performed on a NICOLET 380 FTIR spectrometer  over a range from 400 cmThe SEM images of the montmorillonite film are presented in −1 and 3617 cm−1 are metal hydroxide coordination hydroxyl -OH and interlayer water hydroxyl -OH stretching vibrations, respectively, the absorption peak at 3441 cm−1 is due to Si-OH, Al-OH, and intramolecular hydrogen bonding [−1 is the antisymmetric stretching vibration of CO2 molecules adsorbed in air. The absorption peaks at 1100–1000 cm−1 are the stretching vibration of Si-O, those at 918 cm−1 are the bending vibrations of Al-OH, those at 787 cm−1 are the stretching vibrations of Al-O, those at 691 cm−1 are the vertical vibrations of Al-OH, and those at 540 cm−1 are the stretching vibrations of Si-O-Al [−1 is the bending vibration of Al-O and Si-O. Kaolinite is essentially the same as montmorillonite, and the absorption peak at 516 cm−1 should also be a stretching vibration of Si-O-Al [ bonding ,36, and  Si-O-Al . The abs Si-O-Al ,39.3+ is often replaced by the low-valence Mg2+ and Fe2+, and Si4+ by Al3+, resulting in montmorillonite having an excess of negative charge, and the weak linkage between layers in the structure makes montmorillonite strongly hygroscopic [−1 is stronger than the peak around 3400 cm−1 [−1 in its infrared spectrum.Montmorillonite is a 2:1 aluminosilicate mineral consisting of two silica–oxygen flakes and one alumina flake combined into a wafer (layer) unit; these are then stacked on top of each other. Each layer has an oxygen ion group on both sides (on the silicon–oxygen sheet), so that no hydrogen bonds can be formed between the layers when they are stacked, but they are linked by “oxygen bridges”, which are weak and fragile, and the grains are smaller than those of kaolinite. The high-valence Alroscopic ,41. This400 cm−1 . Kaolini400 cm−1 . This isMCS) of the MC humidity sensor at different relative humidity levels was calculated as:0 is the initial deflection of MC, Z is the deflection of MC at a different humidity, and ΔRH is the difference in relative humidity before and after the sensor undergoes deflection. The sensitivity response curves of the three humidity sensors at various humidity levels are depicted in By adjusting the relative humidity of the system environment, the deflections of MC-M, MC-K, and MC-MK sensors were examined in the relative humidity range of 10% RH to 80% RH. The sensitivity  of the chamber at five time points after certain numbers of days , followed by measurement of the sensor deflection. The total time for stability testing was 30 days, and responses of sensors were tested at five time points: 0, 5, 10, 20, and 30 days, respectively. The results are shown in Lightweight, inexpensive, and flexible MEMS humidity sensors were developed using clay minerals. Properties such as deflection, sensitivity, wet hysteresis, repeatability, and stability of the montmorillonite-, kaolinite-, and mixed-minerals-coated MC sensors for humidity were all evaluated. All MCs showed good linearity, repeatability, and long-term stability over 30 days. The sensitivity of the montmorillonite humidity sensor was higher than that of the kaolinite humidity sensor, with up to 140.9 nm/%RH. However, the MC-M had poor linearity in the humidity range from 63% RH to 80% RH. The kaolinite humidity sensor displayed the lowest moisture hysteresis of 0.31%, with twice the response and five times the recovery speed of montmorillonite humidity sensors. By comparison, the performance of the montmorillonite/kaolinite mixed-dispersant humidity sensor was somewhere in between, making it more suitable for practical applications. In sum, the proposed clay-based MEMS humidity sensors look to have potential for preparing high-performance humidity sensors, offering a fresh concept for manufacturing new humidity sensors.


Graphene, an isolated atomic plane of graphite, is generally expected to inherit most of graphite’s properties. These expectations are reported to be wrong as far as chemical activity of the two materials is concerned. Indeed, graphite is one of the most inert materials known in nature. In contrast, graphene is shown here to dissociate molecular hydrogen as strongly as the best catalysts known for this reaction. This is attributed to the fact that graphene monolayers are not flat (as within graphite) but unavoidably have nanoscale ripples that serve as active sites for hydrogen splitting. The results have implications for all two-dimensional (2D) materials that being inherently nonflat may exhibit chemical and catalytic properties very different from their bulk counterparts. Graphite is one of the most chemically inert materials. Its elementary constituent, monolayer graphene, is generally expected to inherit most of the parent material’s properties including chemical inertness. Here, we show that, unlike graphite, defect-free monolayer graphene exhibits a strong activity with respect to splitting molecular hydrogen, which is comparable to that of metallic and other known catalysts for this reaction. We attribute the unexpected catalytic activity to surface corrugations , a conclusion supported by theory. Nanoripples are likely to play a role in other chemical reactions involving graphene and, because nanorippling is inherent to atomically thin crystals, can be important for two-dimensional (2D) materials in general. Despite inheriting chemical inertness from graphite and being highly stable in air, graphene has widely (and perhaps somewhat surprisingly) been considered for the use in catalysis –7. The p11917202) and deuterium (D2) gases, we show that graphene acts as a powerful catalyst converting H2 and D2 into hydrogen deuteride (HD) in contrast to graphite and other carbon-based materials under the same conditions. Graphene’s catalytic efficiency per gram exceeds by far that of traditional catalysts for the reaction.In this report, we provide clear evidence for hydrogen dissociation on pristine graphene using three complementary sets of experiments. First, we have compared hydrogen permeation through graphene with that through the so-called “white graphene”, monolayers of hexagonal boron nitride (hBN). This comparison is critical because the two 2D materials are structurally similar but have different electronic spectra which makes hydrogen dissociation possible only on graphene’s nanoripples, according to theory , 19. No SI Appendix, Fig. S1). The bulging could be monitored by atomic force microscopy (AFM), and changes in the membrane position δ with time (9 s−1 m−2)  .10 s−1 m−2 .In stark contrast to graphene, similar containers but sealed with hBN monolayers did not bulge in either helium or hydrogen atmosphere . Such strongly curved nanoripples are routine for graphene membranes. Their rippling was extensively studied by transmission electron microscopy (Ec > 0) for all realistic curvatures and strains (<15%) that can be supported by 2D crystals without breaking .These calculations show a clear difference between graphene and hBN. If their monolayers are flat, the dissociation barrier croscopy  and scancroscopy , 23 and croscopy , 21, 23.The above results suggest a dramatic difference in chemical and catalytic activity of graphene and hBN monolayers, at least with respect to hydrogen. However, with only hundred molecules per hour permeating inside graphene microcontainers , neither3 type)  is strong (sp3 type) , 19, esp3 type) , 25. SucT), the coverage of graphene with hydrogen adatoms is expected to be extremely sparse  . As shown in T exhibited a pronounced D peak, indicating the appearance of numerous sp3 defects. In contrast, similar graphene samples but heated in a helium atmosphere showed no sign of the D peak, proving qualitatively that graphene could react only with hydrogen.At room temperature (re hour) , and indre hour) F. Moreovurvature , 23. Witl strain . Note thSI Appendix, Fig. S6). After exposing the flat graphene to 600 °C in pure H2 for several hours, no sign of the D peak could be discerned in the Raman spectra, in clear contrast to the case of nonflat graphene  and again placed the samples on atomically flat graphite. In this case, the D peak was clearly seen, proving that we would easily see hydrogen adatoms if they were also adsorbed on flat graphene.Next, we used the D peak to assess a role of graphene’s surface roughness in the hydrogenation process. To this end, the above Raman results were compared with those obtained for similarly exfoliated graphene monolayers but placed onto an atomically flat surface of graphite . This hump is likely to be due to small regions of thermally stable graphane, which is formed if graphene is covered with atomic hydrogen on both sides  graphene in He or vacuum reduced the D peak, although a notable hump remained in the relevant spectral region even after several days at 600 °C . Therefore, detection of HD would provide an unequivocal proof for hydrogen dissociation on graphene, and using this reaction, graphene could also be benchmarked against known catalysts.Annealing hydrogenated graphene in helium or vacuum shows that hydrogen adatoms desorb from graphene’s surface Inset of B and theACS Material; SI Appendix, Fig. S8). The powder was well characterized and contained highly corrugated and mostly isolated (nonrestacked) monolayers with the measured specific surface area of ~1,000 m2 g−1 (PH2 = PD2 ≈ 0.5 bar) was then added (SI Appendix). After a certain exposure time, the mixed gas was analyzed by mass spectroscopy to determine the resulting HD concentration, ρHD. At room T, we could not detect any HD either in the presence of graphene or without it . To accelerate the reaction of H2 with D2, the gas mixture was heated up. At 600 °C, the monolayer graphene powder led to formation of HD, and its concentration increased as a function of time saturating at ~15% after approximately 5 h . For graphene, the poisoning is probably caused by formation of chemically inert regions of graphane . The saturation in ρHD at 600 °C occurred after a few hours and was below 50%, indicating poisoning of the reference catalysts , as expected . This agrees well with the fact that few-layer graphene has a much less rippled surface than monolayer graphene. Furthermore, activated charcoal known for its highly porous structure provided numerous broken carbon bonds and oxygen surface groups , graphene excels all the other powders by orders of magnitude. This is helped by the fact that graphene is essentially a surface and has no bulk , whereas the other powders have their bulk mostly inaccessible for the HD production. Even in terms of the surface efficiency (NHD per m2), graphene compares favorably with MgO and ZrO2 and is surpassed only by Cu . From the known NHD, we can estimate the turnover number TON defined as the maximum yield attainable from a catalytic center . Furthermore, additional ripples can be formed by thermal cycling of graphene on various substrates due to different thermal expansion coefficients. Because nanorippling is inherent for all atomically thin crystals, it is worth keeping in mind that the enhancement of chemical and/or catalytic activity is also possible for the case of other 2D materials and for other chemical reactions. For example, bulk MoS2 and other chalcogenides are often used as three-dimensional (3D) catalysts but may exhibit even stronger activity in the 2D form.A flat sheet of graphene is expected to be highly stable and chemically inert under ambient conditions similar to its parent material, graphite. However, graphene monolayers are never perfectly flat because of thermal fluctuations  and practically unavoidable local strain, which generate static nanoscale wrinkles and ripples –23. Our 172 can potentially be stored inside carbon nanotubes. Furthermore, in heterogeneous catalytic reactions involving, for example, graphene-coated metal surfaces and nanoparticles Click here for additional data file.


These results are enabled by an integrated-photonic technology based on wafer-scale high-mobility graphene and pave the way towards the development of optoelectronics-based arrayed-antennas for millimeter-wave technology.Optoelectronics is a valuable solution to scale up wireless links frequency to sub-THz in the next generation antenna systems and networks. Here, we propose a low-power consumption, small footprint building block for 6 G and 5 G new radio wireless transmission allowing broadband capacity . We demonstrate a wireless datalink based on graphene, reaching setup limited sub-THz carrier frequency and multi-Gbit/s data rate. Our device consists of a graphene-based integrated optoelectronic mixer capable of mixing an optically generated reference oscillator approaching 100 GHz, with a baseband electrical signal. We report >96 GHz optoelectronic bandwidth and −44 dB upconversion efficiency with a footprint significantly smaller than those of state-of-the-art photonic transmitters (i.e., <0.1 mm 2 footprint, providing an alternative approach for the realization of millimeter-wave transmitters.Here, the authors report the realization of a sub-THz wireless data link based on a graphene-integrated optoelectronic mixer with a >96 GHz bandwidth, −44 dB upconversion efficiency and <0.1 mm While 5 G keeps its promises, advanced 5 G has more potential to implement2. 5 G NR access operates in the sub-1 GHz to 100 GHz spectrum2, and supports various use cases, including time-critical services for consumers, enterprises, and public institutions across multiple sectors2. NR is currently a standard in the 3rd Generation Partnership Project (3GPP)2, and a new generation of antenna systems is being developed3. In the last decade, mobile networks have increased carried traffic by almost 300 times, and network speeds have increased hundreds of times1. In the journey toward 6 G, new extremely demanding and immersive applications will require a further upgrade of signal processing functions with improved signal integrity, frequency, and capacity2. The need for broader bandwidth capacities in wireless networks can be satisfied by increasing the carrier frequency (CF). Therefore, the sub-THz frequency range (90–300 GHz) is becoming more and more appealing6 and, given the potential to provide hundreds of Gbit/s over short distances, it will be a key enabler for 6 G systems4. Figure 7  and the receiver (downconversion) and is usually implemented through superheterodyne schemes13 involving frequency mixers14. The approaches proposed to date for sub-THz datastream upconversion are, as discussed below, based on: (i) electronic upconverters (ii) conventional microwave photonic transmitters based on modulators and photodetectors. In the following, we compare these techniques with a third scheme, enabled by our device.The fast rise of data-hungry and performance-demanding applications, e.g., digital twins, AI computing, autonomous driving, robotic surgery, digital biology, call for the need for novel access technology. Advanced 5 G and 6 G will make use of New Radio (NR) access technology14, resulting in up/downconversion14. Electronic circuits non-idealities push the operating conditions far from theoretical figures15 as the CF increases. The generation of high spectral purity electronic oscillators at frequencies >100 GHz is the major bottleneck limiting the performances of sub-THz systems16, since phase noise (PN) grows with frequency. Indeed, to generate the high CF, a relatively low frequency (tens of GHz) electronic LO is upconverted, i.e., multiplied, amplified, and filtered multiple times18 , where N is the multiplication factor20, and a non-negligible contribution comes from the noise figure of cascaded amplification stages21. Moreover, by increasing f x l , electronic circuit design becomes critical15, and mismatch in length and loading between differential lines can cause skew and signal degradation15. As CF increases, it is thus necessary to use compensation techniques for PN reduction, transmission line parasitics mitigation, and protection from spurious electromagnetic fields. As a result, the system’s complexity increases24.The first techniques rely on a typical scheme used to generate the sub-THz frequencies, and are based on electronic components mixing a high-frequency electrical local oscillator (LO) with a radio data signals18 Fig. . This te12. Highly pure LO’s can be obtained from two optical wavelengths spaced by the required frequency26, coupled to a fast photodetector (PD). These two optical wavelengths can generate very stable electrical tones with low PN. E.g., by using optical combs, ref. 25 reports <100 dBc/Hz at 10 KHz from the 300 GHz CF and ref. 26 reports −118 dBc/Hz at 10 MHz from the 331 GHz CF. Several wireless links employing photonic transmitters have been reported in recent years  are reported in most of the literature, as shown in Table 28 requires the use of integrated devices, and electronics is currently the only commercial solution for high-density integration29. As a matter of fact, most of the demonstrated photonic transmitters present in literature are based on bulk discrete systems, with few examples of integrated or partially integrated solutions . An OEM is a fast photomixer able to generate the high-frequency LO through optical detection, and directly mix the LO with a baseband electrical datastream30  waveguide-integrated G-OEM embedded with a sub-THz coplanar waveguide (CPW). The G-OEM exhibits high conversion efficiency (−44 dB) and record (92–96 GHz) frequency operation compared to state-of-the-art G-OEMs43. The device was fabricated using hBN-encapsulated single crystal CVD graphene52 with high carrier mobility (27000 cm2 V−1 s−1 at room temperature). We report a 4 Gbit/s wireless link at sub-THz (93 GHz) CF, by directly mixing a baseband electrical signal (2 GHz CF) with a 91 GHz optical LO using one single device. The device reveals high potential in terms of speed, far beyond the limits of our experimental setup. The photonic upconverter footprint is <<0.1 mm2, considering the active area, without access pads for on chip probing. This active area is of the same order as the active area occupied by electronic up/down converters54, and is much smaller than any other integrated-photonic transmitter based on the scheme in Fig. 56, or at the LO level57. In the latter case, optical phase shifters need to be integrated in the antenna element58. The sub-THz upconversion functionality is currently realized using sub-THz electronics, comprising multi-stage mixers and amplifiers14, schematically shown in Fig. 59. The proposed solution based on our G-OEM only requires baseband (IF) electronics (BW <10 GHz), while the upconversion is carried out by mixing the IF with an optically generated LO, routed to each antenna element using photonic waveguides instead of sub-THz electrical transmission lines59. The distribution of the sub-THz LO by means of electrical transmission lines can be in general power hungry since it requires the use of active sub-THz elements e.g., buffers and amplifiers59, which are necessary to compensate for transmission lines losses and keep the SNR at acceptable levels22 all along the path through the antenna elements. Using the integrated G-OEM the sub-THz signal distribution is avoided in favor of optical routing of the LO to each antenna element. Such solution drastically reduces the electronic circuit complexity and losses since the sub-THz upconverted electrical signal is generated only at the very end of the path, where an amplifying stage is present in proximity to the antenna element.We propose a third, different approach to implement a photonic transmitter, offering significant advantages in terms of power consumption, bandwidth capacity, footprint size, and PN. It is based on a self-mixing devicesee Fig.  without see Fig. , only on62. RF losses can be mitigated using Si substrates with high resistivity >10 KΩ cm61. An alternative solution is the use of a sufficiently thick oxide to avoid interaction between the electromagnetic RF propagating mode with the substrate. Our SiN technology is based on a 15 μm thick box oxide, allowing to decouple the RF mode from the Si substrate, thus minimizing ohmic losses. The electrical CPW embeds at the center of the signal electrode an hBN-encapsulated single-crystal graphene layer, transferred on top of a SiN photonic waveguide. Figure L = 4 μm and W = 50 μm. A second graphene layer acts as electrostatic gate on top of the hBN-encapsulated graphene and is contacted with a metallic electrode , i.e. μc ~ 150 meV for optimal operation, since at such electrostatic doping the photobolometric effect, and so the phoresponsivity, is maximized43  and 270 nm thickness (WGt), allowing single mode operation at 1550 nm optical wavelength. It is worth noting that Si waveguides can be used as a valid alternative to SiN waveguides to perform OEM using graphene. Nevertheless, silicon waveguides suffer from two-photon-absorption at relatively low-power density. In the proposed perspective (optoelectronic antenna array) a relatively high input power could be coupled at the input of the chip, before being routed and split toward the single element. The SiN technology supports high optical power densities without suffering from two-photon absorption63. Moreover, the routing of the local oscillator toward each antenna could require a relatively long path. SiN waveguides offer ultra-low propagation loss compared to Silicon waveguides63. Another advantage of SiN technology is the lower thermo-optic coefficient at telecom wavelengths, making SiN photonic circuits more stable against temperature64. The device comprising the graphene stack and the optical waveguide  on top of a ~30 nm thick hBN flake . After depositing Ni/Au (7/60 nm) top contacts by thermal evaporation37, we place a second graphene/hBN stack (obtained via the same pick-and-flip procedure) onto the first one for both full encapsulation of the device channel and electrical isolation of the top graphene layer. Relatively thick hBN (>15 nm according to ref. 35) is known to crucially screen the roughness of the underlying substrate, resulting in enhanced carrier mobility in graphene65, with optimal results upon full encapsulation in dry conditions66.Figure 2). We observe the typical spectral features of high-quality single-layer graphene68, such as a narrow Lorentzian 2D peak and large intensity ratio between the 2D and G peaks, in addition to a sharp E2g peak from the hBN flake. As a standard indicator for the quality of graphene/hBN stack69, we analyze the full width at half maximum (FWHM) of the 2D peak, obtaining a statistical distribution peaked at 19.5 cm−1  points toward a reduction of strain fluctuations70, which is known to crucially enhance the carrier mobility72.Halfway through the assembly, we use standard scanning microRaman spectroscopy to evaluate the quality of the hBN-supported graphene channel. Figure see Fig.  inset. TR) of the sample as a function of the top-gate potential (Vtg), at room temperature and in air. Figure Vtg ~ 0.5 V. We estimate low doping level of n ~ 3 × 1011 cm−2 at Vtg = 0 V, (assuming 30 nm hBN dielectric with out-of-plane relative permittivity εr = 3). Using the standard fitting procedure from ref. 73  and a contact resistance of 1.7 k Ω μm (1.2 k Ω μm). The clear asymmetry of the field-effect curve indicates a contribution from gate-dependent contact resistance75, which likely affects the mobility estimate (proper four-probe measurements are however not possible in the current device design). Finally, the magnitude of charge inhomogeneity in the CNP region, estimated via the procedure in Fig. 71, falls well below the 1011 cm−2 range, further confirming the expected high device quality71. Supplementary Fig. We measured the two-terminal resistance (μc) is set far from the CNP . At this electrostatic doping, the dominant effect allowing photodetection is carrier heating, which translates into a decrease of the carrier mobility, i.e., into a decrease of graphene electrical conductivity43. The conductivity change can be expressed as:The operating principle of the G-OEM relies on the fundamental physical mechanism of hot carrier generation in a graphene layer coupled to an optical field. The chemical potential . These two are calculated from the Drude formula of77:Where D is the Drude weight and Γ is the transport scattering rate. Both quantities are dependent on the electron’s temperature and on the chemical potential. These lasts change under optical excitation, and can be calculated from the heat equation formula:Where L is the Lorenz number, σ(Te) is the electrical conductivity at temperature Te, Ce is the heat capacity Tph is the phonon’s temperature and P is the optical power density at a specific coordinate of the graphene channel , and εhBN and on its thickness thBN (see 45. This means that graphene conductivity can be modulated at very high frequencies (up to ~500 GHz) by means of an optical field. Therefore, to obtain optoelectronic mixing two optical wavelengths separated by the desired frequency  are coupled to the graphene channel  falls in the sub-THz range, the optical LO induces a time-varying conductivity In Eq.  L is thePconv is then used as figure of merit to evaluate the device performance. It is defined as the ratio between the output power of the upconverted tone at fUP = fele + f_LO and the power of the input electrical signal at frequency fele. Equation 78. Instead, we stress that in our case, i.e, when a graphene photo-bolometer is operated as OEM, no DC bias voltage is needed across the graphene channel41 . We then characterized the response in the range 92–96 GHz using a calibrated commercial electronic downconverter (Mi-Wave 970W-94/387) which downconverts high-frequency electrical signals from the 92–96 GHz range down to the 4–8 GHz range. We used a 44 GHz bandwidth electrical Spectrum Analyzer (Anritzu MS2850A) to measure the downconverted electrical signal. The result is shown in Fig. Methods. Figure Pconv[dB] = Pout[dBm]−Pin[dBm]~−44 dB (see We then characterized the G-OEM as a mm-wave upconverter using the same aforementioned receiver (Mi-Wave 970W-94/387). The experimental setup is detailed in 79. The resulting optical signal was then filtered and amplified to obtain two-phase locked optical wavelengths, separated in frequency by 91 GHz. The central carrier and high order harmonics were suppressed by >30 dB. The optical signal was coupled to the integrated graphene OEM through a lensed fiber butt coupled to the photonic chip. A quadrature phase shift keying (QPSK) baseband signal with CF of 2 GHz was generated starting from two pseudo-random binary sequencies (PRBS), generated using a 65 GS/s digital-to-analog converter (DAC) (Fujitzu LEIA 55–65GSa/s 8-bit DAC), delivering a digital signal with maximum total length of 217 samples. The datarate of the baseband signal was swept in the range 1–4 Gbit/s. The signal was fed to the G-OEM to the “IF” port indicated in Fig. Figure VG) of the device. We used a LO power of ~13.3 dBm and an input baseband electrical power of ~9 dBm. Then, we transmitted a 1 Gbit/s QPSK baseband signal through the wireless link. As shown in Fig. VG ~ −1.8 V, corresponding to ~2.3 V from the CNP voltage (Vtg ~ 0.5 V), i.e., µc~130 meV. Figure VG ~ −1.8 V.To optimize the Error-Vector-Magnitude (EVM) of the received signal we adjusted the working point of the G-OEM by acting on the gate voltage . This would substantially improve the performance of our wireless link, enabling longer link distances. In general, sub-THz antennas can be made more efficient by making use of on axis and off-axis elements along the path of the link83. Moreover, the performances of complex telecom radio links such as massive MIMO can be further optimized by implementing advanced techniques using, e.g., reconfigurable reflecting/transmitting surfaces84, and employing forward-error correction techniques (which have not been used during our experiment).The reason for the EVM deterioration as a function of datarate should be attributed to the complexity of the experimental setup that affects the signal-to-noise-ratio (SNR) of the wireless link as bandwidth increases. First, the electrical bandwidth of the full transmission chain, resulting from the electrical bandwidth of all the used components (transmission filter + antenna), is 2 GHz (with center frequency 93 GHz) which determines the maximum electrical bandwidth of the input signal (max. data rate of 4 Gbit/s). Second, the electrical signal generated by the DAC exhibits a degradation in terms of SNR while increasing the data rate, see 2 V−1 s−1) is beneficial compared to low mobility , in agreement with experimental results present in literature42. We then show that a reduction of contact resistance down to 500 Ωµm can allow a performance boost. The resulting total upconversion efficiency improvement can be at least ~11 dB, meaning that the graphene photonic upconverter can attain at least ~−33 dB conversion efficiency with small design efforts. This performance boost, together with the possibility to operate at frequencies of 500 GHz46, would allow to reach and surpass state-of-the-art performances18. Indeed, the sole implementation of the discussed two improvements (use of 48 dB gain antennas and optimized mixing conversion efficiency up to −33 dB) would allow to increase the power at the receiver by >40 dB in the 2 m wireless link, which would drastically improve the SNR allowing higher modulation formats , or equivalently enable >100 m wireless links, keeping the same performances reported in the present work15 in terms of datarate.The intrinsic performances of the photonic upconverter are discussed in 87. Each antenna element based on our proposed scheme contains a G-OEM providing ~−40 dBm. To attain total output power of 15 dBm, a 30 dB amplifying stage is needed for each element. Each amplifier should require few tens of mW power to keep the power consumption within some W. Available electronics88 allows ~20 mW power consumption for each element, to obtain ~30 dB power amplification. Concerning the optoelectronic mixer, it should require negligible power compared to the amplifying stage . The G-OEM power consumption can be improved acting on the mobility of the graphene detector. This is quantitatively discussed in 89 reported 0.5 A/W external responsivity with <0.6 V applied to the detector contacts, and compact size (<6 μm2 active region). These devices could be advantageously used in antenna arrays. Indeed, the detector presented in89 provides a responsivity allowing comparable performances as the one presented in our work in terms of conversion efficiency, but thanks to plasmonic enhancement it requires only an optical LO input power <0 dBm and an IF input power ~0 dBm if used as G-OEM, thus matching the power consumption requirements of the single antenna element. Finally, an antenna array with such characteristics should preserve high gain to keep the same performances as the one presented in our work, in terms of link distance and data rate. At this regard, 40 dB gain have been already demonstrated at carrier frequencies >100 GHz for 16 × 16 antenna arrays90.We now briefly quantitatively discuss the proposed photonic-aided antenna array presented in Fig. 37. The carrier mobility necessary for effective G-OEM operation (>104 cm2 V−1 s−1 at room temperature), crucially requires decoupling of the graphene channel from extrinsic scattering sources91. As demonstrated both for exfoliated graphene flakes66, and CVD-grown graphene single crystals93, screening of substrate roughness is paramount. The only reliable strategy currently available to achieve this requires the use of thick hBN35. Although large-scale growth of single or few-layer single-crystalline hBN is well established, the few-layer thickness limit does not guarantee adequate screening, resulting in carrier mobility in line to that of graphene on SiO2 (<104 cm2 V−1 s−1)94. The synthesis of scalable counterparts of thick hBN flakes  is a sensitive topic. Relevant advances in crystals dimensions can be found in ref. 95, where a 2 × 5 cm2 trilayer hBN crystals growth has been demonstrated. Similarly, the growth of large area  thick (5 nm) hBN have been shown in96, with graphene mobility values approaching ~104 cm2 V−1 s−1. We showed that the presented G-OEM fabrication protocol is compatible with CVD-grown materials , making it ready for the integration of large-scale thick hBN films.Finally, let us comment on the perspective for scalability of the proposed G-OEM. We stress that the CVD graphene employed as channel and gate material is obtained via growth and transfer methods with established wafer-scale capabilities28). Approaching 100 GHz CF, electronic technology is showing its limits, while the common photonic implementation is still far from allowing the realization of single antenna elements. The present work assesses the merit of the realization of an integrated optoelectronic sub-THz upconverter suitable for single or multiple antenna systems, opening new perspectives for the use of integrated photonics in next-generation antenna arrays in 5 G and 6 G NR, potentially solving the issues related to the concurrent technologies. We show setup limited record frequency operation (93 GHz) and datarate (4 Gbit/s), using high-quality CVD graphene allowing high values of upconversion efficiency (~−44 dB) compared to state-of-the-art G-OEMs97. Eventually, we describe the pathways towards a substantial increment of both datarate and conversion efficiency by acting on the design at both the system and the device level. We use our device as a photonic upconverter, nevertheless it can be used as downconverter as well43, thus allowing the realization of the receiver using the same graphene technology, in view of the realization of a G-OEM-based full-link. This work opens the route to compact, low-power, cost-effective sub-THz antenna array systems fully based on graphene as active material, with performances potentially overcoming state-of-the-art limitations18.In summary, we have reported a wireless link based on graphene, using a hybrid electronic/photonic approach based on an integrated device, the G-OEM. This transmitter targets radio applications in the sub-THz band to improve performance parameters such as frequency accuracy, PN, upconversion efficiency, and to envisage an integrated solution that fits in the sub-THz antenna element footprint. The realization of sub-THz radio links enables telecom operators to achieve network densification while optimizing overall network capacity and latency performance  on a second stamp, to obtain graphene exposed on top of hBN when the stack is finally released on the target substrate. Two polymer membranes—poly(bisphenol A carbonate)polycarbonate (PC) and poly (PVA)—are deposited on a polydimethylsiloxane (PDMS) stamp, which is attached to a glass slide. With the aid of a micromechanical stage, this structure is used to pick-up an hBN flake and then a portion of a graphene crystal from SiO2 (steps 1 and 2). Subsequently, the resulting stack is put in contact with a second underlying PDMS stamp (step 3). To transfer the graphene/hBN from the first to the second stamp, the solubility of PVA in water is exploited. Indeed, when a drop of water is released between the two stamps, the PVA is dissolved, and the first stamp is detached from graphene/hBN (step 4). Subsequently, the second stamp is flipped and aligned to the SiN photonic waveguide. The hBN/graphene stack is thus deposited, leaving the graphene exposed (step 5). The sample is heated on the assembly stage to improve the adhesion to the substrate (step 6). The graphene is patterned by electron beam lithography followed by oxygen plasma etching into a 50 × 8 µm2 rectangle. Two contacts are fabricated on top of graphene  using electron beam lithography followed by thermal evaporation of Ni/Au and lift-off (step 7). To fabricate the graphene gate, the pick-and-flip technique is used again (steps 1–4), and a second hBN/graphene stack is deposited on the device (steps 8 and 9). The top graphene is finally contacted with the gate electrode (step 10). By doing so, the top hBN flake has the double function of encapsulant for graphene and of top-gate dielectric.The complete flow developed for the fabrication of the G-OEM is depicted in Supplementary Fig. 2 . One side of the device was AC coupled to ground, while the other side was connected to the second port of the VNA. The electrical power resulting from the photocurrent flowing through the 50Ω load of the VNA was measured as a function of the electrical frequency driving the MZM. The result of the characterization is shown in Fig. The optoelectronic frequency response of the G-EOM allows to evaluate of the optical LO frequency detectable by the device, and corresponds to the optoelectronic bandwidth of the device when used as photodetector. The characterization was performed using two experimental setups, covering two different frequency windows. The scheme in Supplementary Fig. f0 = 46–48 GHz. We operated the MZM in double sideband—suppressed carrier (DSB-SC) mode79, to obtain two optical wavelengths separated by 2f0. To further suppress the central wavelength, we used a band-stop narrow fiber grating filter centered at 1.55 μm, with optical bandwidth of ~0.241 nm(~30 GHz). The resulting signal was then amplified and filtered again with a 1 nm (~125 GHz) optical pass-band filter to reduce the amplified spontaneous emission (ASE) power of the optical amplifier. The resulting spectrum of the optical signal obtained with an optical spectrum analyzer (OSA) is shown in Supplementary Fig. Because of the frequency limitation of the VNA, we used a different setup to characterize the optoelectronic bandwidth of the G-EOM in the frequency range used for the wireless transmission experiment. First, we implemented a phase-locked dual-wavelength tunable laser source shown in Supplementary Fig. f0 = 92–96 GHz. The G-OEM was then connected to an electronic downconverter (Mi-Wave 970W-94/387), which downconverted the sub-THz signal in the range 4–8 GHz. The input RF port of the downconverter had a WR-10 waveguide connection. A 1-mm coaxial to WR-10 transition was used to connect the RF probes to the electronic component, as shown in the image of Supplementary Fig. The two wavelengths were then coupled to the G-OEM to measure the optoelectronic frequency response of the device in the range around the wireless link experiment CF. The setup is shown in Supplementary Fig. fLO = 91 GHz. When the device is used as optoelectronic mixer, there is no need to apply any DC bias voltage along the graphene channel as can be deduced from equations S4-S10 in the fRF = fIF + fLO = [92 −96] GHz, and so in the range 4–8 GHz after downconversion. The signal was visualized on a spectrum analyzer.The setup used to characterize the G-OEM conversion efficiency is shown in Supplementary Fig. Supplementary InformationPeer Review File