Top 18 Institutions Leading Quantum Computing Research in 2024
Most recent entries in quantum computing advances are “Observation of energy-resolved many-body localization,” published in Nature Physics; “A ...
Physical Review Letters
This year, MPS is among the leaders in quantum computing research. So far in 2024, Max Planck Society scientists have published “A Auantum-logic Gate Between Distant Quantum-network Modules” in Science and “Topological Two-Dimensional Floquet Lattice on a Single Superconducting Qubit” in <anchor>Physical Review Letters</anchor>, among dozens of other published research pieces.
Phys. Rev. Lett. 126, 163602 (2021) - Topological Two-Dimensional Floquet Lattice on a Single Superconducting Qubit
## Physical Review Letters

### Topological Two-Dimensional Floquet Lattice on a Single Superconducting Qubit

##### Daniel Malz and Adam Smith

##### Phys. Rev. Lett. 126, 163602 – Published 23 April 2021

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ArticleReferencesCiting Articles (21)Supplemental Material

AbstractAuthorsArticle Text— Introduction.—— Theoretical description.—— Topological frequency conversion.—— Experiment.—— Results.—— Extension to qubit arrays.—— Discussion.—— ACKNOWLEDGMENTSSupplemental MaterialReferences





#### Abstract

Current noisy intermediate-scale quantum (NISQ) devices constitute powerful platforms for analog quantum simulation. The exquisite level of control offered by state-of-the-art quantum computers make them especially promising to implement time-dependent Hamiltonians. We implement quasiperiodic driving of a single qubit in the IBM Quantum Experience and thus experimentally realize a temporal version of the half-Bernevig-Hughes-Zhang Chern insulator. Using simple error mitigation, we achieve consistently high fidelities of around 97%. From our data we can infer the presence of a topological transition, thus realizing an earlier proposal of topological frequency conversion by Martin, Refael, and Halperin. Motivated by these results, we theoretically study the many-qubit case, and show that one can implement a wide class of Floquet Hamiltonians, or time-dependent Hamiltonians in general. Our study highlights promises and limitations when studying many-body systems through multifrequency driving of quantum computers.

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- Received 11 December 2020

- Revised 1 March 2021

- Accepted 22 March 2021

DOI:https://doi.org/10.1103/PhysRevLett.126.163602



Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Open access publication funded by the Max Planck Society.

Published by the American Physical Society

#### Physics Subject Headings (PhySH)

1. Research Areas

1. Physical Systems

1. Techniques

Atomic, Molecular & OpticalCondensed Matter, Materials & Applied Physics

#### Authors & Affiliations

- 1Max Planck Institute for Quantum Optics, Hans-Kopfermann-Straße 1, D-85748 Garching, Germany

- 2Munich Center for Quantum Science and Technology, Schellingstraße 4, D-80799 München, Germany

- 3Department of Physics, TFK, Technische Universität München, James-Franck-Straße 1, D-85748 Garching, Germany

- 4School of Physics and Astronomy, University of Nottingham, Nottingham, NG7 2RD, United Kingdom

- 5Centre for the Mathematics and Theoretical Physics of Quantum Non-Equilibrium Systems, University of Nottingham, Nottingham, NG7 2RD, United Kingdom

- *These authors contributed equally to this work.

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#### Images

- ###### Figure 1

Tomography data for M=1, ω1=0.125. The top three panels compare experimentally measured Pauli expectation values against exact numerical simulation. We also show the purity of the measured state, which we fit by the function 1/2+ae−t/λ, where a=0.387 and λ≈109μs is compatible with the device coherence time as measured by IBM. Note that a<0.5 as the measurement sequence take a finite time, such that the qubit has lost purity even when the simulation time is zero. The bottom panel shows the fidelity F=|⟨ψ|ϕ⟩|2 between the measured state projected onto the Bloch sphere, |ψ⟩, and the numerically simulated state, |ϕ⟩. We fit the fidelity with ae−t/ξ, where a≈0.99 and ξ≈2.71ms, which verifies the effectiveness of error mitigation by projecting onto the Bloch sphere.

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- ###### Figure 2

Work done by the two incommensurate drives, calculated using Eq. ( 8). The experimental data for M=1, ω1=0.125 measured at 800 points is compared with a numerical simulation of the same setup. The experimental data is fitted with a line (colored dashed lines) using least-squares regression, for which the 95% confidence interval for the slope is shown as the colored region. The expected slope is shown as black dashed lines.

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- ###### Figure 3

Experimentally extracted Chern number as a function of M. The Chern number is extracted from the linear least-squares regression fit to the work done by each drive, and using Eq. ( 6). The error bars correspond to the 95% confidence intervals for the fit. The experimental data are compared against the numerical simulation of the same setup (blue dots) and with the exact value of the Chern number for the corresponding phase of the BHZ model (dashed black curve). The shaded blue region corresponds to a simple heuristic error model based on the average fidelity 0.971 of the error mitigated experimental data [ 32]. This error model confirms that the comparatively large deviations of the measured Chern number that we observe are produced already from low loss in fidelity (≈3%). Insets show the distribution of experimental data on the Bloch sphere under dynamics for M=1 and M=3, illustrating qualitative differences of the time evolution in each of the two phases |M|<2 and |M|>2.

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