Clifford gates play a role in the optimisation of Clifford+T circuits. Reducing the count and the depth of Clifford gates, as well as the optimal scheduling of T gates, influence the hardware and the time costs of executing quantum circuits. This work focuses on circuits protected by the surface quantum error-correcting code. The result of compiling a quantum circuit for the surface code is called a topological assembly. We use queuing theory to model a part of the compiled assemblies, evaluate the models, and make the empiric observation that at least for certain Clifford+T circuits (e.g. adders), the assembly's execution time does not increase when the available hardware is restricted. This is an interesting property, because it shows that T gate scheduling and Clifford gate optimisation have the potential to save both hardware and execution time.
The need for T gate scheduling resulted in the need of controlling distilleries, and the first investigations have been presented in @cite_9 . Therein, the buffer had a fixed size, and could store seven distilled states. Once the buffer was full, the distillery was stopped (no distillations were started until the first buffered state was not consumed by a T gate). Otherwise, the buffer would have overflown. In that work a simplistic look-ahead strategy for calculating the number of next T gates, and necessary distilled T states, was presented. That strategy was used to predict when the buffer would be full.
@cite_9
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We study the online problem of multiplexing packets with arbitrary deadlines in bounded multi-buffer switch. In this model, a switch consists of m input buffers each with bounded capacity B and one output port. Each arriving packet is associated with a value and a deadline that specifies the time limit till the packet can be transmitted. At each time step the switch can select any non-empty buffer and transmit one packet from that buffer. In the preemptive model, stored packets may be preempted from their buffers due to lack of buffer space or discarded due to the violation of the deadline constraints. If preemption is not allowed, every packet accepted and stored in the buffer must be transmitted before its deadline has expired. The goal is to maximize the benefit of the packets transmitted by their deadlines. To date, most models for packets with deadlines assumed a single buffer. To the best of our knowledge this is the first time a bounded multi-buffer switch is used with arbitrary deadline constraints Our main result is a 9.82-competitive deterministic algorithm for packets with arbitrary values and deadlines. Note that the greedy algorithm is not competitive. For the non-preemptive model we present a 2-competitive deterministic algorithm for the unit value packets. For arbitrary values we present a randomized algorithm whose competitiveness is logarithmic in the ratio between the largest and the smallest value of the packets in the sequence We consider a multiclass multiplexer with support for multiple service classes and dedicated buffers for each service class. Under specific scheduling policies for sharing bandwidth among these classes, we seek the asymptotic (as the buffer size goes to infinity) tail of the buffer overflow probability for each dedicated buffer. We assume dependent arrival and service processes as is usually the case in models of bursty traffic. In the standard large deviations methodology, we provide a lower and a matching (up to first degree in the exponent) upper bound on the buffer overflow probabilities. We introduce a novel optimal control approach to address these problems. In particular, we relate the lower bound derivation to a deterministic optimal control problem, which we explicitly solve. Optimal state trajectories of the control problem correspond to typical congestion scenarios. We explicitly and in detail characterize the most likely modes of overflow. We specialize our results to the generalized processor sharing policy (GPS) and the generalized longest queue first policy (GLQF). The performance of strict priority policies is obtained as a corollary. We compare the GPS and GLQF policies and conclude that GLQF achieves smaller overflow probabilities than GPS for all arrival and service processes for which our analysis holds. Our results have important implications for traffic management of high-speed networks and can be used as a basis for an admission control mechanism which guarantees a different loss probability for each class. In this paper, we propose an efficient and fast object detector which can process hundreds of frames per second. To achieve this goal we investigate three main aspects of the object detection framework: network architecture, loss function and training data (labeled and unlabeled). In order to obtain compact network architecture, we introduce various improvements, based on recent work, to develop an architecture which is computationally light-weight and achieves a reasonable performance. To further improve the performance, while keeping the complexity same, we utilize distillation loss function. Using distillation loss we transfer the knowledge of a more accurate teacher network to proposed light-weight student network. We propose various innovations to make distillation efficient for the proposed one stage detector pipeline: objectness scaled distillation loss, feature map non-maximal suppression and a single unified distillation loss function for detection. Finally, building upon the distillation loss, we explore how much can we push the performance by utilizing the unlabeled data. We train our model with unlabeled data using the soft labels of the teacher network. Our final network consists of 10x fewer parameters than the VGG based object detection network and it achieves a speed of more than 200 FPS and proposed changes improve the detection accuracy by 14 mAP over the baseline on Pascal dataset. We consider buffer management of unit packets with deadlines for a multi-port device with reconfiguration overhead. The goal is to maximize the throughput of the device, i.e., the number of packets delivered by their deadline. For a single port or with free reconfiguration, the problem reduces to the well-known packets scheduling problem, where the celebrated earliest-deadline-first (EDF) strategy is optimal 1-competitive. However, EDF is not 1-competitive when there is a reconfiguration overhead. We design an online algorithm that achieves a competitive ratio of 1 - o(1) when the ratio between the minimum laxity of the packets and the number of ports tends to infinity. This is one of the rare cases where one can design an almost 1-competitive algorithm. One ingredient of our analysis, which may be interesting on its own right, is a perturbation theorem on EDF for the classical packets scheduling problem. Specifically, we show that a small perturbation in the release and deadline times cannot significantly degrade the optimal throughput. This implies that EDF is robust in the sense that its throughput is close to the optimum even when the deadlines are not precisely known.