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.
Nevertheless, previous work has not answered the following questions: 1) are T state buffers always needed? In case they are, what will be the optimal buffer size? How can the buffer size be computed? Can the need for buffering be circumvented? In @cite_9 , once the buffer capacity was capped, the distillery control did not generate additional time overheads in the resulting assemblies.
@cite_9
2167407752 2168965212 1984382275 2791940919
Existing ABR algorithms face a significant challenge in estimating future capacity: capacity can vary widely over time, a phenomenon commonly observed in commercial services. In this work, we suggest an alternative approach: rather than presuming that capacity estimation is required, it is perhaps better to begin by using only the buffer, and then ask when capacity estimation is needed. We test the viability of this approach through a series of experiments spanning millions of real users in a commercial service. We start with a simple design which directly chooses the video rate based on the current buffer occupancy. Our own investigation reveals that capacity estimation is unnecessary in steady state; however using simple capacity estimation (based on immediate past throughput) is important during the startup phase, when the buffer itself is growing from empty. This approach allows us to reduce the rebuffer rate by 10-20 compared to Netflix's then-default ABR algorithm, while delivering a similar average video rate, and a higher video rate in steady state. 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. This paper proposes a new class of online policies for scheduling in input-buffered crossbar switches. Given an initial configuration of packets at the input buffers, these policies drain all packets in the system in the minimal amount of time provided that there are no further arrivals. These policies are also throughput optimal for a large class of arrival processes which satisfy strong-law of large numbers. We show that it is possible for policies in our class to be throughput optimal even if they are not constrained to be maximal in every time slot. Most algorithms for switch scheduling take an edge based approach; in contrast, we focus on scheduling (a large enough set of) the most congested ports. This alternate approach allows for lower-complexity algorithms, and also requires a non-standard technique to prove throughput-optimality. One algorithm in our class, Maximum Vertex-weighted Matching (MVM) has worst-case complexity similar to Max-size Matching, and in simulations shows slightly better delay performance than Max-(edge)weighted-Matching (MWM). In this paper, we propose a new relaying scheme, referred to as priority-based max-link relay selection, for buffer-aided decode-and-forward cooperative networks. We give the first priority to the relay buffers having status full, the second priority to the relay buffers having status empty, and the third priority to the relay buffers having status neither full nor empty. The best relay node is selected corresponding to the link having the highest channel gain among the links within a priority class. By adopting a Markov chain approach to analyze the state transition matrix that models the evolution of the buffers status, we derive analytical expressions for the outage probability and the average bit error rate. Analytical expressions for the steady-state probability vector are also obtained, and through these expressions, it is shown that states with the same probabilities can be grouped, thus reducing the size of the state transition matrix. We propose a general state-grouping-based method to obtain the reduced state transition matrix, which in turn reduces the computational complexity in obtaining the steady-state distribution. Our analytical and simulation results demonstrate that the proposed relaying scheme has better performance gain over the conventional max-link scheme.