Efficient quantum approximation : examining the efficiency of select universal gate sets in approximating 1-qubit quantum gates.

Quantum computation is of current ubiquitous interest in physics, computer science, and the public interest. In the not-so-distant future, quantum computers will be relatively common pieces of research equipment. Eventually, one can expect an actively quantum computer to be a common feature of life. In this work, I study the approximation efficiency of several common universal quantum gate sets at short sequence lengths using an implementation of the Solovay-Kitaev algorithm. I begin by developing from almost nothing the relevant formal mathematics to rigorously describe what one means by the terms universal gate set and covering efficiency. I then describe some interesting results on the asymptotic covering properties of certain classes of universal gate sets and discuss the theorem which the Solovay-Kitaev algorithm is based on. Moving from mathematical introduction to experimental method, I then describe how sets will be compared. I use the commonly studied sets H+T, Pauli+V, V, and Clifford+T to determine which is the most efficient at approximating randomly generated unitaries. By doing so, we get an understanding of how well each set would perform in the context of a general quantum computer processor. This was accomplished by using the same implementation of the Solovay-Kitaev algorithm throughout, with roughly equal-sized preprocessed libraries formed from each gate set, over approximations for 10,000 randomly generated unitary matrices at algorithm depth n=5. Ultimately, the Pauli+V and V sets were the most efficient and had similar performance qualities. On average the Pauli+V set produced approximations of length 15,491 and accuracy 0.0002686. The V basis produced approximations of average sequence length 16,403 and accuracy 0.0001465. This performance is about equal given this particular implementation of the Solovay-Kitaev algorithm. We conclude that this result is somewhat surprising as the general behavior and efficiency of these particular choices of gate set are expected to be similar. It is possible though that the asymptotic efficiencies of these gate sets vary by a relatively wide margin and this has effected the experiment. It is also possible that some aspect of a naive implementation of the Solovay-Kitaev algorithm resulted in the Hadamard gate based sets performing more poorly than the V basis sets overall. Due to constraints on computational power, this result could also be limited to this particular accuracy regime and could even out as tolerance is taken to be arbitrarily small. Further possibilities of this result as well as further work are then discussed

Design and performance of the prototype Schwarzschild-Couder telescope camera

International audienceThe prototype Schwarzschild-Couder Telescope (pSCT) is a candidate for a medium-sized telescope in the Cherenkov Telescope Array. The pSCT is based on a dual-mirror optics design that reduces the plate scale and allows for the use of silicon photomultipliers as photodetectors. The prototype pSCT camera currently has only the central sector instrumented with 25 camera modules (1600 pixels), providing a 2.68-deg field of view (FoV). The camera electronics are based on custom TARGET (TeV array readout with GSa/s sampling and event trigger) application-specific integrated circuits. Field programmable gate arrays sample incoming signals at a gigasample per second. A single backplane provides camera-wide triggers. An upgrade of the pSCT camera that will fully populate the focal plane is in progress. This will increase the number of pixels to 11,328, the number of backplanes to 9, and the FoV to 8.04 deg. Here, we give a detailed description of the pSCT camera, including the basic concept, mechanical design, detectors, electronics, current status, and first light