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Best Approximate Quantum Compiling Problems

Abstract : We study the problem of finding the best approximate circuit that is the closest (in some pertinent metric) to a target circuit, and which satisfies a number of hardware constraints, like gate alphabet and connectivity. We look at the problem in the CNOT+rotation gate set from a mathematical programming standpoint, offering contributions both in terms of understanding the mathematics of the problem and its efficient solution. Among the results that we present, we are able to derive a 14-CNOT 4-qubit Toffoli decomposition from scratch, and show that the Quantum Shannon Decomposition can be compressed by a factor of two without practical loss of fidelity.
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Submitted on : Monday, December 13, 2021 - 11:33:23 AM
Last modification on : Tuesday, September 6, 2022 - 12:06:06 PM

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Liam Madden, Andrea Simonetto. Best Approximate Quantum Compiling Problems. ACM Trans.Quant.Comput., 2022, 3 (2), pp.7. ⟨10.1145/3505181⟩. ⟨hal-03476912⟩



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