2018/05/31 by Matthew Amy · 1 citation
Physics and Astronomy · Computer Science · #quant-ph #cs.LO
paper · pdf · doi:10.4204/eptcs.287.1
published as EPTCS 287, 2019, pp. 1-21 · In Proceedings QPL 2018, arXiv:1901.09476
arxiv created 2019/01/29 · arxiv updated 2019/01/30
We introduce a framework for the formal specification and verification of quantum circuits based on the Feynman path integral. Our formalism, built around exponential sums of polynomial functions, provides a structured and natural way of specifying quantum operations, particularly for quantum implementations of classical functions. Verification of circuits over all levels of the Clifford hierarchy with respect to either a specification or reference circuit is enabled by a novel rewrite system for exponential sums with free variables. Our algorithm is further shown to give a polynomial-time decision procedure for checking the equivalence of Clifford group circuits. We evaluate our methods by performing automated verification of optimized Clifford+T circuits with up to 100 qubits and thousands of T gates, as well as the functional verification of quantum algorithms using hundreds of qubits. Our experiments culminate in the automated verification of the Hidden Shift algorithm for a class of Boolean functions in a fraction of the time it has taken recent algorithms to simulate.