When executing the quantum approximate optimization algorithm (QAOA) on a quantum circuit simulator to solve the combinatorial optimization problem, large-scale computing power is required and the simulation speed is slow. We propose techniques to accelerate quantum circuit simulations (QCS) of QAOA, using mathematical optimization to compress quantum operations, incorporating efficient bitwise operations to further reduce computational complexity, and exploiting the different levels of parallelism of modern multi-core processors , the study case shows the effectiveness of solving the maximum cut problem. Experimental results show significant performance improvements on a virtual quantum computer running a 16-core, 32-thread AMD Ryzen 9 5950X processor, up to 17 times higher than the state-of-the-art simulator QuEST. We believe this work opens new possibilities for accelerating various QAOA applications.

     Boolean matching is an important problem in logic synthesis and verification. Despite being well-studied for conventional Boolean circuits, its treatment for reversible logic circuits remains largely, if not completely, missing. This work provides the first such study. Given two (black-box) reversible logic circuits that are promised to be matchable, we check their equivalences under various input/output negation and permutation conditions subject to the availability/unavailability of their inverse circuits. Notably, among other results, we show that the equivalence up to input negation and permutation is solvable in quantum polynomial time, while its classical complexity is exponential. This result is arguably the first demonstration of quantum exponential speedup in solving design automation problems. Also, as a negative result, we show that the equivalence up to both input and output negations is not solvable in quantum polynomial time unless UNIQUE-SAT is, which is unlikely. This work paves the theoretical foundation of Boolean matching reversible circuits for potential applications, e.g., in quantum circuit synthesis.

     Qsyn is an open-source quantum circuit synthesis (QCS) framework to research, develop, and experiment. It is more developer-friendly than other modern QCS frameworks in three aspects: (1) Rich command-line interface for flexible algorithm designs and testing scenarios. (2) Detailed access to many data representations on different abstract levels. (3) Rigid developing environment to ensure development qualities. Besides, the embedded algorithms in Qsyn also outperform other modern platforms.