Peephole Optimization for Quantum Approximate Synthesis

Peephole optimization of quantum circuits provides a method of leveraging standard circuit synthesis approaches into scalable quantum circuit optimization. One application of this technique partitions an entire circuit into a series of peepholes and produces multiple approximations of each partitioned subcircuit. A single approximation of each subcircuit is then selected to form optimized result circuits. We propose a series of improvements to the final phase of this architecture, which include the addition of error awareness and a better method of approximating the correctness of the result. We evaluated these proposed improvements on a set of benchmark circuits using the IBMQ FakeWashington simulator. The results demonstrate that our best-performing method provides an average reduction in Total Variational Distance (TVD) and Jensen-Shannon Divergence (JSD) of 18.2% and 15.8%, respectively, compared with the Qiskit optimizer. This also constitutes an improvement in TVD of 11.4% and JSD of 9.0% over existing solutions.