Optimization driven quantum circuit reduction

Implementing a quantum circuit on specific hardware with a reduced available gate set is often associated with a substantial increase in the length of the equivalent circuit. This process is also known as transpilation and due to decoherence, it is mandatory to keep quantum circuits as short as possible, without affecting functionality. In this work we propose three different transpilation approaches, based on a localized term-replacement scheme, to substantially reduce circuit lengths while preserving the unitary operation implemented by the circuit. The first variant is based on a stochastic search scheme, and the other variants are driven by a database retrieval scheme and a machine learning based decision support. We show that our proposed methods generate short quantum circuits for restricted gate sets, superior to the typical results obtained by using various qiskit and Berkley quantum synthesis toolkit optimization levels. Our method can be applied to different gate sets and scales well with an arbitrary number of qubits.