Probabilistic method for finding optimal quantum circuits

In the operation of a quantum computer, it is known that the number of possible gate configurations, which are also referred to as quantum circuits, increases exponentially with the number of qubits. For this reason, it is necessary to devise methods for finding the optimal quantum circuit for a given target task in a realistic time. We use a random search technique to find quantum circuits that implement perfect quantum state preparation or unitary operator synthesis with arbitrary targets [1]. This approach is based on the recent discovery that there is a large multiplicity of quantum circuits that achieve unit fidelity in performing an arbitrary target operation [2]. We show that the fraction of perfect-fidelity quantum circuits increases rapidly as soon as the circuit size exceeds the minimum circuit size required for achieving unit fidelity. This result implies that near-optimal quantum circuits for a variety of quantum information processing tasks can be identified relatively easily by trying only a few randomly chosen quantum circuits and optimizing their parameters. We apply the random search method to the problem of decomposing the four-qubit Toffoli gate and find a 15-CNOT-gate decomposition.

References:

[1] S. Ashhab, F. Yoshihara, M. Tsuji, M. Sato, and K. Semba, ‘Quantum circuit synthesis via a random combinatorial search’, Phys. Rev. A 109, 052605 (2024).

[2] S. Ashhab, N. Yamamoto, F. Yoshihara, and K. Semba, ‘Numerical analysis of quantum circuits for state preparation and unitary operator synthesis’, Phys. Rev. A 106, 022426 (2022).