Quantum circuit synthesis via a random combinatorial search
arxiv(2023)
摘要
We use a random search technique to find quantum gate sequences that
implement perfect quantum state preparation or unitary operator synthesis with
arbitrary targets. This approach is based on the recent discovery that there is
a large multiplicity of quantum circuits that achieve unit fidelity in
performing a given target operation, even at the minimum number of single-qubit
and two-qubit gates needed to achieve unit fidelity. 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. In
addition to analyzing the case where the CNOT gate is the elementary two-qubit
gate, we consider the possibility of using alternative two-qubit gates. In
particular, we analyze the case where the two-qubit gate is the B gate, which
is known to reduce the minimum quantum circuit size for two-qubit operations.
We apply the random search method to the problem of decomposing the 4-qubit
Toffoli gate and find a 15 CNOT-gate decomposition.
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