Optimizing Parameterized Quantum Circuits with Free-Axis Selection
Variational quantum algorithms, which utilize Parametrized Quantum Circuits
(PQCs), are promising tools to achieve quantum advantage for optimization
problems on near-term quantum devices. Their PQCs have been conventionally
constructed from parametrized rotational angles of single-qubit gates around
predetermined set of axes, and two-qubit entangling gates, such as CNOT gates.
We propose a method to construct a PQC by continuous parametrization of both
the angles and the axes of its single-qubit rotation gates. The method is based
on the observation that when rotational angles are fixed, optimal axes of
rotations can be computed by solving a system of linear equations whose
coefficients can be determined from the PQC with small computational overhead.
The method can be further simplified to select axes freely from continuous
parameters with rotational angles fixed to half rotation or $\pi$. We show the
simplified free-axis selection method has better expressibility against other
structural optimization methods when measured with Kullback-Leibler (KL)
divergence. We also demonstrate PQCs with free-axis selection are more
effective to search the ground states of Hamiltonians for quantum chemistry and
combinatorial optimization. Because free-axis selection allows designing PQCs
without specifying their single-qubit rotational axes, it may significantly
improve the handiness of PQCs.
Hiroshi C. Watanabe Rudy Raymond Yu-ya Ohnishi Eriko Kaminishi Michihiko Sugawara