Characterization, synthesis, and optimization of quantum circuits over
multiple-control $\textit{Z}$-rotation gates: A systematic study
- URL: http://arxiv.org/abs/2304.08758v1
- Date: Tue, 18 Apr 2023 06:34:18 GMT
- Title: Characterization, synthesis, and optimization of quantum circuits over
multiple-control $\textit{Z}$-rotation gates: A systematic study
- Authors: Shihao Zhang and Junda Wu and Lvzhou Li
- Abstract summary: We study quantum circuits composed of multiple-control $Z$-rotation (MCZR) gates as primitives.
We present a gate-exchange strategy together with a flexible iterative algorithm for effectively optimizing the depth of any MCZR circuit.
- Score: 4.385466953937176
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: We conduct a systematic study of quantum circuits composed of
multiple-control $Z$-rotation (MCZR) gates as primitives, since they are
widely-used components in quantum algorithms and also have attracted much
experimental interest in recent years. Herein, we establish a
circuit-polynomial correspondence to characterize the functionality of quantum
circuits over the MCZR gate set with continuous parameters. An analytic method
for exactly synthesizing such quantum circuit to implement any given diagonal
unitary matrix with an optimal gate count is proposed, which also enables the
circuit depth optimal for specific cases with pairs of complementary gates.
Furthermore, we present a gate-exchange strategy together with a flexible
iterative algorithm for effectively optimizing the depth of any MCZR circuit,
which can also be applied to quantum circuits over any other commuting gate
set.
Besides the theoretical analysis, the practical performances of our circuit
synthesis and optimization techniques are further evaluated by numerical
experiments on two typical examples in quantum computing, including diagonal
Hermitian operators and Quantum Approximate Optimization Algorithm (QAOA)
circuits with tens of qubits, which can demonstrate a reduction in circuit
depth by 33.40\% and 15.55\% on average over relevant prior works,
respectively. Therefore, our methods and results provide a pathway for
implementing quantum circuits and algorithms on recently developed devices.
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