Automated quantum circuit optimization with randomized replacements

TL;DR

This novel automated protocol for approximate circuit rewriting is a refined evolution of automated optimization techniques based on the ZX-calculus, where a greedy strategy is added that selectively replaces ZX-diagrams with small phase angles with stochastic mixtures of the identity and carefully chosen over-rotations.

Abstract

Quantum circuit optimization - the process of transforming a quantum circuit into an equivalent one with reduced time and space requirements - is crucial for maximizing the utility of current and near-future quantum devices. While most automated optimization techniques focus on transforming circuits into equivalent ones that implement the same unitary, we show that substantial new opportunities for resource reduction can be achieved by (1) allowing approximate local transformations and (2) employing mixed quantum channels to approximate pure circuits. Our novel automated protocol for approximate circuit rewriting is a refined evolution of automated optimization techniques based on the ZX-calculus, where we add a greedy strategy that selectively replaces ZX-diagrams with small phase angles with stochastic mixtures of the identity and carefully chosen over-rotations, which are designed to reduce the overall gate count in expectation while staying within a strict error budget. This approach yields modest two-qubit gate count reduction in random quantum circuits, and achieves a substantial reduction in structured circuits such as the quantum Fourier transform. Fundamentally, our protocol converts experimental noise due to gate applications into deliberately engineered random noise, outperforming many other approximation methods on average. These results highlight the potential of mixed-channel approximations to enhance future quantum circuit performance, suggesting new directions for resource-aware automated quantum compilation beyond pure unitary channels.

Figures (4)

• Figure 1: (a) Circuit $U$ run repeatedly on a quantum computer (top) can be approximated using a mixture of slightly different circuits $V_n$ (bottom), which reduces average gate count. (b) Intuitive picture showing how a circuit containing $Z$-phase gate $Z_\alpha$ can be approximated by a mixture of phase-squashed circuit ($Z_\alpha$ replaced by identity) with probability $p$ and an "overrotated" circuit with $Z_{\tilde{\theta}}$ ($\tilde{\theta} > \alpha$), with probability $(1-p)$.
• Figure 2: Average two-qubit gate count results of the approximation protocol for (a) random quantum circuit for $L = 8$ qubits, (b) quantum Fourier transform for $L=8$ qubits, and (c) quantum Fourier transform for $L=24$ qubits, all as functions of identity replacement probability $p$, and under error budget $\varepsilon$. The inset in (a) shows a zoomed-in section of the plot. The legend in (c) applies in (a) and (b).
• Figure 3: Diamond distance for the random quantum circuit ($L = 6$, $N_\text{real} = 100$, $p = 0.8$) as a function of error budget $\varepsilon$. All realizations are shown in light gray, their mean is in blue, the maximum in orange, and the minimum in green. The dashed line shows the error budget.
• Figure 4: The average Frobenius distance for the random quantum circuit (left) and the quantum Fourier transform (right), both for $L=8$.