POPQC: Parallel Optimization for Quantum Circuits (Extended Version)

• URL: http://arxiv.org/abs/2506.13720v1
• Date: Mon, 16 Jun 2025 17:26:27 GMT
• Title: POPQC: Parallel Optimization for Quantum Circuits (Extended Version)
• Authors: Pengyu Liu, Jatin Arora, Mingkuan Xu, Umut A. Acar,
• Abstract summary: Optimization of quantum programs or circuits is a fundamental problem in quantum computing.<n>Recent work proposed a new approach that pursues a weaker form of optimality called local optimality.<n>We present a parallel algorithm for local optimization of quantum circuits.
• Score: 2.043850178316957
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Optimization of quantum programs or circuits is a fundamental problem in quantum computing and remains a major challenge. State-of-the-art quantum circuit optimizers rely on heuristics and typically require superlinear, and even exponential, time. Recent work proposed a new approach that pursues a weaker form of optimality called local optimality. Parameterized by a natural number $\Omega$, local optimality insists that each and every $\Omega$-segment of the circuit is optimal with respect to an external optimizer, called the oracle. Local optimization can be performed using only a linear number of calls to the oracle but still incurs quadratic computational overheads in addition to oracle calls. Perhaps most importantly, the algorithm is sequential. In this paper, we present a parallel algorithm for local optimization of quantum circuits. To ensure efficiency, the algorithm operates by keeping a set of fingers into the circuit and maintains the invariant that a $\Omega$-deep circuit needs to be optimized only if it contains a finger. Operating in rounds, the algorithm selects a set of fingers, optimizes in parallel the segments containing the fingers, and updates the finger set to ensure the invariant. For constant $\Omega$, we prove that the algorithm requires $O(n\lg{n})$ work and $O(r\lg{n})$ span, where $n$ is the circuit size and $r$ is the number of rounds. We prove that the optimized circuit returned by the algorithm is locally optimal in the sense that any $\Omega$-segment of the circuit is optimal with respect to the oracle.

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