POPQC: Parallel Optimization for Quantum Circuits (Extended Version)

2025-06-16

AI Summary

Quantum circuit optimization suffers from high time complexity and poor parallelizability. This paper introduces the first parallel local optimization algorithm for quantum circuits, modeling local optimality as an efficiently parallelizable problem—specifically, via a novel “finger”-based mechanism. Our approach overcomes traditional sequential bottlenecks through dynamic segmentation and invariant-preserving updates, achieving $O(n log n)$ work and $O(r log n)$ span in the work-span model, where $r$ is a key structural parameter. The algorithm guarantees that the output circuit is $Omega$-locally optimal globally, while invoking an external optimizer only linearly many times. To our knowledge, this is the first local optimization framework for quantum compilation with provable parallel complexity bounds and formal correctness guarantees.

Technology Category

• Search and Optimization: Local Search
• Machine Learning: Optimization
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• Security and Privacy: Large-scale security measurements

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 $O(nlg{n})$ work and $O(rlg{n})$ 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.

Problem

• Optimizing quantum circuits efficiently with parallel algorithms
• Reducing quadratic overhead in local quantum circuit optimization
• Ensuring local optimality of Ω-segments in quantum circuits

Innovation

• Parallel algorithm for local quantum circuit optimization
• Uses finger set to maintain optimization invariant
• Ensures local optimality with linear oracle calls