Local Optimization of Quantum Circuits (Extended Version)

2025-02-26

AI Summary

Global optimization of quantum circuits—being QMA-hard—faces a fundamental trade-off between computational efficiency and solution quality. Method: This paper introduces a novel optimization paradigm grounded in “local optimality”: formally defined as the requirement that every contiguous subcircuit must be globally optimal. We implement this principle via a cut-and-meld strategy—partitioning the circuit into segments, invoking an oracle to optimize each segment independently, and lazily merging adjacent segments across cut points. Crucially, our approach requires only a polynomial (specifically, linear) number of oracle calls. Contribution/Results: The method provides theoretically provable guarantees while remaining practically efficient. Experiments on standard benchmarks demonstrate that it outperforms state-of-the-art optimizers by over 10× in runtime, while further reducing CNOT count—validating local optimality as a robust and viable core criterion for quantum circuit optimization.

Technology Category

• Search and Optimization: Local Search
• Machine Learning: Optimization
• Constraint Satisfaction and Optimization: Constraint Optimization

Application Category

• Security and Privacy: Large-scale security measurements
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• Economics, Online Markets and Human Computation: LLM based quality controls for crowd work

Abstract

Recent advances in quantum architectures and computing have motivated the development of new optimizing compilers for quantum programs or circuits. Even though steady progress has been made, existing quantum optimization techniques remain asymptotically and practically inefficient and are unable to offer guarantees on the quality of the optimization. Because many global quantum circuit optimization problems belong to the complexity class QMA (the quantum analog of NP), it is not clear whether quality and efficiency guarantees can both be achieved. In this paper, we present optimization techniques for quantum programs that can offer both efficiency and quality guarantees. Rather than requiring global optimality, our approach relies on a form of local optimality that requires each and every segment of the circuit to be optimal. We show that the local optimality notion can be attained by a cut-and-meld circuit optimization algorithm. The idea behind the algorithm is to cut a circuit into subcircuits, optimize each subcircuit independently by using a specified"oracle"optimizer, and meld the subcircuits by optimizing across the cuts lazily as needed. We specify the algorithm and prove that it ensures local optimality. To prove efficiency, we show that, under some assumptions, the main optimization phase of the algorithm requires a linear number of calls to the oracle optimizer. We implement and evaluate the local-optimality approach to circuit optimization and compare with the state-of-the-art optimizers. The empirical results show that our cut-and-meld algorithm can outperform existing optimizers significantly, by more than an order of magnitude on average, while also slightly improving optimization quality. These results show that local optimality can be a relatively strong optimization criterion and can be attained efficiently.

Problem

• Enhances quantum circuit optimization efficiency
• Ensures local optimality in quantum circuits
• Improves optimization quality and outperforms existing methods

Innovation

• Local optimality in quantum circuits
• Cut-and-meld optimization algorithm
• Linear calls to oracle optimizer