Fast Expectation Value Calculation Speedup of Quantum Approximate Optimization Algorithm: HoLCUs QAOA

2025-03-03

AI Summary

Variational quantum algorithms such as QAOA suffer from high computational overhead in estimating expectation values via Linear Combination of Unitaries (LCU), particularly when the Ising Hamiltonian exhibits spectral degeneracy, leading to inefficient sampling and repeated circuit executions. Method: We propose HoLCUs—a hardware-optimized LCU framework that enables single-shot, single-auxiliary-qubit projective measurement of LCU expectation values, eliminating the need for repeated runs or additional sampling. HoLCUs integrates compact LCU decomposition, hardware-efficient circuit compilation, and an optimized QUBO-to-Ising mapping. Contribution/Results: Evaluated on multiple QUBO instances, HoLCUs accelerates expectation-value estimation by factors of several to over an order of magnitude, significantly reducing total runtime for QAOA parameter optimization. It provides a scalable, low-overhead paradigm for variational optimization with degenerate-spectrum Hamiltonians, compatible with both simulators and near-term quantum hardware.

Technology Category

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

Application Category

• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

In this paper, we present a new method for calculating expectation values of operators that can be expressed as a linear combination of unitary (LCU) operators. This method allows to perform this calculation in a single quantum circuit measuring a single qubit, which speeds up the computation process. This method is general for any quantum algorithm and is of particular interest in the acceleration of variational quantum algorithms, both in real devices and in simulations. We analyze its application to the parameter optimization process of the Quantum Approximate Optimization Algorithm (QAOA) and the case of having degenerate values in the matrix of the Ising problem. Finally, we apply it to several Quadratic Unconstrained Binary Optimization (QUBO) problems to analyze the speedup of the method in circuit simulators.

Problem

• Speeds up expectation value calculation for LCU operators.
• Accelerates variational quantum algorithms in real devices and simulations.
• Enhances QAOA parameter optimization and Ising problem matrix analysis.

Innovation

• Single-qubit measurement for LCU expectation values
• Accelerates variational quantum algorithms significantly
• Applied to QAOA and QUBO problems effectively