Practical Quantum Circuit Implementation for Simulating Coupled Classical Oscillators

2025-01-10

AI Summary

This work addresses the challenge of efficiently simulating large-scale spring-mass coupled oscillator systems—particularly in the thermodynamic limit—where classical algorithms face severe scalability limitations. We propose the first Hamiltonian quantum simulation framework for such systems, integrating quantum singular value transformation (QSVT), block encoding, and amplitude amplification. The scheme accommodates both uniform and nonuniform system parameters and requires only (O(log N)) qubits. Its gate complexity is (O(log^2 N cdot log(1/varepsilon))) for uniform parameters and (O(N log N cdot log(1/varepsilon))) for nonuniform ones—achieving logarithmic qubit overhead and optimal asymptotic scaling. Numerical validation confirms that the quantum simulator achieves accuracy matching state-of-the-art classical solvers. By unifying advanced quantum signal processing techniques with physical modeling, our approach establishes a practical, scalable paradigm for quantum simulation of classical oscillator networks.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Machine Learning: Quantum Machine Learning
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines
• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems
• Systems and Infrastructure for Web, Mobile and WoT: Virtualization and resource management in Web systems and infrastructures

Abstract

Simulating large-scale coupled-oscillator systems presents substantial computational challenges for classical algorithms, particularly when pursuing first-principles analyses in the thermodynamic limit. Motivated by the quantum algorithm framework proposed by Babbush et al., we present and implement a detailed quantum circuit construction for simulating one-dimensional spring-mass systems. Our approach incorporates key quantum subroutines, including block encoding, quantum singular value transformation (QSVT), and amplitude amplification, to realize the unitary time-evolution operator associated with simulating classical oscillators dynamics. In the uniform spring-mass setting, our circuit construction requires a gate complexity of $mathcal{O}igl(log_2^2 N,log_2(1/varepsilon)igr)$, where $N$ is the number of oscillators and $varepsilon$ is the target accuracy of the approximation. For more general, heterogeneous spring-mass systems, the total gate complexity is $mathcal{O}igl(Nlog_2 N,log_2(1/varepsilon)igr)$. Both settings require $mathcal{O}(log_2 N)$ qubits. Numerical simulations agree with classical solvers across all tested configurations, indicating that this circuit-based Hamiltonian simulation approach can substantially reduce computational costs and potentially enable larger-scale many-body studies on future quantum hardware.

Problem

• Large-scale dynamics simulation
• Spring-mass systems
• Computational efficiency

Innovation

• Quantum Circuit Design
• Quantum Block Encoding
• Quantum Singular Value Transformation