Practical Quantum Circuit Implementation for Simulating Coupled Classical Oscillators

• URL: http://arxiv.org/abs/2501.06100v1
• Date: Fri, 10 Jan 2025 16:53:56 GMT
• Title: Practical Quantum Circuit Implementation for Simulating Coupled Classical Oscillators
• Authors: Natt Luangsirapornchai, Peeranat Sanglaor, Apimuk Sornsaeng, Stephane Bressan, Thiparat Chotibut, Kamonluk Suksen, Prabhas Chongstitvatana,
• Abstract summary: We present and implement a detailed quantum circuit construction for simulating one-dimensional spring-mass systems. This circuit-based Hamiltonian simulation approach can substantially reduce computational costs and potentially enable larger-scale many-body studies on future quantum hardware.
• Score: 1.3140209441982318
• License:
• 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 $\mathcal{O}\bigl(\log_2^2 N\,\log_2(1/\varepsilon)\bigr)$, 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 $\mathcal{O}\bigl(N\log_2 N\,\log_2(1/\varepsilon)\bigr)$. 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.

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