Practical Quantum Circuit Implementation for Simulating Coupled Classical Oscillators

Natt Luangsirapornchai, Peeranat Sanglaor, Apimuk Sornsaeng, Stephane Bressan, Thiparat Chotibut, Kamonluk suksen, Prabhas Chongstitvatana,


ABSTRACT

Simulating large-scale coupled-oscillator systems presents substantial computational challenges for classical algorithms, particularly when investigating the thermodynamics limit from first principles. Babbush et al. [1] introduced a quantum algorithm framework and a theoretical foundation that can efficiently simulate such systems using Hamiltonian simulation techniques. In this work, we present and implement an explicit quantum circuit to efficiently simulate one-dimensional coupled-oscillator systems.
 
Our circuit incorporates fundamental quantum subroutines, including block encoding, quantum singular value transformation (QSVT), and amplitude amplification. We show that the total time complexity of our circuit is O(log2 N log(1/ε)) for uniform spring-mass systems and O(N logN log(1/ε)) for generalized systems, where N is the number of oscillators and ε represents the truncation error. Both implementations require only O(logN) qubits. Our quantum simulation results show excellent agreement with classical methods, showcasing a practical implementation of Hamiltonian simulation and highlighting the potential for circuit-based algorithm to simulate many-body systems on larger-scale quantum computers.

[1] Ryan Babbush, Dominic W. Berry, Robin Kothari, Rolando D. Somma and Nathan Wiebe. "Exponential quantum speedup in simulating coupled classical oscillators." Physical Review X, 13(4), December 2023.