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.