Quantum simulation of highly-oscillatory many-body Hamiltonians for near-term devices

• URL: http://arxiv.org/abs/2312.08310v1
• Date: Wed, 13 Dec 2023 17:29:29 GMT
• Title: Quantum simulation of highly-oscillatory many-body Hamiltonians for near-term devices
• Authors: Guannan Chen, Mohammadali Foroozandeh, Chris Budd, Pranav Singh
• Abstract summary: We develop a fourth-order Magnus expansion based quantum algorithm for the simulation of many-body problems. We exploit symmetries of the Hamiltonian and achieve a surprising reduction in the expansion. Our algorithms are able to take time-steps that are larger than the wavelength of oscillation of the time-dependent Hamiltonian.
• Score: 2.487329273327606
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We develop a fourth-order Magnus expansion based quantum algorithm for the simulation of many-body problems involving two-level quantum systems with time-dependent Hamiltonians, $\mathcal{H}(t)$. A major hurdle in the utilization of the Magnus expansion is the appearance of a commutator term which leads to prohibitively long circuits. We present a technique for eliminating this commutator and find that a single time-step of the resulting algorithm is only marginally costlier than that required for time-stepping with a time-independent Hamiltonian, requiring only three additional single-qubit layers. For a large class of Hamiltonians appearing in liquid-state nuclear magnetic resonance (NMR) applications, we further exploit symmetries of the Hamiltonian and achieve a surprising reduction in the expansion, whereby a single time-step of our fourth-order method has a circuit structure and cost that is identical to that required for a fourth-order Trotterized time-stepping procedure for time-independent Hamiltonians. Moreover, our algorithms are able to take time-steps that are larger than the wavelength of oscillation of the time-dependent Hamiltonian, making them particularly suited for highly-oscillatory controls. The resulting quantum circuits have shorter depths for all levels of accuracy when compared to first and second-order Trotterized methods, as well as other fourth-order Trotterized methods, making the proposed algorithm a suitable candidate for simulation of time-dependent Hamiltonians on near-term quantum devices.

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