Improved Quantum Computing with the Higher-order Trotter Decomposition

Abstract

In designing quantum control, it is generally required to simulate the controlled system evolution with a classical computer. However, computing the time evolution operator can be quite resource-consuming since the total Hamiltonian is often hard to diagonalize. In this paper, we mitigate this issue by substituting the time evolution segments with their Trotter decompositions, which reduces the propagator into a combination of single-qubit operations and fixed-time system evolutions. The resulting procedure can provide substantial speed gain with acceptable costs in the propagator error. As a demonstration, we apply the proposed strategy to improve the efficiency of the gradient ascent pulse engineering algorithm for searching optimal control fields. Furthermore, we show that the higher-order Trotter decompositions can provide efficient Ansätze for the variational quantum algorithm, leading to improved performance in solving the ground-state problem. The strategy presented here is also applicable for many other quantum optimization and simulation tasks.

9 pages, 7 figures

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• Quantum Computing
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• Simple pulses for elimination of leakage in weakly nonlinear qubits
• Simulating Hamiltonian dynamics with a truncated Taylor series
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• Accelerating two-dimensional electronic spectroscopy simulations with a probe qubit protocol
• Optimal-order Trotter-Suzuki decomposition for quantum simulation on noisy quantum computers
• Characterization of overparametrization in the simulation of realistic quantum systems
• Full-counting statistics of particle distribution on a digital quantum computer