Doubling the order of approximation via the randomized product formula

Abstract

Randomization has been applied to Hamiltonian simulation in a number of ways to improve the accuracy or efficiency of product formulas. Deterministic product formulas are often constructed in a symmetric way to provide accuracy of even order 2k. We show that by applying randomized corrections, it is possible to more than double the order to 4k + 1 (corresponding to a doubling of the order of the error). In practice, applying the corrections in a quantum algorithm requires some structure to the Hamiltonian, for example the Pauli strings as are used in the simulation of quantum chemistry.

arXiv comment12 pages, no figure. Comments are welcome

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Cited by in corpus (8)

• Continuous Hamiltonian dynamics on digital quantum computers without discretization error
• Quantum error mitigation for Fourier moment computation
• Simple and high-precision Hamiltonian simulation by compensating Trotter error with linear combination of unitary operations
• Early Fault-Tolerant Quantum Algorithms in Practice: Application to Ground-State Energy Estimation
• Selection and improvement of product formulae for best performance of quantum simulation
• Complexity of Digital Quantum Simulation in the Low-Energy Subspace: Applications and a Lower Bound
• Halving the Cost of Quantum Algorithms with Randomization
• Faster Algorithmic Quantum and Classical Simulations by Corrected Product Formulas