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.

12 pages, no figure. Comments are welcome

References in corpus (6)

• Simulated Quantum Computation of Molecular Energies
• Simulating Hamiltonian dynamics with a truncated Taylor series
• Digital quantum simulation of fermionic models with a superconducting circuit
• Chemical Basis of Trotter-Suzuki Errors in Quantum Chemistry Simulation
• Concentration for random product formulas
• Compilation by stochastic Hamiltonian sparsification

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