Sergey Bravyi, Giuseppe Carleo, et al.
Quantum
Multi-product formulas (MPFs) are linear combinations of Trotter circuits offering high-quality simulation of Hamiltonian time evolution with fewer Trotter steps. Here we report two contributions aimed at making multi-product formulas more viable for near-term quantum simulations. First, we extend the theory of Trotter error with commutator scaling developed by Childs et al. [A. M. Childs et al., Phys. Rev. X 11, 011020 (2021)10.1103/PhysRevX.11.011020] to multi-product formulas. Our result implies that multi-product formulas can achieve a quadratic reduction of Trotter error in 1-norm (nuclear norm) on arbitrary time intervals compared with the regular product formulas without increasing the required circuit depth or qubit connectivity. The number of circuit repetitions grows only by a constant factor. Second, we introduce dynamic multi-product formulas with time-dependent coefficients chosen to minimize a certain efficiently computable proxy for the Trotter error. We use a minimax estimation method to make dynamic multi-product formulas robust to uncertainty from algorithmic errors, sampling, and hardware noise. We call this method the minimax MPF and we provide a rigorous bound on its error.
Sergey Bravyi, Giuseppe Carleo, et al.
Quantum
Sergey Bravyi, Oliver Dial, et al.
Journal of Applied Physics
Sergey Bravyi, Anirban Chowdhury, et al.
QIP 2022
Dmitri Maslov, Jin-Sung Kim, et al.
Nature Physics