Unbiased Hamiltonian Simulation by Reversing Trotter Error Dynamics

Abstract

Owing to their simplicity and low overhead, Suzuki--Trotter formulas remain the de facto Hamiltonian simulation methods on current quantum computing platforms. Systematic Trotter errors, however, will quickly become limiting when scaling to larger problems and aiming for higher accuracy. We present a mechanism that removes the systematic error of any $k$-th order Suzuki--Trotter simulation, at the cost of a constant sampling overhead. The key insight is that the Trotter error is itself a coherent dynamics to be reversed, rather than a deviation to be bounded. By identifying the structure of this error in a suitable form, we carry out that reversal through quasi-probabilistic decompositions. The resulting algorithm, called Probabilistic Trotter Error Reversal (PTER), is unbiased, improves the gate-count scaling compared to Suzuki--Trotter formulas, and still retains their simplicity. Numerical simulations of a Heisenberg spin chain support the predicted resource advantage already at modest system sizes.