Optimal-order Trotter-Suzuki decomposition for quantum simulation on noisy quantum computers

TL;DR

This paper investigates the use of higher-order Trotter-Suzuki decompositions for quantum simulations on noisy quantum computers, showing that reduced gate errors make higher-order methods more effective in minimizing overall simulation errors.

Contribution

It demonstrates that higher-order Trotter-Suzuki decompositions become advantageous for quantum simulation when gate errors are significantly reduced, optimizing overall simulation accuracy.

Findings

Higher-order Trotterization reduces total simulation error with lower gate errors.

Optimal Trotter order depends on the balance between mathematical and physical errors.

Reducing gate errors by an order of magnitude makes higher-order methods beneficial.

Abstract

The potential of employing higher orders of the Trotter-Suzuki decomposition of the evolution operator for more effective simulations of quantum systems on a noisy quantum computer is explored. By examining the transverse-field Ising model and the XY model, it is demonstrated that when the gate error is decreased by approximately an order of magnitude relative to typical modern values, higher-order Trotterization becomes advantageous. This form of Trotterization yields a global minimum of the overall simulation error, comprising both the mathematical error of Trotterization and the physical error arising from gate execution.