Symmetric Trotterization in digital quantum simulation of quantum spin dynamics

TL;DR

This paper evaluates the effectiveness of symmetric second-order Trotterization in digital quantum simulation of the transverse-field Ising model on IBM Quantum hardware, finding it does not outperform first-order Trotterization due to quantum errors.

Contribution

The study provides an empirical assessment of symmetric Trotterization's accuracy on real quantum hardware, highlighting its limitations in NISQ devices.

Findings

Symmetric Trotterization does not improve accuracy over first-order in experiments.

Quantum errors dominate over Trotter error in current NISQ devices.

Higher-order Trotterization may be less beneficial in noisy quantum simulations.

Abstract

A higher-order Suzuki-Trotter decomposition or Trotterization can be exploited to mitigate the Trotter error in digital quantum simulation. This work revisits the second-order symmetric Trotterization in terms of the Trotter error, where quantum many-body spin dynamics of the transverse-field Ising model is simulated. While the work presents a pedagogical way to exploit a real quantum computer, the effectiveness of the symmetric Trotterization is evaluated in a prototype superconducting quantum device on IBM Quantum Experience. It turns out that the symmetric Trotterization does not provide higher accuracy than the first-order Trotterization in the testbed using the transverse-field Ising model. The result indicates that apart from the quantum errors, such as logical gate error and readout error, the use of a higher-order Trotterization should be circumspect, and the Trotter error would play an insignificant role in particular applications in an early stage of realized noisy intermediate-scale quantum (NISQ) devices.