Conserved charges in the quantum simulation of integrable spin chains

When simulating the time evolution of quantum many-body systems on a digital quantum computer, one faces the challenges of quantum noise and of the Trotter error due to time discretization. For certain spin chains, it is possible to discretize the time evolution preserving integrability, so that an extensive set of conserved charges are exactly conserved after discretization. In this work we implement, on real quantum computers and on classical simulators, the integrable Trotterization of the spin-1/2 Heisenberg XXX spin chain. We study how quantum noise affects the time evolution of several conserved charges, and observe the decay of the expectation values. We in addition study the early time behaviors of time evolution, which can potentially be used to benchmark quantum devices and algorithms in the future. We also provide an efficient method to generate the conserved charges at higher orders.

Automated summary

When simulating the time evolution of quantum many-body systems on a digital quantum computer, the challenges of quantum noise and Trotter error due to time discretization need to be addressed. However, for certain spin chains, it is possible to discretize the time evolution while preserving integrability and exactly conserving a set of conserved charges. In this study, we implemented the integrable Trotterization of the spin-1/2 Heisenberg XXX spin chain on real quantum computers and classical simulators, studying the effects of quantum noise on the time evolution of conserved charges and providing an efficient method to generate conserved charges at higher orders.