Exact real time dynamics with free fermions in disguise

TL;DR

This paper reveals a hidden free fermionic structure in quantum spin chains, enabling exact real-time dynamics solutions and quantum circuit implementations, thereby expanding the scope of classically simulable quantum many-body systems.

Contribution

It introduces a novel hidden fermionic framework for quantum spin chains, distinct from Jordan-Wigner, allowing exact dynamics calculations and quantum circuit constructions.

Findings

Exact solutions for real-time dynamics in spin chains

Construction of quantum circuits for simulation on quantum computers

Extension of classically simulable quantum many-body processes

Abstract

We consider quantum spin chains with a hidden free fermionic structure, distinct from the Jordan-Wigner transformation and its generalizations. We express selected local operators with the hidden fermions. This way we can exactly solve the real time dynamics in various physical scenarios, including the computation of selected dynamical two point functions, in continuous or discrete time. In the latter case we build a quantum circuit that can be implemented on a quantum computer. With this we extend the family of classically simulable quantum many-body processes.