Quantum simulation of ferromagnetic Heisenberg model

TL;DR

This paper proposes two validation tests for quantum simulators implementing the ferromagnetic Heisenberg model, demonstrating their robustness and potential for experimental validation without error correction.

Contribution

It introduces novel protocols for validating quantum simulators of the ferromagnetic Heisenberg model using state transfer and state recovery techniques.

Findings

Tests are robust against parametric errors.

Protocols do not require error correction.

Applicable to large quantum simulators.

Abstract

Large quantum simulators, with sufficiently many qubits to be impossible to simulate classically, become hard to experimentally validate. We propose two tests of a quantum simulator with Heisenberg interaction in a linear chain of spins. In the first, we propagate half of a singlet state through a chain of spin with a ferromagnetic interaction and subsequently recover the state with an antiferromagnetic interaction. The antiferromagnetic interaction is intrinsic to the system while the ferromagnetic one can be simulated by a sequence of time-dependent controls of the antiferromagnetic interaction and Suzuki-Trotter approximations. In the second test, we use the same technique to transfer a spin singlet state from one end of a spin chain to the other. We show that the tests are robust against parametric errors in operation of the simulator and may be applicable even without error correction.