Efficient variational simulation of non-trivial quantum states

TL;DR

This paper introduces a hybrid variational protocol for efficiently preparing complex quantum states, including GHZ, critical, and topologically ordered states, with linear scaling in system size, applicable to near-term quantum devices.

Contribution

It presents a novel hybrid quantum-classical variational method capable of preparing non-trivial quantum states with perfect fidelity and linear resource scaling.

Findings

Successfully prepares GHZ, critical, and topologically ordered states.

States that the protocol can prepare ground states across the entire phase diagram.

Demonstrates the utility of variational ans"atze for describing complex quantum states.

Abstract

We provide an efficient and general route for preparing non-trivial quantum states that are not adiabatically connected to unentangled product states. Our approach is a hybrid quantum-classical variational protocol that incorporates a feedback loop between a quantum simulator and a classical computer, and is experimentally realizable on near-term quantum devices of synthetic quantum systems. We find explicit protocols which prepare with perfect fidelities (i) the Greenberger-Horne-Zeilinger (GHZ) state, (ii) a quantum critical state, and (iii) a topologically ordered state, with $L$ variational parameters and physical runtimes $T$ that scale linearly with the system size $L$. We furthermore conjecture and support numerically that our protocol can prepare, with perfect fidelity and similar operational costs, the ground state of every point in the one dimensional transverse field Ising model phase diagram. Besides being practically useful, our results also illustrate the utility of such variational ans\"atze as good descriptions of non-trivial states of matter.