The stabilizer ground state and applications to quantum simulation

TL;DR

This paper introduces the optimal stabilizer ground state concept for quantum simulation, enabling efficient Clifford circuit approximations of ground states with high fidelity, and demonstrates a scalable, resource-efficient method for its evaluation and refinement.

Contribution

It defines the optimal stabilizer ground state, proposes a genetic algorithm for its identification, and shows its application in efficient quantum simulation techniques.

Findings

The method achieves high fidelity in approximating true ground states.

The resource cost scales polynomially with system size.

The approach demonstrates potential quantum advantage in simulation tasks.

Abstract

The stabilizer ground state is defined is the lowest energy stabilizer state with respect to a given Hamiltonian. In many cases it is highly degenerate and does not give a unique stabilizer state. We define the optimal stabilizer ground state as the stabilizer ground state which has the highest fidelity with the true ground state. This is useful in quantum simulation contexts as it allows for a Clifford circuit approximation of a ground state that can be further refined towards the true ground state. We show how the optimal stabilizer ground state may be evaluated. We show applications of this state in the context of measurement-based deterministic imaginary time evolution (MITE), which converges to the ground state with high efficiency. By classically selecting the optimal stabilizer generator group and employing the stabilizer tableaux formalism, the method prepares the corresponding stabilizer ground state with maximal fidelity. The identification and refinement of this generator group are performed using a genetic algorithm tailored to the structure of the target Hamiltonian. The complexity analysis further demonstrates that algorithm's quantum resource cost scales polynomially with system size, highlighting its high efficiency and potential quantum advantage.