Projection algorithm for state preparation on quantum computers

TL;DR

This paper introduces an efficient quantum state preparation method that isolates quantum numbers and energy levels using minimal auxiliary qubits, with exponential accuracy improvements over time, demonstrated on nuclear and spin models.

Contribution

The proposed projection algorithm efficiently prepares many-body states on quantum computers using a simple auxiliary qubit and time evolution, improving over previous methods.

Findings

Requires only one auxiliary qubit for state preparation.

Accuracy increases exponentially with evolution time.

Demonstrated on nuclear shell and Heisenberg models.

Abstract

We present an efficient method to prepare states of a many-body system on quantum hardware, first isolating individual quantum numbers and then using time evolution to isolate the energy. Our method in its simplest form requires only one additional auxiliary qubit. The total time evolved for an accurate solution is proportional to the ratio of the spectrum range of the trial state to the gap to the lowest excited state, and the accuracy increases exponentially with the time evolved. Isolating the quantum numbers is efficient because of the known eigenvalues, and increases the gap thus shortening the propagation time required. The success rate of the algorithm, or the probability of producing the desired state, is a simple function of measurement times and phases and is dominated by the square overlap of the original state to the desired state. We present examples from the nuclear shell model and the Heisenberg model. We compare this algorithm to previous algorithms for short evolution times and discuss potential further improvements.