High-fidelity quantum state preparation using neighboring optimal control

TL;DR

This paper introduces a novel application of neighboring optimal control theory for high-fidelity, single-shot preparation of multi-qubit states, demonstrated by preparing Bell states with extremely low error probabilities.

Contribution

It applies neighboring optimal control formalism to quantum state preparation, achieving high fidelity in a single shot, which was previously used mainly for quantum gates.

Findings

Achieved error probability of ~10^{-6} for Bell state preparation.

Demonstrated the method's potential for fault-tolerant quantum state preparation.

Validated the approach with a proof-of-principle example.

Abstract

We present an approach to single-shot high-fidelity preparation of an $n$-qubit state based on neighboring optimal control theory. This represents a new application of the neighboring optimal control formalism which was originally developed to produce single-shot high-fidelity quantum gates. To illustrate the approach, and to provide a proof-of-principle, we use it to prepare the two qubit Bell state $|\beta_{01}\rangle = (1/\sqrt{2})\left[\, |01\rangle + |10\rangle\,\right]$ with an error probability $\epsilon\sim 10^{-6}$ ($10^{-5}$) for ideal (non-ideal) control. Using standard methods in the literature, these high-fidelity Bell states can be leveraged to fault-tolerantly prepare the logical state $|\overline{\beta}_{01}\rangle$.