Nonlinear quantum gates for a Bose-Einstein condensate

TL;DR

This paper develops a rigorous framework for implementing quantum gates in Bose-Einstein condensates by solving nonlinear evolution equations, enabling high-contrast interferometry and quantum information processing in nonlinear quantum regimes.

Contribution

It introduces a novel method to construct quantum gates within nonlinear quantum mechanics, specifically tailored for Bose-Einstein condensates, expanding the paradigm of quantum interferometry and logic.

Findings

Feasible nonlinear Hadamard gates devised for BECs

High-contrast nonlinear Ramsey interferometry achieved

Framework extends quantum information processing to nonlinear regimes

Abstract

Quantum interferometry and quantum information processing have been proposed for Bose-Einstein condensates (BECs), but BECs are described in complicated ways such as using quantum field theory or using a nonlinear differential equation. Nonlinear quantum mechanics does not mesh well with the superposition principle at the heart of interferometry and quantum information processing but could be compatible. Thus, we develop a rigorous foundation for quantum gates, obtained by solving the equation for evolution, and then we employ this foundation, combined with quantum-control techniques and appropriate state-sampling techniques, to devise feasible nonlinear Hadamard gates and thereby feasible, i.e., high-contrast, nonlinear Ramsey interferometry. Our approach to BEC interferometry and quantum logic shifts the paradigm by enlarging to the case of nonlinear quantum mechanics, which we apply to the cases of BEC interferometry and quantum information processing.