Quantum state preparation and one qubit logic from third-order nonlinear interactions

TL;DR

This paper proposes a method for preparing and manipulating path-like temporal-mode qubits using third-order nonlinear interactions, enabling high-fidelity state preparation and arbitrary single-qubit rotations with feasible experimental setups.

Contribution

It introduces a novel approach to generate and control TM qubits via third-order nonlinear interactions, including a method for implementing any Pauli gate.

Findings

Achieved qubit fidelities close to one.

Demonstrated linear evolution of TMs within the medium.

Provided a feasible experimental scheme for arbitrary qubit transformations.

Abstract

We present a study on preparing and manipulating path-like temporal-mode (TM) qubits based on third-order nonlinear interactions. Specifically, we consider the process of frequency conversion via difference frequency generation. To prepare a qubit, we aim to use Gaussian input states to a nonlinear waveguide. The coupling between the input state and a specific TM is maximized, obtaining qubits prepared with fidelities close to one. TMs evolve linearly within the medium; therefore, it is possible to define rotations around any axis contained in the $xy$ plane, allowing spanning the full Bloch sphere in two steps. Particularly, we present a method to obtain any of the Pauli quantum gates by varying geometric or user-accessible parameters in a given experimental configuration. Our study allows for experimentally feasible proposals capable of controllable arbitrary qubit transformations.