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A Programmable Single-Qubit Quantum Gate

A. L. Aguayo-Alvarado, Francisco A. Domínguez-Serna, W. De La Cruz, Karina Garay-Palmett

Published Jan 1, 2023• 0 citations
Publisher

Abstract

We present a design for an integrated single-qubit quantum gate based on the third order nonlinear process of difference frequency generation. A theoretical model is presented for the transformation of the qubit with device-external parameters.
DOI
10.1364/cleo_at.2023.jth2a.28

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We present a novel proposal for the implementation of temporal-modes quantum gates based on the third-order nonlinear process of difference frequency generation in an integrated photonic circuit, which allows switching from one Pauli gate to another by tuning the phase difference between the two pump pulses (in case of the σx\sigma_{x}σx​ and σy\sigma_{y}σy​ Pauli gates) and between the two states comprising the basis of single temporal-modes qubits (in the case of the σz\sigma_{z}σz​ Pauli gate). We demonstrate that our proposal enables the preparation of any single temporal-mode qubit and rotations on the Bloch sphere by changing externally controllable parameters. We also analyze the effects of fabrication errors on the predicted quantum gate fidelity, finding that even if some waveguide parameter deviates from the design, slight tuning of pump wavelengths can lead to recovering high fidelity values.
Photons are preferable carriers of quantum information having little interaction with environment. Most crucial elements of photonic quantum information processing are two qubit gates. Although usage of controlled-not gates for photonic two qubit operations is common, controlled-phase gates provide more versatile utilization by enabling desired phase difference to be generated between qubits. Ability to determine the phase after fabrication yields extra benefit. We demonstrate a design of integrated photonic controlled-phase gate with programmable phase difference. We used a unique and practical polarization rotator which is ring resonator with a single notch.
We present a study on preparing and manipulating 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 x y 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 when time-ordering effects are ignored. Our study allows for experimentally feasible proposals capable of controllable arbitrary qubit transformations.
This work presents a feasible design of an integrated photonic circuit performing as a device for single-qubit preparation and rotations through the third-order nonlinear process of difference frequency generation (DFG) and defined in the temporal mode basis. The first stage of our circuit includes the generation of heralded single photons by spontaneous four-wave mixing in a micro-ring cavity engineered for delivering a single-photon state in a unique temporal mode. The second stage comprises the implementation of DFG in a spiral waveguide with controlled dispersion properties for reaching color qubit preparation fidelity close to unity. We present the generalized rotation operator related to the DFG process, a methodology for the device design, and qubit preparation fidelity results as a function of user-accessible parameters.