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Journal of the Optical Society of America B

Programmable color qubit quantum gates

Ana Aguayo Alvarado, Francisco A. Domínguez-Serna, Ferney Castro-Simanca, W. de la Cruz, Karina Garay-Palmett

Published Dec 23, 2024• 2 citations

Abstract

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 $\sigma_{x}$ and $\sigma_{y}$ Pauli gates) and between the two states comprising the basis of single temporal-modes qubits (in the case of the $\sigma_{z}$ 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.

DOI: 10.1364/josab.542468

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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

\sigma_{x}

and

\sigma_{y}

Pauli gates) and between the two states comprising the basis of single temporal-modes qubits (in the case of the

\sigma_{z}

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.

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.

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 propose a protocol for a two-qubit quantum phase gate based upon the reflection of photon pulses from a quantum dot in a cavity. Depending on the state of the quantum dot the reflected photons acquire a conditional phase shift. The key ingredient is the ultrafast control of the quantum dot energies by electric fields, which allows for tuning the exciton and biexciton successively into resonance with the cavity mode. The complete dynamics of the gate are simulated, revealing a fidelity of about 0.9. The proposed scheme uses position coding and is therefore well suited to the implementation in an integrated photonic quantum processor.