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Микроэлектроника

CNOT Quantum Gate Based on Spatial Photonic Qubits Under Resonant Electro-Optical Control

Alexander V. Tsukanov, I. Yu. Kateev

Published Nov 13, 2024• 0 citations
Publisher

Abstract

A theoretical model of a quantum node that implements the two-qubit CNOT operation with use of photonic qubits with spatial encoding is considered. Each qubit is represented by a pair of modes supporting an arbitrary superposition of single-photon states. The active element of the node is a single or double quantum dot with a tunable frequency, which coherently exchanges an energy quantum with the modes. The spectral characteristics of the quantum node elements are simulated. The probability of implementation of a controlled inversion of the qubit state is calculated depending on the system parameters.

DOI
10.31857/s0544126924040022

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A theoretical model of a quantum node that implements the two-qubit CNOT operation with use of photonic qubits with spatial encoding is considered. Each qubit is represented by a pair of modes supporting an arbitrary superposition of single-photon states. The active element of the node is a single or double quantum dot with a tunable frequency, which coherently exchanges an energy quantum with the modes. The spectral characteristics of the quantum node elements are simulated. The probability of implementation of a controlled inversion of the qubit state is calculated depending on the system parameters.
Abstract We consider a theoretical model of a quantum node that implements a two-qubit controlled-NOT (CNOT) operation on photonic qubits with spatial encoding. Each of the qubits is represented by a pair of modes that support an arbitrary superposition of single-photon states. The active element of the node is a single or double quantum dot (QD) with a tunable frequency, coherently exchanging an energy quantum with the modes. The spectral characteristics of the elements of the quantum node are simulated. The probability of performing a controlled inversion of the qubit state is calculated, depending on the system parameters.
To date, all work concerning the construction of quantum logic gates, an essential part of quantum computing, has focused on operating in one degree of freedom (DOF) for quantum systems. Here, we investigate the possibility of achieving scalable photonic quantum computing based on two DOFs for quantum systems. We construct a deterministic hyper-controlled-not (hyper-CNOT) gate operating in both the spatial mode and polarization DOFs for a photon pair simultaneously, using the giant optical Faraday rotation induced by a single-electron spin in a quantum dot inside a one-side optical microcavity as a result of cavity quantum electrodynamics. With this hyper-CNOT gate and linear optical elements, two-photon four-qubit cluster entangled states can be prepared and analyzed, which give an application to manipulate more information with less resources. We analyze the experimental feasibility of this hyper-CNOT gate and show that it can be implemented with current technology.
Generating strong interactions between single quanta of light and matter is central to quantum information science, and a key component of quantum computers and long-distance quantum networks. In quantum information processing, these interactions are required to create elementary logic operations (quantum gates) between stationary matter quantum bits (qubits) and photonic qubits that can be transmitted over long distances. Efficient quantum gates between photonic and matter qubits are a crucial enabler for a broad range of applications that include robust quantum networks, nondestructive quantum measurements, and strong photon-photon interactions. So far these qubit-photon gates have been achieved using single atoms and at microwave frequencies in circuit QED systems. Their implementation with solidstate quantum emitters, however, has remained a difficult challenge. We demonstrate that the qubit state of a photon can be controlled by a single solid-state qubit composed of a quantum dot (QD) strongly coupled to an optical nanocavity. We show that the QD acts as a coherently controllable qubit system that conditionally flips the polarization of a photon reflected from the cavity mode on picosecond timescales. This operation implements a controlled NOT (cNOT) logic gate between the QD and the incident photon, which is a universal quantum operation that can serve as a general light-matter interface for remote entanglements and quantum computations. Our results represent an important step towards an all solid-state implementation of quantum networks and quantum computers, and provide a versatile approach for controlling and probing interactions between a photon and a single quantum emitter on ultra-fast timescales.
We report on the theoretical design and simulation of a photonic quantum circuit that operates as a single-photon, two-qubit swap gate. In this approach, the circuit is implemented in Titanium indiffused LiNbO3 channel waveguides, and polarization and spatial encoding are utilized to realize the qubits. A set of basic components comprising a dual periodically poled waveguide for two simultaneous Type-0 and Type-I non-linear interactions, as well as the passive routing and active electro-optically controllable devices, are the main building blocks in this circuit. Simulations are carried out by making use of the numerical beam propagation method incorporated within RSoft program package.
We consider one- and two-qubit operations on charge qubits that represent double quantum dots with one electron in each of them. The dots are formed inside a high-Q semiconductor cavity (disk, toroidal, or spherical) in the antinodes of one of its optical eigenmodes; the frequencies of the transitions between the ground (logic) and excited (auxiliary) states of the discrete electron spectrum in quantum dots are close to the frequency of this mode. The precise tuning of the transition frequency is performed by applying an electric potential on the qubit control gate. Within the model of qubits coherently interacting with a cavity quantum field, a few methods for controlling their states are developed. In particular, we propose different variants for implementing two-qubit CNOT and CZ gates and generating qubit entangled states. By the example of a micro-disk cavity, we calculate the operating characteristics that ensure a high rate of quantum gate implementation.
We describe an optical implementation of a CNOT gate in which the control qubit is the polarization of a single photon and the target qubit is the spatial parity of the same photon. The gate is implemented with a polarization- sensitive spatial light modulator. We characterize the operation of the gate using quantum process tomography and the spatial parity is analyzed with a modified Mach-Zehnder interferometer. We also demonstrate the CNOT-gate operation with arbitrary rotation of the target qubit and discuss the possibility of implementing multi-qubit CNOT gates using the same approach.