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Journal of Optical Communications

Implementation of a polarization-encoded quantum CNOT gate

Debajyoti Samanta

Published Nov 8, 2022• 1 citation
Publisher

Abstract

Abstract Optics has been successfully used for data processing. The basic building blocks of quantum computers are the quantum gates. Here, a quantum CNOT gate is proposed. To implement the gate advantages of polarization-based encoding technique and optical Kerr material-based switching are utilized. CS2 can show this type of switching feature. An Nd-YAG laser source of 1.064 μm wavelength is used to implement the scheme. Intensity of the laser pulse should be of the order of 1018 W/m2 to excite the 2nd order nonlinearity of the isotropic nonlinear material.

DOI
10.1515/joc-2022-0015

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Abstract Optics has been successfully used for data processing. The basic building blocks of quantum computers are the quantum gates. Here, a quantum CNOT gate is proposed. To implement the gate advantages of polarization-based encoding technique and optical Kerr material-based switching are utilized. CS2 can show this type of switching feature. An Nd-YAG laser source of 1.064 μm wavelength is used to implement the scheme. Intensity of the laser pulse should be of the order of 1018 W/m2 to excite the 2nd order nonlinearity of the isotropic nonlinear material.
The design for an all optical XOR gate is proposed. The basic idea is to split the input beams and let them cancel or strengthen each other selectively or flip the encoded information based on their polarization properties. The information is encoded in terms of polarization of the beam. Polarization of a light beam is well understood hence the design should be feasible to implement. The truth table of the optical circuit is worked out and compared with the expected truth table. Then it is demonstrated that the design complies with the linear behavior of the XOR function. In the next section, based on a similar idea, the design of an all optical CNOT gate is proposed. The truth table for the gate is verified. Then, it is discussed how this approach can be used for Linear Optics Quantum Computation (LOQC). It is shown that with a Hadamard gate and a rotation gate, the CNOT gate makes up a universal set of quantum gates based on linear optics. This novel approach requires no additional power supply, extra input beam or ancilla photon to operate. It also doesn't require the expensive and complex single photon source and detector. Only narrowband laser sources are required to operate these gates.
A new method based on quantum encoders is developed for implementing quantum computational gates, especially the CNOT gate. Photonic qubits are used where ∣0> and ∣1> represent horizontal ∣H> and vertical ∣V> polarized photons, respectively. By the use of polarizing beam splitters (PBSs) and entangled two-photon states in a certain experimental scheme, each input qubit state is copied, with a certain probability of success, into four equivalent input qubit states. The present method concentrates on the special case where the initial two-qubit state is separable. The CNOT gate (multiplied by 2) is decomposed into a summation of four unitary matrices each of dimension 4×4 and where each of these unitary matrices operates on a corresponding copy of the input two-qubit state. By adding the amplitudes of the four two-qubit states, which is obtained in a decoding interference experiment, the CNOT gate is implemented.
Femtosecond lasers enable three-dimensional direct writing of waveguides inside bulk transparent materials and have been applied to the fabrication of integrated photonic quantum logic gates. Up to now, the controlled-NOT (CNOT) gate, the key two-qubit quantum gate, has been realized only for polarization-encoded photonic qubits, which consists of three partially polarizing directional couplers (DCs) or two polarizing DCs. In this work, we demonstrate the femtosecond laser direct writing of a path-encoded CNOT gate formed by five DCs all with precisely controlled splitting ratios and stable symmetric phases inside glass for the first time. The quantum CNOT operation is performed using single photons with an average fidelity higher than 0.98. This provides a novel venue for the fabrication of large-scale 3D quantum computation circuits based on femtosecond laser writing.
Unlike classical digital computers in which a bit can represent either 1 or 0 at any time, quantum computers use a two-level system, i.e., a qubit, to implement logical operations based on quantum mechanical laws, which can represent both values at once. Owing to the superposition property of qubits, quantum computers have natural parallel processing advantages and thus have potential to exceed the computational efficiency of classical computers for particular tasks. Quantum logic gates are the generalization of classical logic gates in computational networks. It has been proved that two-qubit quantum gates together with one-qubit quantum gates are adequate for constructing networks with any possible quantum computational property. Directional couplers are the most critical elementsfor constructing the quantum gates. In recent years, photonic quantum technologies have emerged as a promising experimental platform for quantum computing. Single photons have robust noise resistance, long coherence time, high transmission speed and great compatibility with other systems. They can be easily manipulated and encoded in any of several degrees of freedom, for example, polarization, path, spatial mode or time bin. Optical waveguide technology enables the realizing of complex optical schemes comprised of many elements with desired scalability, stability and miniaturization. Femtosecond laser direct writing of waveguide has been adopted as a powerful tool for integrated quantum photonics with characteristics of rapidness, cost-effectiveness, mask-less and single-step process. In particular, it has the ability to build arbitrary three-dimensional circuits directly inside bulk materials, which is impossible to achieve with conventional lithography. In this article we review the femtosecond laser writing and quantum characterization of directional coupler and important one-qubit and two-qubit optical quantum logic gates, such as Hadamard gate, Pauli-X gate, controlled-NOT gate, and controlled-Phase gate. The qubits in these gates are usually encoded through optical paths or polarizations of photons. The key to the realization of polarization-encoded one-qubit gates is to achieve flexible wave-plate operations, which is described in detail. Controlled-NOT gate and controlled-phase gate are the most crucial two-qubit gates in the linear optics computation and sometimes they can be converted into each other by adding some one-qubit gates or special superposition states. Many different kinds of waveguide circuits have been used to implement these two-qubit gates. The outlook and challenges for the femtosecond laser writing of three-qubit gates, such as Toffoli gate and Fredkin gate, are briefly introduced.