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Journal of Optical Communications

An All-Optical System for Implementing Integrated Hadamard-Pauli Quantum Logic

Baishali Sarkar, Sourangshu Mukhopadhyay

Published Jul 2, 2019• 6 citations
Publisher

Abstract

Abstract In quantum optical computing both of Pauli X, Y, Z gates and Hadamard gate are essential and important issues. Several proposals are given for addressing these issues. In this paper, the authors propose polarization encoded all-optical schemes which implement Hadamard logic, Pauli X, Pauli Y and Pauli Z gates followed by Hadamard logic gate separately. An integrated scheme is also proposed where three Pauli gates (X, Y and Z) followed by a single Hadamard gate is developed using polarization encoding mechanism. The outputs of the proposed systems follow the truth tables of the respective operations exactly. As the systems use the polarization character of light, so fully quantum optical operations with superfast speed are achieved.

DOI
10.1515/joc-2019-0093

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Abstract In quantum optical computing both of Pauli X, Y, Z gates and Hadamard gate are essential and important issues. Several proposals are given for addressing these issues. In this paper, the authors propose polarization encoded all-optical schemes which implement Hadamard logic, Pauli X, Pauli Y and Pauli Z gates followed by Hadamard logic gate separately. An integrated scheme is also proposed where three Pauli gates (X, Y and Z) followed by a single Hadamard gate is developed using polarization encoding mechanism. The outputs of the proposed systems follow the truth tables of the respective operations exactly. As the systems use the polarization character of light, so fully quantum optical operations with superfast speed are achieved.
Pauli‐Y type of quantum gate is a significant name in the logic family of quantum gates, as this gate deals with complex qubits. It has many significant applications in quantum computing. In this study, the authors propose a new method of generation of Pauli‐Y gate by the proper uses of optical polarisation encoding and phase encoding jointly. This quantum gate can be implemented by dibit and tribit mechanisms instead of single qubit system, where tribit‐based system deals with the high degree of error sensitivity.
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.
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.
Transverse modes of optical fields are proposed to be used as qubits for the implementation of quantum Hadamard gate. Mach-Zehnder Interferometer (MZI), phase shifter, y-junction beam splitters and other optical devices are utilized to realize a quantum Hadamard gate. The possibility of this encoding scheme was designed, simulated and verified through rigorous numerical analyses using the Beam propagation method. The proposed gate has the potential of being more compact and easily realizable than some other optical implementation proposals since it is based on planar light wave circuit technology and can be constructed very easily by using a Mach-Zehnder Interferometer. The Results proved that the design is able to perform the required Hadamard transformation and the conclusion was reached that the model was a successful implementation of a quantum Hadamard gate.