Quantum computing is a paradigm of computing using physical systems, which operate according to quantum mechanical principles. Since 2017, functioning quantum processing units with limited capabilities are available on the cloud. There are two models of quantum computing in the literature: discrete variable and continuous variable models. The discrete variable model is an extension of the binary logic of digital computing with quantum bits |0⟩ and |1⟩ . In the continuous variable model, the quantum state space is infinite-dimensional and the quantum state is expressed with an infinite number of basis elements. In the physical implementation of quantum computing, however, the quantized energy levels of the electromagnetic field come in multiple values, naturally realizing the multi-valued logic of computing. Hence, to implement the discrete variable model (binary logic) of quantum computing, the temperature control is needed to restrict the energy levels to the lowest two to express the binary quantum states |0⟩ and |1⟩. The physical realization of the continuous variable model naturally implements the multi-valued logic of computing because any physical system always has the highest level of quantized energy observed i.e., the quantum state space is always finite dimensional. In 2001, Knill, Laflamme, and Milburn proved that linear optics realizes universal quantum computing in the qubit-based model. Optical quantum computers by Xanadu, under the phase space representation of quantum optics, naturally realizes the multi-valued logic of quantum computing at room temperature. Optical quantum computers use optical signals, which are most compatible with the fiber optics communication network. They are easily fabricable for mass production, robust to noise, and have low latency. Optical quantum computing provides flexibility to the users for determining the dimension of the computational space for each instance of computation. Additionally, nonlinear quantum optical effects are incorporated as nonlinear quantum gates. That flexibility of user-defined dimension of the computational space and availability of nonlinear gates lead to a faithful implementation of quantum neural networks in optical quantum computing. This dissertation provides a full description of a multi-class data quantum classifier on ten classes of the MNIST dataset. In this dissertation, I provide the background information of optical quantum computing as an ideal candidate material for building the future classical-quantum hybrid internet for its numerous benefits, among which the compatibility with the existing communications/computing infrastructure is a main one. I also show that optical quantum computing can be a hardware platform for realizing the multi- valued logic
Quantum computing is a paradigm of computing using physical systems, which operate according to quantum mechanical principles. Since 2017, functioning quantum processing units with limited capabilities are available on the cloud. There are two models of quantum computing in the literature: discrete variable and continuous variable models. The discrete variable model is an extension of the binary logic of digital computing with quantum bits |0⟩ and |1⟩ . In the continuous variable model, the quantum state space is infinite-dimensional and the quantum state is expressed with an infinite number of basis elements. In the physical implementation of quantum computing, however, the quantized energy levels of the electromagnetic field come in multiple values, naturally realizing the multi-valued logic of computing. Hence, to implement the discrete variable model (binary logic) of quantum computing, the temperature control is needed to restrict the energy levels to the lowest two to express the binary quantum states |0⟩ and |1⟩. The physical realization of the continuous variable model naturally implements the multi-valued logic of computing because any physical system always has the highest level of quantized energy observed i.e., the quantum state space is always finite dimensional. In 2001, Knill, Laflamme, and Milburn proved that linear optics realizes universal quantum computing in the qubit-based model. Optical quantum computers by Xanadu, under the phase space representation of quantum optics, naturally realizes the multi-valued logic of quantum computing at room temperature. Optical quantum computers use optical signals, which are most compatible with the fiber optics communication network. They are easily fabricable for mass production, robust to noise, and have low latency. Optical quantum computing provides flexibility to the users for determining the dimension of the computational space for each instance of computation. Additionally, nonlinear quantum optical effects are incorporated as nonlinear quantum gates. That flexibility of user-defined dimension of the computational space and availability of nonlinear gates lead to a faithful implementation of quantum neural networks in optical quantum computing. This dissertation provides a full description of a multi-class data quantum classifier on ten classes of the MNIST dataset. In this dissertation, I provide the background information of optical quantum computing as an ideal candidate material for building the future classical-quantum hybrid internet for its numerous benefits, among which the compatibility with the existing communications/computing infrastructure is a main one. I also show that optical quantum computing can be a hardware platform for realizing the multi- valued logic
This thesis covers several topics in optical quantum computation. A quantum computer is a computational device which is able to manipulate information by performing unitary operations on some physical system whose state can be described as a vector (or mixture of vectors) in a Hilbert space. The basic unit of information, called the qubit, is considered to be a system with two orthogonal states, which are assigned logical values of 0 and 1. Photons make excellent candidates to serve as qubits. They have little interactions with the environment. Many operations can be performed using very simple linear optical devices such as beam splitters and phase shifters. Photons can easily be processed through circuit-like networks. Operations can be performed in very short times. Photons are ideally suited for the long-distance communication of quantum information. The great difficulty in constructing an optical quantum computer is that photons naturally interact weakly with one another. This thesis first gives a brief review of two early approaches to optical quantum computation. It will describe how any discrete unitary operation can be performed using a single photon and a network of beam splitters, and how the Kerr effect can be used to construct a two photon logic gate. Second, this work provides a thorough introduction to the linear optical quantum computer developed by Knill, Laflamme, and Milburn. It then presents this author's results on the reliability of this scheme when implemented using imperfect photon detectors. This author finds that quantum computers of this sort cannot be built using current technology. Third, this dissertation describes a method for constructing a linear optical quantum computer using nearly orthogonal coherent states of light as the qubits. It shows how a universal set of logic operations can be performed, including calculations of the fidelity with which these operations may be accomplished. It discusses methods for reducing and correcting errors and recovering from failed operations. Lastly it describes an analysis of the long distance transmission of the coherent state qubits and shows how transmission errors can be corrected.
In this Near Intermediate-Scale Quantum era, there are two types of near-term quantum devices available on cloud: superconducting quantum processing units (QPUs) based on the discrete variable model and linear optics (photonics) QPUs based on the continuous variable (CV) model. Quantum computation in the discrete variable model is performed in a finite dimensional quantum state space and the CV model in an infinite dimensional space. In implementing quantum algorithms, the CV model offers more quantum gates that are not available in the discrete variable model. CV-based photonic quantum computers provide additional flexibility of controlling the length of the output vectors of quantum circuits, using different methods of measurement and the notion of cutoff dimension.
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.
If suitable quantum optical interactions were available, transforming the field mode operators in a nonlinear fashion, the all-photonics platform could be one of the strongest contenders for realizing a quantum computer. While single-photon qubits may be processed directly, “brighter” logical qubits may be embedded in individual oscillator modes, using so-called bosonic codes, for an in-principle fault-tolerant processing. In this paper, we show how elements of all-optical, universal, and fault-tolerant quantum computation can be implemented using only beam splitters together with single-mode cubic phase gates in reasonable numbers, and possibly off-line squeezed-state or single-photon resources. Our approach is based on a decomposition technique combining exact gate decompositions and approximate Trotterization. This allows for efficient decompositions of certain nonlinear continuous-variable multimode gates into the elementary gates, where the few cubic gates needed may even be weak or all identical, thus facilitating potential experiments. The final gate operations include two-mode controlled phase rotation and three-mode Rabi-type Hamiltonian gates, which are shown to be employable for realizing high-fidelity single-photon two-qubit entangling gates or creating high-quality Gottesman-Kitaev-Preskill states. We expect our method to be of general use with various applications, including those that rely on quartic Kerr-type interactions. Published by the American Physical Society 2024
Optical photons present many interesting aspects in the context of the research for suitable physical representations of quantum bits. Photons are chargeless particles, and do not interact strongly with each other, or even with most matter. They can be guided along long distances with low loss in optical fibers, delayed efficiently using phase shifters, and combined easily using beamsplitters. Photons exhibit typical quantum phenomena, such as the interference produced in two-slit experiments. Furthermore, in principle, photons can be made interact with each other if carefully handled. There are many practical problems with this approach; nevertheless it presents, beyond what has already been noted, an appealing conceptual simplicity.The purpose of this work is to present - at least, in its fundamental principles - a set of optical photon quantum gates that is universal for quantum computation. To do so, we begin by gathering the necessary mathematical and physical tools. We discuss canonical quantization for the electromagnetic field, and we formalize in an abstract context the characteristic properties of every realization of the Fock canonical commutation relationships (CCR). We analize the class of the spaces where it is possible to give such a realization, and that naturally lend themselves to host the physical model of our interest. Once acquired these bases, we turn ourselves to a particular optic system, the Mach-Zehnder interferometer, and we study the general properties of this system and of its essential constituents. At this point we choose a particular encoding of quantum bit and we look at the optical devices just discussed as elements of a quantum circuit. We then discuss the fundamental ideas that may guide the implementation of some important quantum gates: Hadamard gate, π/8 gate and controlled-NOT. We conclude by showing that these three quantum gates form a universal set of gates for quantum computation.
Optical photons present many interesting aspects in the context of the research for suitable physical representations of quantum bits. Photons are chargeless particles, and do not interact strongly with each other, or even with most matter. They can be guided along long distances with low loss in optical fibers, delayed efficiently using phase shifters, and combined easily using beamsplitters. Photons exhibit typical quantum phenomena, such as the interference produced in two-slit experiments. Furthermore, in principle, photons can be made interact with each other if carefully handled. There are many practical problems with this approach; nevertheless it presents, beyond what has already been noted, an appealing conceptual simplicity.The purpose of this work is to present - at least, in its fundamental principles - a set of optical photon quantum gates that is universal for quantum computation. To do so, we begin by gathering the necessary mathematical and physical tools. We discuss canonical quantization for the electromagnetic field, and we formalize in an abstract context the characteristic properties of every realization of the Fock canonical commutation relationships (CCR). We analize the class of the spaces where it is possible to give such a realization, and that naturally lend themselves to host the physical model of our interest. Once acquired these bases, we turn ourselves to a particular optic system, the Mach-Zehnder interferometer, and we study the general properties of this system and of its essential constituents. At this point we choose a particular encoding of quantum bit and we look at the optical devices just discussed as elements of a quantum circuit. We then discuss the fundamental ideas that may guide the implementation of some important quantum gates: Hadamard gate, π/8 gate and controlled-NOT. We conclude by showing that these three quantum gates form a universal set of gates for quantum computation.