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AIP conference proceedings

Optically simulated universal quantum computation

Diego Francisco, Silvia Adriana Ledesma, Niklaus Ursus Wetter, Jaime Frejlich

Published Jan 1, 2008• 0 citations
Publisher

Abstract

Recently, classical optics based systems to emulate quantum information processing have been proposed. The analogy is based on the possibility of encoding a quantum state of a system with a 2N‐dimensional Hilbert space as an image in the input of an optical system. The probability amplitude of each state of a certain basis is associated with the complex amplitude of the electromagnetic field in a given slice of the laser wavefront. Temporal evolution is represented as the change of the complex amplitude of the field when the wavefront pass through a certain optical arrangement. Different modules that represent universal gates for quantum computation have been implemented. For instance, unitary operations acting on the qbits space (or U(2) gates) are represented by means of two phase plates, two spherical lenses and a phase grating in a typical image processing set up. In this work, we present CNOT gates which are emulated by means of a cube prism that splits a pair of adjacent rays incoming from the input image. As an example of application, we present an optical module that can be used to simulate the quantum teleportation process. We also show experimental results that illustrate the validity of the analogy. Although the experimental results obtained are promising and show the capability of the system for simulate the real quantum process, we must take into account that any classical simulation of quantum phenomena, has as fundamental limitation the impossibility of representing non local entanglement. In this classical context, quantum teleportation has only an illustrative interpretation.

DOI
10.1063/1.2926791

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Recently, classical optics based systems to emulate quantum information processing have been proposed. The analogy is based on the possibility of encoding a quantum state of a system with a 2N‐dimensional Hilbert space as an image in the input of an optical system. The probability amplitude of each state of a certain basis is associated with the complex amplitude of the electromagnetic field in a given slice of the laser wavefront. Temporal evolution is represented as the change of the complex amplitude of the field when the wavefront pass through a certain optical arrangement. Different modules that represent universal gates for quantum computation have been implemented. For instance, unitary operations acting on the qbits space (or U(2) gates) are represented by means of two phase plates, two spherical lenses and a phase grating in a typical image processing set up. In this work, we present CNOT gates which are emulated by means of a cube prism that splits a pair of adjacent rays incoming from the input image. As an example of application, we present an optical module that can be used to simulate the quantum teleportation process. We also show experimental results that illustrate the validity of the analogy. Although the experimental results obtained are promising and show the capability of the system for simulate the real quantum process, we must take into account that any classical simulation of quantum phenomena, has as fundamental limitation the impossibility of representing non local entanglement. In this classical context, quantum teleportation has only an illustrative interpretation.
A classical optics setup to simulate the quantum teleportation process is presented. The analogy is based on the possibility of encoding a quantum state of a system with a 2N-dimensional Hilbert space as an image in the input of an optical system. The probability amplitude of each state of a basis is associated with the complex amplitude of the electromagnetic field in a given region of the laser wavefront. Temporal evolutions are represented as changes of the complex amplitude of the field when the wavefront is modified by different optical elements. The classical optics representation of quantum state as images and of universal quantum gates as optical processors is shown. The design and operation of an optical module that is used to simulate the quantum teleportation process are discussed. Experimental results where the teleportation of a one qbit state is simulated are shown.
We present an optical module to simulate one step of a quantum walk algorithm. The quantum state of a system with a 2N2N2N-dimensional Hilbert space is encoded in the spatial distribution of the amplitude of the electromagnetic field in a plane. In such spatial encoding, the probability amplitude of each state of a basis is associated with the complex electromagnetic amplitude in a given slice of the laser wave front. We discuss the design and operation of an optical module that is used to implement one step of a quantum walk algorithm. Using this module, composed by standard optical elements, the evolution of the quantum state corresponds to the application of a Hadamard gate on a single qubit (representing the two-dimensional quantum coin) followed by a displacement of the NNN-dimensional quantum walker conditioned on the state of the coin. We show the actual implementation of the method and discuss its characteristics and limitations.
Abstract Quantum computing has attracted much attention in recent decades, since it is believed to solve certain problems substantially faster than traditional computing methods. Theoretically, such an advance can be obtained by networks of the quantum operators in universal gate sets, one famous example of which is formed by quantum Control‐not gate and single qubit gates. However, realizing a device that performs practical quantum computing is tricky. This is because it requires a scalable qubit system with long coherence time and good controls, which is harsh for most current platforms. Here, it is demonstrated that the information process based on a relatively stable system—classical optical system, can be considered as an analogy of universal quantum computing. By encoding the information via the polarization state of classical beams, the optical computing elements that correspond to the universal gate set are presented and their combination for a general information process is theoretically illustrated. Taking the analogy of two‐qubit processor as an example, it is experimentally verified that the proposal works well. Considering the potential of optical system for reliable and low‐energy‐consuming computation, the results open a new way toward advanced information processing with high quality and efficiency.
This paper describes a novel approach to emulate a universal quantum computer with a wholly classical system, one that uses a signal of bounded duration and amplitude to represent an arbitrary quantum state. The signal may be of any modality (e.g. acoustic, electromagnetic, etc.) but this paper will focus on electronic signals. Individual qubits are represented by in-phase and quadrature sinusoidal signals, while unitary gate operations are performed using simple analog electronic circuit devices. In this manner, the Hilbert space structure of a multi-qubit quantum state, as well as a universal set of gate operations, may be fully emulated classically. Results from a programmable prototype system are presented and discussed.
In recent years, there has been heightened interest in quantum teleportation, which allows for the transfer of unknown quantum states over arbitrary distances. Quantum teleportation not only serves as an essential ingredient in long-distance quantum communication, but also provides enabling technologies for practical quantum computation. Of particular interest is the scheme proposed by D. Gottesman and I. L. Chuang [(1999) Nature 402:390-393], showing that quantum gates can be implemented by teleporting qubits with the help of some special entangled states. Therefore, the construction of a quantum computer can be simply based on some multiparticle entangled states, Bell-state measurements, and single-qubit operations. The feasibility of this scheme relaxes experimental constraints on realizing universal quantum computation. Using two different methods, we demonstrate the smallest nontrivial module in such a scheme--a teleportation-based quantum entangling gate for two different photonic qubits. One uses a high-fidelity six-photon interferometer to realize controlled-NOT gates, and the other uses four-photon hyperentanglement to realize controlled-Phase gates. The results clearly demonstrate the working principles and the entangling capability of the gates. Our experiment represents an important step toward the realization of practical quantum computers and could lead to many further applications in linear optics quantum information processing.
We present here a classical optics device based on an imaging architecture as an analogy of a quantum system where the violation of the Bell inequality can be evidenced. Quantum states are encoded using an electromagnetic wave modulated in amplitude and phase. Unitary operations involved in the measurement of the observables are simulated with the use of a coherent optical processor. The images obtained in the output of the process contain all the information about the possible outcomes of the joint measurement. By measuring the intensity distribution in the image plane we evaluate the mean values of the simulated observables. The obtained experimental results show how some correlations of Clauser-Horne-Shimony-Holt-type exceed the upper bound imposed by the local realism hypothesis as a consequence of the joint effect of entanglement and two-particle interference.