Abstract In this paper, a novel method for the emulation of qutrit and ququart based quantum computers is proposed. The Hilbert space and Bloch sphere representations of qutrits are initially discussed, preceding the emulation of a single qutrit using a classical system. The signal representing the state of the quantum system is defined as the sum of quadrature and in-phase 2-dimensional space-varying signals, which represent the basis states of the quantum system. Focus is mainly conferred on the frequency-domain representation of the signal, due to an innate bijective mapping found between the dimensions in the Hilbert space and the frequencies of the signal. An m -qutrit addressing scheme is then proposed which is used in the application of quantum ternary gates and measurement operations. The proposed theory is then used to simulate a ternary version of the Deutsch-Jozsa algorithm on MATLAB. This paper also includes a section on the extension of the theory to the case of ququarts. It concludes with a brief introduction to a potential system for emulation, and lists algorithms that can be implemented on the proposed system.
Abstract In this paper, a novel method for the emulation of qutrit and ququart based quantum computers is proposed. The Hilbert space and Bloch sphere representations of qutrits are initially discussed, preceding the emulation of a single qutrit using a classical system. The signal representing the state of the quantum system is defined as the sum of quadrature and in-phase 2-dimensional space-varying signals, which represent the basis states of the quantum system. Focus is mainly conferred on the frequency-domain representation of the signal, due to an innate bijective mapping found between the dimensions in the Hilbert space and the frequencies of the signal. An m -qutrit addressing scheme is then proposed which is used in the application of quantum ternary gates and measurement operations. The proposed theory is then used to simulate a ternary version of the Deutsch-Jozsa algorithm on MATLAB. This paper also includes a section on the extension of the theory to the case of ququarts. It concludes with a brief introduction to a potential system for emulation, and lists algorithms that can be implemented on the proposed system.
Quantum computers provide a fundamentally new computing paradigm that promises to revolutionize our ability to solve broad classes of problems. Surprisingly, the basic mathematical structures of gate-based quantum computing, such as unitary operations on a finite-dimensional Hilbert space, are not unique to quantum systems but may be found in certain classical systems as well. Previously, it has been shown that one can represent an arbitrary multi-qubit quantum state in terms of classical analog signals using nested quadrature amplitude modulated signals. Furthermore, using digitally controlled analog electronics one may manipulate these signals to perform quantum gate operations and thereby execute quantum algorithms. The computational capacity of a single signal is, however, limited by the required bandwidth, which scales exponentially with the number of qubits when represented using frequency-based encoding. To overcome this limitation, we introduce a method to extend this approach to multiple parallel signals. Doing so allows a larger quantum state to be emulated with the same gate time required for processing frequency-encoded signals. In the proposed representation, each doubling of the number of signals corresponds to an additional qubit in the spatial domain. Single quit gate operations are similarly extended so as to operate on qubits represented using either frequency-based or spatial encoding schemes. Furthermore, we describe a method to perform gate operations between pairs of qubits represented using frequency or spatial encoding or between frequency-based and spatially encoded qubits. Finally, we describe how this approach may be extended to represent qubits in the time domain as well.
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.
Quantum computers can outperform classical computers in certain tasks. However, there are still many challenges to the current quantum computers such as decoherence and fault tolerance, and other drawbacks such as portability and accessibility. In this study, we circumvent these issues by realizing an analog quantum emulation device (AQED) where each qubit state is represented by a unique analog signal. It is possible to do this because previously it was shown that Hermitian operations on a Hilbert space are not unique to quantum systems and can also be applied to a basis of complex signals that form a Hilbert space. Orthogonality of the complex signal basis can be maintained by separating the signals into the frequency domain or the spatial domain. We study both these approaches and present a comparison. We finally realize the entire device on a UMC 180nm processing node and demonstrate the computational advantage of an AQED by emulating Grover's search algorithm (GSA) and Quantum Fourier Transform (QFT). We also present the equivalent quantum volume achieved by this device.
In this paper we present a novel approach to emulating a universal quantum computer with a 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 we focus our discussion here on electronic signals. Unitary gate operations are performed using analog electronic circuit devices, such as four-quadrant multipliers, operational amplifiers, and analog filters, although non-unitary operations may be performed as well. In this manner, the Hilbert space structure of the quantum state, as well as a universal set of gate operations, may be fully emulated classically. The required bandwidth scales exponentially with the number of qubits, however, thereby limiting the scalability of the approach, but the intrinsic parallelism, ease of construction, and classical robustness to decoherence may nevertheless lead to capabilities and efficiencies rivaling that of current high performance computers.
Quantum Image Processing is a recent highlight in the quantum computing field. All previous methods for representing the images as quantum states were defined using qubits. One Quantum Image Representation (QIR) method using qutrits is present in the literature. Inspired by the qubit methods and the higher state-space available for qutrits, multiple QIR methods using qutrits are worked out in this paper. The ternary quantum gates required for the representations are described, and then the implementation details for five qutrit-based QIR methods are given. All the methods have been simulated in software, and example circuits are provided.
We discuss a new approach to simulate quantum algorithms using classical probabilistic bits and circuits. Each qubit (a two-level quantum system) is initially mapped to a vector in an eight dimensional probability space (equivalently, to a classical random variable with eight probabilistic outcomes). The key idea in this mapping is to store both the amplitude and phase information of the complex coefficients that describe the qubit state in the probabilities. Due to the identical tensor product structure of combining multiple quantum systems as well as multiple probability spaces, n qubits are then mapped to a tensor product of n 8-dimensional probabilistic vectors (i.e., the Hilbert space of dimension 2n is mapped to a probability space of dimension 8n). After this initial mapping, we show how to implement the analogs of single-qubit and two-qubit gates in the probability space using correlation-inducing operations on these classical random variables. The key defining feature of both the mapping to the probability space and the transformations in this space (i.e., operations on the random variables) is that they are not linear, but instead affine. Using this architecture, the evolution of the 2n complex coefficients of the quantum system can be tracked in the joint fully-correlated probabilities of the polynomial number of random variables. We then give specific procedures for implementing (1) the Deutsch-Jozsa algorithm, and (2) the Quantum Fourier Transform in the probability space. Identical to the Quantum case, simulating the Quantum Fourier Transform in the probability space requires O(n) probabilistic bits and O(n2) (i.e., quadratic in the number of quantum bits) operations.