We present a new implementation of quantum computation that treats quantum computers as a special type of Bayesian Network called a QuDot Net. QuDot Nets allow for the efficient representation of some qubit systems. Single qubit quantum gates can be implemented as edge transformations on QuDot Nets. The X, H, R(k), M and SWAP gates are discussed in detail and results show linear scaling as the number of qubits are increased. We show that measurement and semi-quantum control gates can be efficiently implemented using QuDot Nets and present results from a QuDot Net implementation of the terminal Quantum Fourier Transform. We show how QuDot Nets can implement coherent control gates using multi-digraphs by labelling parallel edges. Lastly, we discuss implications to quantum foundations if a classical implementation of quantum computation is realized.
We present a new implementation of quantum computation that treats quantum computers as a special type of Bayesian Network called a QuDot Net. QuDot Nets allow for the efficient representation of some qubit systems. Single qubit quantum gates can be implemented as edge transformations on QuDot Nets. The X, H, R(k), M and SWAP gates are discussed in detail and results show linear scaling as the number of qubits are increased. We show that measurement and semi-quantum control gates can be efficiently implemented using QuDot Nets and present results from a QuDot Net implementation of the terminal Quantum Fourier Transform. We show how QuDot Nets can implement coherent control gates using multi-digraphs by labelling parallel edges. Lastly, we discuss implications to quantum foundations if a classical implementation of quantum computation is realized.
We begin with a review of a well-known class of networks, Classical Bayesian (CB) nets (also called causal probabilistic nets by some). Given a situation which includes randomness, CB nets are used to calculate the probabilities of various hypotheses about the situation, conditioned on the available evidence. We introduce a new class of networks, which we call Quantum Bayesian (QB) nets, that generalize CB nets to the quantum mechanical regime. We explain how to use QB nets to calculate quantum mechanical conditional probabilities (in case of either sharp or fuzzy observations), and discuss the connection of QB nets to Feynman Path integrals. We give examples of QB nets that involve a single spin-[Formula: see text] particle passing through a configuration of two or three Stern—Gerlach magnets. For the examples given, we present the numerical values of various conditional probabilities, as calculated by a general computer program specially written for this purpose.
The tutorial introduces quantum computing to a general audience. It begins with the concept of qubit and its representation, followed by 1-qubit quantum gates and qubit measurement. It will then move on to 2-qubit states, entanglement, and 2-qubit gates. Switching gears, the tutorial will discuss quantum Fourier transforms, unitary transforms, and quantum arithmetic. Finally, we will go through a simple quantum algorithm and discuss solid-state implementations of networks of qubits, highlighting the challenges for reading and controlling them. We conclude with future perspectives.
We begin with a review of a well known class of networks, Classical Bayesian (CB) nets (also called causal probabilistic nets by some). Given a situation which includes randomness, CB nets are used to calculate the probabilities of various hypotheses about the situation, conditioned on the available evidence. We introduce a new class of networks, which we call Quantum Bayesian (QB) nets, that generalize CB nets to the quantum mechanical regime. We explain how to use QB nets to calculate quantum mechanical conditional probabilities (in case of either sharp or fuzzy observations), and discuss the connection of QB nets to Feynman Path integrals. We give examples of QB nets that involve a single spin-half particle passing through a configuration of two or three Stern-Gerlach magnets. For the examples given, we present the numerical values of various conditional probabilities, as calculated by a general computer program especially written for this purpose.
Qudit is a multi-level computational unit alternative to the conventional 2-level qubit. Compared to qubit, qudit provides a larger state space to store and process information, and thus can provide reduction of the circuit complexity, simplification of the experimental setup and enhancement of the algorithm efficiency. This review provides an overview of qudit-based quantum computing covering a variety of topics ranging from circuit building, algorithm design, to experimental methods. We first discuss the qudit gate universality and a variety of qudit gates including the pi/8 gate, the SWAP gate, and the multi-level-controlled gate. We then present the qudit version of several representative quantum algorithms including the Deutsch-Jozsa algorithm, the quantum Fourier transform, and the phase estimation algorithm. Finally we discuss various physical realizations for qudit computation such as the photonic platform, iron trap, and nuclear magnetic resonance.
Quantum computing and quantum information science are two recently discovered and rapidly growing fields of physics that show substantial promise in providing new and valuable technologies in the foreseeable future. Large-scale quantum computers, if ever realized experimentally, are likely to outperform their classical counterparts in a number of important computational tasks, the most important of which may be the accurate simulation of many-body quantum systems such as the ones encountered in physics, chemistry and life sciences. This thesis investigates the problem of controlling quantum systems for the purpose of performing quantum information processing tasks. The problem is approached from a theoretical and simulational viewpoint. The work contained here encompasses a range of levels of abstraction. Firstly, we discuss the decomposition of abstract multiqubit logic gates into sequences of simple elementary gates. Secondly, we study the local commutational properties of two-qubit gates using local gate invariants. Thirdly, we develop methods for the physical implementation of the elementary gates through the control of specific quantum systems, possibly in the presence of noise and decoherence. We present a new, almost optimal n-qubit gate decomposition based on the cosine-sine decomposition, which utilizes a likewise new intermediate quantum circuit structure we call a uniformly controlled gate. We then show how they can be used in constructing a general state transformation circuit. Both of the resulting circuits can be efficiently implemented using nearest-neighbor gates which makes their physical realization simpler. A local gate invariant is introduced which can be used to assess the suitability of two-qubit gates for serving as the entangling gate in elementary gate libraries. Finally, we develop numerical optimization methods for finding near-optimal control sequences for generating oneand two-qubit gates, both in closed quantum systems and in the presence of Markovian noise.
A quantum gate is the quantum analog of the classical logic gate of digital computers. It is a basic structural unit of a quantum circuit which operates on a small number of qubits to deliver a predefined output. A quantum circuit is a graphical representation of the sequence of the quantum gates used and the measurements performed in a quantum computation. Various quantum logic gates, namely, the Hadamard, T phase, NOT, Pauli-X, controlled NOT (CNOT), controlled-Z, SWAP and controlled phase gates as well as higher-level Toffoli and Fredkin gates are described. Conventions of reading quantum circuit diagrams are explained. Operation of a quantum full adder consisting of registers and gates is discussed, elaborating the role of the NOT gate, the sum calculation with CNOTgates and the carry C-out calculation with Toffoli gates. A primary tool used for performing arithmetic operations on a quantum computer is the quantum Fourier transform (QFT). The QFT adder and multiplier circuits are presented.