Related papers: Quantum logic as a sum over classical logic gates
Scholars have wondered for a long time whether quantum mechanics (QM) subtends a quantum concept of truth which originates quantum logic (QL) and is radically different from the classical (Tarskian) concept of truth. We show in this paper…
We consider classical and quantum mechanics related to an additional noncommutativity, symmetric in position and momentum coordinates. We show that such mechanical system can be transformed to the corresponding one which allows employment…
In this paper we show that there is a direct correspondence between quantum Boolean operations and certain forms of classical (non-quantum) logic known as Reed-Muller expansions. This allows us to readily convert Boolean circuits into their…
This work discusses simple examples how quantum systems are obtained as subsystems of classical statistical systems. For a single qubit with arbitrary Hamiltonian and for the quantum particle in a harmonic potential we provide explicitly…
The origin and nature of time in complex systems is explored using quantum (or 'Feynman') clocks and the signals produced by them. Networks of these clocks provide the basis for the evolution of complex systems. The general concept of…
We propose that neuromorphic computing can perform quantum operations. Spiking neurons in the active or silent states are connected to the two states of Ising spins. A quantum density matrix is constructed from the expectation values and…
It is straightforward to give a sum-over-paths expression for the transition amplitudes of a quantum circuit as long as the gates in the circuit are balanced, where to be balanced is to have all nonzero transition amplitudes of equal…
We present a quantum algorithm that additively approximates the value of a tensor network to a certain scale. When combined with existing results, this provides a complete problem for quantum computation. The result is a simple new way of…
The nature of quantum computation is discussed. It is argued that, in terms of the amount of information manipulated in a given time, quantum and classical computation are equally efficient. Quantum superposition does not permit quantum…
We propose a method for implementation of an universal set of one- and two-quantum-bit gates for quantum computation in the system of two coupled electrons with constant non-diagonal exchange interaction. Suppression of the exchange…
Simulation of quantum matters is a significant application of quantum computers. In contrast to the unitary operation which can be realized naturally on a quantum computer, the implementation of nonunitary operation, widely used in…
Systems of spin 1, such as triplet pairs of spin-1/2 fermions (like orthohydrogen nuclei) make useful three-terminal elements for quantum computation, and when interconnected by qubit equality relations are universal for quantum…
The development of quantum algorithms based on quantum versions of random walks is placed in the context of the emerging field of quantum computing. Constructing a suitable quantum version of a random walk is not trivial: pure quantum…
This is an exposition of some basic mathematical aspects of quantum logic gates. At first we established some general formulas for the case of arbitrary quantum gate A with unique restriction A^2=I. The explicit form of the generators and…
Nyquist-Shannon sampling theorem, instrumental in classical telecommunication technologies, is extended to quantum systems supporting a unitary representation of a finite group $G$. Two main ideas from the classical theory having natural…
Manin, Feynman, and Deutsch have viewed quantum computing as a kind of universal physical simulation procedure. Much of the writing about quantum logic circuits and quantum Turing machines has shown how these machines can simulate an…
The strongest evidence for superiority of quantum annealing on spin glass problems has come from comparing simulated quantum annealing using quantum Monte Carlo (QMC) methods to simulated classical annealing [G. Santoro et al., Science 295,…
A quantum unitary gate is realized in this paper by perturbing a free charged particle in a one-dimensional box with a time- and position-varying electric field. The perturbed Hamiltonian is composed of a free particle Hamiltonian plus a…
A hidden gauge theory structure of quantum mechanics which is invisible in its conventional formulation is uncovered. Quantum mechanics is shown to be equivalent to a certain Yang-Mills theory with an infinite-dimensional gauge group and a…
An elementary application of Algorithmic Complexity Theory to the polygonal approximations of curved billiards-integrable and chaotic-unveils the equivalence of this problem to the procedure of quantization of classical systems: the scaling…