Related papers: Models of Quantum Turing machines
Quantum computers are important examples of processes whose evolution can be described in terms of iterations of single step operators or their adjoints. Based on this, Hamiltonian evolution of processes with associated step operators $T$…
Schr\"odinger's equation serves as a fundamental component in characterizing quantum systems, wherein both quantum state tomography and Hamiltonian learning are instrumental in comprehending and interpreting quantum systems. While numerous…
This paper is devoted to the construction of what we will call {\em exactly solvable models}, i.e. of quantum mechanical systems described by an Hamiltonian $H$ whose eigenvalues and eigenvectors can be explicitly constructed out of some…
Deutsch, Feynman, and Manin viewed quantum computing as a kind of universal physical simulation procedure. Much of the writing about quantum Turing machines has shown how these machines can simulate an arbitrary unitary transformation on a…
This paper extends work done to date on quantum computation by associating potentials with different types of computation steps. Quantum Turing machine Hamiltonians, generalized to include potentials, correspond to sums over tight binding…
Quantum walks, both discrete and continuous, serve as fundamental tools in quantum information processing with diverse applications. This work introduces a hybrid quantum walk model that integrates the coin mechanism of discrete walks with…
An algorithm for quantum computing Hamiltonian cycles of simple, cubic, bipartite graphs is discussed. It is shown that it is possible to evolve a quantum computer into an entanglement of states which map onto the set of all possible paths…
We give background material and some details of calculations for two recent papers [1,2] where we derived a path integral representation of the transition element for supersymmetric and nonsupersymmetric nonlinear sigma models in one…
This paper is an introduction to diagrammatic methods for representing quantum processes and quantum computing. We review basic notions for quantum information and quantum computing. We discuss topological diagrams and some issues about…
We introduce evolved quantum Boltzmann machines as a variational ansatz for quantum optimization and learning tasks. Given two parameterized Hamiltonians $G(\theta)$ and $H(\phi)$, an evolved quantum Boltzmann machine consists of preparing…
Quantum process tomography conventionally uses a multitude of initial quantum states and then performs state tomography on the process output. Here we propose and study an alternative approach which requires only a single (or few) known…
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…
A quantum walk places a traverser into a superposition of both graph location and traversal "spin." The walk is defined by an initial condition, an evolution determined by a unitary coin/shift-operator, and a measurement based on the…
Quantum computing is concerned with computer technology based on the principles of quantum mechanics, with operations performed at the quantum level. Quantum computational models make it possible to analyze the resources required for…
Foundations of the theory of quantum Turing machines are investigated. The protocol for the preparation and the measurement of quantum Turing machines is discussed. The local transition functions are characterized for fully general quantum…
According to Deutsch, a universal quantum Turing machine (UQTM) is able to perform, in repeating a fixed unitary transformation on the total system, an arbitrary unitary transformation on an arbitrary data state, by including a program as…
Most modern classical processors support so-called von Neumann architecture with program and data registers. In present work is revisited similar approach to models of quantum processors. Deterministic programmable quantum gate arrays are…
The practical use of non-Hermitian (i.e., typically, PT-symmetric) phenomenological quantum Hamiltonians is discussed as requiring an explicit reconstruction of the {\em ad hoc} Hilbert-space metrics which would render the time-evolution…
Quantum computers will work by evolving a high tensor power of a small (e.g. two) dimensional Hilbert space by local gates, which can be implemented by applying a local Hamiltonian H for a time t. In contrast to this quantum engineering,…
The Hamiltonian cycle problem (HCP), which is an NP-complete problem, consists of having a graph G with n nodes and m edges and finding the path that connects each node exactly once. In this paper we compare some algorithms to solve a…