scholarly journals The matrix product representation for the q-VBS state of one-dimensional higher integer spin model

2010 ◽  
Vol 374 (31-32) ◽  
pp. 3112-3115 ◽  
Author(s):  
Kohei Motegi
Keyword(s):  
Spin Model ◽  
Matrix Product ◽  
Product Representation ◽  
One Dimensional ◽  
Integer Spin ◽  
The Matrix

scholarly journals Noise in one-dimensional measurement-based quantum computing

2017 ◽  
Vol 17 (15&16) ◽  
pp. 1372-1397
Author(s):  
Nairi Usher ◽  
Dan E. Browne
Keyword(s):  
Quantum Computing ◽  
Quantum Computer ◽  
Cluster State ◽  
Building Blocks ◽  
Quantum Circuit ◽  
Matrix Product ◽  
One Dimensional ◽  
Matrix Product State ◽  
The Matrix ◽  
Correlation Space

Measurement-Based Quantum Computing (MBQC) is an alternative to the quantum circuit model, whereby the computation proceeds via measurements on an entangled resource state. Noise processes are a major experimental challenge to the construction of a quantum computer. Here, we investigate how noise processes affecting physical states affect the performed computation by considering MBQC on a one-dimensional cluster state. This allows us to break down the computation in a sequence of building blocks and map physical errors to logical errors. Next, we extend the Matrix Product State construction to mixed states (which is known as Matrix Product Operators) and once again map the effect of physical noise to logical noise acting within the correlation space. This approach allows us to consider more general errors than the conventional Pauli errors, and could be used in order to simulate noisy quantum computation.

scholarly journals Space-like dynamics in a reversible cellular automaton

2020 ◽  
Vol 2 (2) ◽  
Author(s):  
Katja Klobas ◽  
Tomaz Prosen
Keyword(s):  
Cellular Automaton ◽  
Lattice Gas ◽  
Time Correlation ◽  
Matrix Product ◽  
Product Representation ◽  
Circuit Representation ◽  
Reversible Cellular Automaton ◽  
The Matrix ◽  
Local Space ◽  
Local Observables

In this paper we study the space evolution in the Rule 54 reversible cellular automaton, which is a paradigmatic example of a deterministic interacting lattice gas. We show that the spatial translation of time configurations of the automaton is given in terms of local deterministic maps with the support that is small but bigger than that of the time evolution. The model is thus an example of space-time dual reversible cellular automaton, i.e. its dual is also (in general different) reversible cellular automaton. We provide two equivalent interpretations of the result; the first one relies on the dynamics of quasi-particles and follows from an exhaustive check of all the relevant time configurations, while the second one relies on purely algebraic considerations based on the circuit representation of the dynamics. Additionally, we use the properties of the local space evolution maps to provide an alternative derivation of the matrix product representation of multi-time correlation functions of local observables positioned at the same spatial coordinate.

Effect of mechanical restraint on the rate of corrosion in concrete

1998 ◽  
Vol 25 (1) ◽  
pp. 81-86 ◽  
Author(s):  
N Hearn ◽  
J Aiello
Keyword(s):  
Mix Design ◽  
Concrete Repair ◽  
Accelerated Corrosion ◽  
One Dimensional ◽  
Mechanical Restraint ◽  
Corrosion Rates ◽  
Accelerated Corrosion Tests ◽  
The Matrix ◽  
The Relationship

Experimental work on prismatic concrete specimens was conducted to determine the relationship between mechanical restraint and the rate of corrosion. The current together with the changes in strain of the confining frame were monitored during the accelerated corrosion tests. The effect of mix design and cracking on the corrosion rates was also investigated. The results show that one-dimensional mechanical restraint retards the corrosion process, as indicated by the reduction in the steel loss. Improved quality of the matrix, with and without cracking, reduces the rate of steel loss. In the inferior quality concrete, the effect of cracking on the corrosion rate is minimal.Key words: corrosion, concrete, repair.

scholarly journals Numerical Analysis of Viscoelastic Rotating Beam with Variable Fractional Order Model Using Shifted Bernstein–Legendre Polynomial Collocation Algorithm

2021 ◽  
Vol 5 (1) ◽  
pp. 8
Author(s):  
Cundi Han ◽  
Yiming Chen ◽  
Da-Yan Liu ◽  
Driss Boutat
Keyword(s):  
Numerical Analysis ◽  
Fractional Order ◽  
Governing Equation ◽  
Numerical Solutions ◽  
Bernstein Polynomials ◽  
Matrix Product ◽  
Algebraic Equations ◽  
Rotating Beam ◽  
The Matrix ◽  
The Time Domain

This paper applies a numerical method of polynomial function approximation to the numerical analysis of variable fractional order viscoelastic rotating beam. First, the governing equation of the viscoelastic rotating beam is established based on the variable fractional model of the viscoelastic material. Second, shifted Bernstein polynomials and Legendre polynomials are used as basis functions to approximate the governing equation and the original equation is converted to matrix product form. Based on the configuration method, the matrix equation is further transformed into algebraic equations and numerical solutions of the governing equation are obtained directly in the time domain. Finally, the efficiency of the proposed algorithm is proved by analyzing the numerical solutions of the displacement of rotating beam under different loads.

scholarly journals Optimising Matrix Product State Simulations of Shor's Algorithm

Quantum ◽  
2019 ◽  
Vol 3 ◽  
pp. 116 ◽  
Author(s):  
Aidan Dang ◽  
Charles D. Hill ◽  
Lloyd C. L. Hollenberg
Keyword(s):  
Dimensional Structure ◽  
Matrix Product ◽  
Product State ◽  
One Dimensional ◽  
Matrix Product State ◽  
Shor's Algorithm ◽  
The One ◽  
High Level ◽  
Space Requirements ◽  
Factoring Algorithm

We detail techniques to optimise high-level classical simulations of Shor's quantum factoring algorithm. Chief among these is to examine the entangling properties of the circuit and to effectively map it across the one-dimensional structure of a matrix product state. Compared to previous approaches whose space requirements depend on r, the solution to the underlying order-finding problem of Shor's algorithm, our approach depends on its factors. We performed a matrix product state simulation of a 60-qubit instance of Shor's algorithm that would otherwise be infeasible to complete without an optimised entanglement mapping.

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