The Circuit Model of Quantum Computation and Its Simulation with Mathematica

2012 ◽  
pp. 43-55 ◽  
Author(s):  
Vladimir P. Gerdt ◽  
Alexander N. Prokopenya
Keyword(s):  
Quantum Computation ◽  
Circuit Model

scholarly journals Generation of elementary gates and Bell’s states using controlled adiabatic evolutions

2019 ◽  
Vol 17 (03) ◽  
pp. 1950020
Author(s):  
Abderrahim Benmachiche ◽  
Ali Sellami ◽  
Sherzod Turaev ◽  
Derradji Bahloul ◽  
Azeddine Messikh ◽  
...  
Keyword(s):  
Quantum Computation ◽  
Open Systems ◽  
Circuit Model ◽  
Quantum Gates ◽  
Single Quantum ◽  
New Model ◽  
Adiabatic Quantum Computation ◽  
Usual Quantum

Fundamental quantum gates can be implemented effectively using adiabatic quantum computation or circuit model. Recently, Hen combined the two approaches to introduce a new model called controlled adiabatic evolutions [I. Hen, Phys. Rev. A, 91(2) (2015) 022309]. This model was specifically designed to implement one and two-qubit controlled gates. Later, Santos extended Hen’s work to implement [Formula: see text]-qubit controlled gates [A. C. Santos and M. S. Sarandy, Sci. Rep., 5 (2015) 15775]. In this paper, we discuss the implementation of each of the usual quantum gates, as well as demonstrate the possibility of preparing Bell’s states using the controlled adiabatic evolutions approach. We conclude by presenting the fidelity results of implementing single quantum gates and Bell’s states in open systems.

Quantum game simulator, using the circuit model of quantum computation

2009 ◽  
Vol 180 (10) ◽  
pp. 1990-1998 ◽  
Author(s):  
Panagiotis Vlachos ◽  
Ioannis G. Karafyllidis
Keyword(s):  
Quantum Computation ◽  
Circuit Model ◽  
Quantum Game

scholarly journals Measurement-based quantum computation cannot avoid byproducts

2014 ◽  
Vol 12 (05) ◽  
pp. 1450026 ◽  
Author(s):  
Tomoyuki Morimae
Keyword(s):  
Quantum Computation ◽  
Error Correcting Code ◽  
Circuit Model ◽  
Measurement Device ◽  
No Signaling ◽  
Quantum Error

In the circuit model of quantum computation, a desired unitary gate can be implemented deterministically, whereas in the measurement-based model the unitary gate is implemented up to a byproduct operator. In order to compensate byproducts, following measurement angles must be adjusted, or classical results must be corrected. Such a feed-forwarding requires some classical processing and tuning of the measurement device, which cause the delay of computation and the additional decoherence. We show that if we respect the no-signaling principle, which is one of the most fundamental principles in physics, byproducts cannot be avoided in measurement-based quantum computation. Furthermore, we also show by using the idea of the quantum error correcting code that due to the no-signaling principle, not all byproducts are allowed in measurement-based quantum computation.

scholarly journals Quantum software engineering. Pt. I: Quantum Circuit (Gate) Model based Computing – education Lectures and pedagogical workshop

2020 ◽  
pp. 129-201
Author(s):  
Sergey Ulyanov ◽  
Andrey Reshetnikov ◽  
Olga Tyatyushkina ◽  
Vladimir Korenkov
Keyword(s):  
Software Engineering ◽  
Quantum Computation ◽  
Quantum Algorithms ◽  
Quantum Algorithm ◽  
Quantum Circuit ◽  
Circuit Model ◽  
Topological Quantum ◽  
Definition Of ◽  
Topological Quantum Computation ◽  
Main Ideas

All the quantum algorithms are based on a certain quantum computing model, varying from the quantum circuit, one-way quantum computation, adiabatic quantum computation and topological quantum computation. These four models are equivalent in computational power; among them, the quantum circuit model is most frequently used. In the circuit model, it has been proved that arbitrary single-qubit rotations plus twoqubit controlled-NOT gates are universal, i.e. they can provide a set of gates to implement any quantum algorithm. This article discusses the goal for this research: it is to given a lightning-fast (as-barebones-as-possible) definition of the quantum circuit model computing and leisurely development of quantum computation before actually getting around to sophisticated algorithms. In this article the main ideas of quantum software engineering is described.

Classical simulation of quantum computation, the gottesman-Knill theorem, and slightly beyond

2010 ◽  
Vol 10 (3&4) ◽  
pp. 258-271 ◽  
Author(s):  
M. Van den Nest
Keyword(s):  
Normal Form ◽  
Quantum Computation ◽  
Simple Proof ◽  
Quantum Circuit ◽  
Circuit Model ◽  
Computational Power ◽  
Classical Simulation ◽  
Starting Point

We study classical simulation of quantum computation, taking the Gottesman-Knill theorem as a starting point. We show how each Clifford circuit can be reduced to an equivalent, manifestly simulatable circuit (normal form). This provides a simple proof of the Gottesman-Knill theorem without resorting to stabilizer techniques. The normal form highlights why Clifford circuits have such limited computational power in spite of their high entangling power. At the same time, the normal form shows how the classical simulation of Clifford circuits fits into the standard way of embedding classical computation into the quantum circuit model. This leads to simple extensions of Clifford circuits which are classically simulatable. These circuits can be efficiently simulated by classical sampling (``weak simulation'') even though the problem of exactly computing the outcomes of measurements for these circuits (``strong simulation'') is proved to be $\#\mathbf{P}$-complete---thus showing that there is a separation between weak and strong classical simulation of quantum computation.

Single-server blind quantum computation with quantum circuit model

2018 ◽  
Vol 17 (6) ◽  
Author(s):  
Xiaoqian Zhang ◽  
Jian Weng ◽  
Xiaochun Li ◽  
Weiqi Luo ◽  
Xiaoqing Tan ◽  
...  
Keyword(s):  
Quantum Computation ◽  
Quantum Circuit ◽  
Circuit Model ◽  
Single Server ◽  
Blind Quantum Computation
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