# Design of an Efficient Quantum Circuit Simulator

20 Dec 2010-pp 50-55

TL;DR: An efficient simulator is proposed which can simulate a quantum circuit specified using the proposed quantum hardware descriptive language (QHDL) and to incorporate more components in the gate library.

Abstract: Work is in progress throughout the globe to efficiently use the potential of the quantum theory of computation over their classical counterpart and hence there is a need of building quantum computing hardware The target of building quantum computers can be achieved if we have better tools for the design of quantum hardware Quantum circuit simulators are tools for the logic verification of quantum circuits and they can be an essential component of quantum CAD tools in the future This work is the extension of the previous work by the authors [6], in order to increase the efficiency of the simulator and to incorporate more components in the gate library In this paper we have proposed an efficient simulator which can simulate a quantum circuit specified using the proposed quantum hardware descriptive language (QHDL)

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TL;DR: A general direct simulator for 1WQC, called OWQS, is presented and the simulator is adjusted to simulate the measurement patterns with a generalized flow without calculating the measurement probabilities which is called extended one-way quantum computation simulator (EOWQS).

Abstract: In one-way quantum computation (1WQC) model, universal quantum computations are performed using measurements to designated qubits in a highly entangled state. The choices of bases for these measurements as well as the structure of the entanglements specify a quantum algorithm. As scalable and reliable quantum computers have not been implemented yet, quantum computation simulators are the only widely available tools to design and test quantum algorithms. However, simulating the quantum computations on a standard classical computer in most cases requires exponential memory and time. In this paper, a general direct simulator for 1WQC, called OWQS, is presented. Some techniques such as qubit elimination, pattern reordering and implicit simulation of actions are used to considerably reduce the time and memory needed for the simulations. Moreover, our simulator is adjusted to simulate the measurement patterns with a generalized flow without calculating the measurement probabilities which is called extended one-way quantum computation simulator (EOWQS). Experimental results validate the feasibility of the proposed simulators and that OWQS and EOWQS are faster as compared with the well-known quantum circuit simulators, i.e., QuIDDPro and libquantum for simulating 1WQC model. (This paper is an extended version of the paper presented at Euromicro DSD conference (Nikahd et al., 2012) 1].)

6 citations

### Cites methods from "Design of an Efficient Quantum Circ..."

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TL;DR: Techniques such as qubit elimination, implicit and in-place matrix-vector multiplication and pattern reordering are utilized to considerably reduce the time and memory needed for the simulations of one-way quantum computation model.

Abstract: In one-way quantum computation (1WQC) model, universal quantum computations are performed using measurements to designated qubits in a highly entangled state The choices of basis for these measurements as well as the structure of the entanglements specify a quantum algorithm Although a number of methods have been proposed to simulate quantum circuit model on classical computers, no efficient tool has been developed to simulate the 1WQC model directly In this paper, some techniques such as qubit elimination, implicit and in-place matrix-vector multiplication and pattern reordering are utilized to considerably reduce the time and memory needed for the simulations These techniques were implemented in a tool called One-Way Quantum computation Simulator (OWQS) Experimental results validate the efficiency of the proposed approach

3 citations

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TL;DR: OWQS is modified in a way that it utilizes the graph-based representation of system states using algebraic decision diagram (ADD) in order to benefit from the similarities in the quantum states of 1WQC.

Abstract: In the one-way quantum computation (1WQC) model, computations are done by correlated sequences of entanglement, measurement and local corrections commands. As scalable and reliable quantum computers have not been implemented yet, the only widely available tools for designing and testing quantum algorithms are quantum computation simulators. However, simulating quantum computations on a standard classical computer in most cases requires very large memory and time. Recently, an array-based simulator, called one-way quantum computation simulator (OWQS) has been proposed to directly simulate the 1WQC model. OWQS outperforms the previously proposed quantum computation simulators to simulate the 1WQC model. In this paper, OWQS is modified in a way that it utilizes the graph-based representation of system states using algebraic decision diagram (ADD) in order to benefit from the similarities in the quantum states of 1WQC. This simulator is called graph-based OWQS, GOWQS. Experimental results validate the considerable improvement of the proposed simulator as compared to OWQS.

2 citations

### Cites background from "Design of an Efficient Quantum Circ..."

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19 Jul 2019

TL;DR: The main purpose of this work is to illustrate a full adder circuit by using a standard Mathematica add-on package, to show effective computational design by using analogy of classical circuits.

Abstract: A correct simulation of a quantum circuit on a classical computer is more important because of their future use. The main purpose of this work is to illustrate a full adder circuit by using a standard Mathematica add-on package. The circuit can be constructed by using CNOT-based quantum gates. The program provides a curriculum unit, to generate the basic elements that make up quantum circuit. This paper shows effective computational design by using analogy of classical circuits. We presented an explicit example to show efficiency of the 4 qubit full adder circuit on classical computer. The method given in this paper can be used to design various quantum circuits.

### Cites background from "Design of an Efficient Quantum Circ..."

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TL;DR: In this article, a general direct simulator for 1WQC, called OWQS, is presented, where some techniques such as qubit elimination, pattern reordering and implicit simulation of actions are used to considerably reduce the time and memory needed for the simulations.

Abstract: In one-way quantum computation (1WQC) model, universal quantum computations are performed using measurements to designated qubits in a highly entangled state. The choices of bases for these measurements as well as the structure of the entanglements specify a quantum algorithm. As scalable and reliable quantum computers have not been implemented yet, quantum computation simulators are the only widely available tools to design and test quantum algorithms. However, simulating the quantum computations on a standard classical computer in most cases requires exponential memory and time. In this paper, a general direct simulator for 1WQC, called OWQS, is presented. Some techniques such as qubit elimination, pattern reordering and implicit simulation of actions are used to considerably reduce the time and memory needed for the simulations. Moreover, our simulator is adjusted to simulate the measurement patterns with a generalized flow without calculating the measurement probabilities which is called extended one-way quantum computation simulator (EOWQS). Experimental results validate the feasibility of the proposed simulators and that OWQS and EOWQS are faster as compared with the well-known quantum circuit simulators, i.e., QuIDDPro and libquantum for simulating 1WQC model.

##### References

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01 Jan 2000

TL;DR: In this article, the quantum Fourier transform and its application in quantum information theory is discussed, and distance measures for quantum information are defined. And quantum error-correction and entropy and information are discussed.

Abstract: Part I Fundamental Concepts: 1 Introduction and overview 2 Introduction to quantum mechanics 3 Introduction to computer science Part II Quantum Computation: 4 Quantum circuits 5 The quantum Fourier transform and its application 6 Quantum search algorithms 7 Quantum computers: physical realization Part III Quantum Information: 8 Quantum noise and quantum operations 9 Distance measures for quantum information 10 Quantum error-correction 11 Entropy and information 12 Quantum information theory Appendices References Index

25,929 citations

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01 Dec 2010

TL;DR: This chapter discusses quantum information theory, public-key cryptography and the RSA cryptosystem, and the proof of Lieb's theorem.

Abstract: Part I. Fundamental Concepts: 1. Introduction and overview 2. Introduction to quantum mechanics 3. Introduction to computer science Part II. Quantum Computation: 4. Quantum circuits 5. The quantum Fourier transform and its application 6. Quantum search algorithms 7. Quantum computers: physical realization Part III. Quantum Information: 8. Quantum noise and quantum operations 9. Distance measures for quantum information 10. Quantum error-correction 11. Entropy and information 12. Quantum information theory Appendices References Index.

14,183 citations

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TL;DR: This special issue of Mathematical Structures in Computer Science contains several contributions related to the modern field of Quantum Information and Quantum Computing, with a focus on entanglement.

Abstract: This special issue of Mathematical Structures in Computer Science contains several contributions related to the modern field of Quantum Information and Quantum Computing.
The first two papers deal with entanglement. The paper by R. Mosseri and P. Ribeiro presents a detailed description of the two-and three-qubit geometry in Hilbert space, dealing with the geometry of fibrations and discrete geometry. The paper by J.-G.Luque et al. is more algebraic and considers invariants of pure k-qubit states and their application to entanglement measurement.

12,173 citations

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TL;DR: A number of physical systems, spanning much of modern physics, are being developed for this task, ranging from single particles of light to superconducting circuits, and it is not yet clear which, if any, will ultimately prove successful as discussed by the authors.

Abstract: Quantum mechanics---the theory describing the fundamental workings of nature---is famously counterintuitive: it predicts that a particle can be in two places at the same time, and that two remote particles can be inextricably and instantaneously linked These predictions have been the topic of intense metaphysical debate ever since the theory's inception early last century However, supreme predictive power combined with direct experimental observation of some of these unusual phenomena leave little doubt as to its fundamental correctness In fact, without quantum mechanics we could not explain the workings of a laser, nor indeed how a fridge magnet operates Over the last several decades quantum information science has emerged to seek answers to the question: can we gain some advantage by storing, transmitting and processing information encoded in systems that exhibit these unique quantum properties? Today it is understood that the answer is yes Many research groups around the world are working towards one of the most ambitious goals humankind has ever embarked upon: a quantum computer that promises to exponentially improve computational power for particular tasks A number of physical systems, spanning much of modern physics, are being developed for this task---ranging from single particles of light to superconducting circuits---and it is not yet clear which, if any, will ultimately prove successful Here we describe the latest developments for each of the leading approaches and explain what the major challenges are for the future

1,969 citations

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TL;DR: The physical limitations due to quantum mechanics on the functioning of computers are analyzed in this paper, where the physical limitations of quantum mechanics are discussed and the physical limits of quantum computing are analyzed.

Abstract: The physical limitations, due to quantum mechanics, on the functioning of computers are analyzed.

1,640 citations

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