NDLI: Duality quantum computer and the efficient quantum simulations

Content Provider	Springer Nature Link
Author	Wei, Shi Jie Long, Gui Lu
Copyright Year	2016
Abstract	Duality quantum computing is a new mode of a quantum computer to simulate a moving quantum computer passing through a multi-slit. It exploits the particle wave duality property for computing. A quantum computer with n qubits and a qudit simulates a moving quantum computer with n qubits passing through a d-slit. Duality quantum computing can realize an arbitrary sum of unitaries and therefore a general quantum operator, which is called a generalized quantum gate. All linear bounded operators can be realized by the generalized quantum gates, and unitary operators are just the extreme points of the set of generalized quantum gates. Duality quantum computing provides flexibility and a clear physical picture in designing quantum algorithms, and serves as a powerful bridge between quantum and classical algorithms. In this paper, after a brief review of the theory of duality quantum computing, we will concentrate on the applications of duality quantum computing in simulations of Hamiltonian systems. We will show that duality quantum computing can efficiently simulate quantum systems by providing descriptions of the recent efficient quantum simulation algorithm of Childs and Wiebe (Quantum Inf Comput 12(11–12):901–924, 2012) for the fast simulation of quantum systems with a sparse Hamiltonian, and the quantum simulation algorithm by Berry et al. (Phys Rev Lett 114:090502, 2015), which provides exponential improvement in precision for simulating systems with a sparse Hamiltonian.
Starting Page	1189
Ending Page	1212
Page Count	24
File Format	PDF
ISSN	15700755
Journal	Quantum Information Processing
Volume Number	15
Issue Number	3
e-ISSN	15731332
Language	English
Publisher	Springer US
Publisher Date	2016-03-02
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Duality computer Duality quantum computer Duality computing mode Quantum divider Quantum combiner Duality parallelism Quantum simulation Linear combination of unitary operators Quantum Information Technology, Spintronics Quantum Computing Data Structures, Cryptology and Information Theory Quantum Physics Mathematical Physics
Content Type	Text
Resource Type	Article
Subject	Statistical and Nonlinear Physics Theoretical Computer Science Signal Processing Electronic, Optical and Magnetic Materials Electrical and Electronic Engineering Modeling and Simulation

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1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
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Duality Quantum Computing and Duality Quantum Information Processing

Mathematical Theory of Duality Quantum Computers

Duality quantum computing

Unitary equivalent classes of one-dimensional quantum walks

A graph theoretical approach to states and unitary operations

Generalized duality quantum computers acting on mixed states

Selecting efficient phase estimation with constant-precision phase shift operators

Determination of locally perfect discrimination for two-qubit unitary operations

The rational approximations of the unitary groups

Duality quantum computer and the efficient quantum simulations

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