Density matrix formalism of duality quantum computer and the solution of zero-wave-function paradox

Cui, Jingxin; Zhou, Tao; Long, Gui Lu

doi:10.1007/s11128-011-0243-0

Cited by 20 publications

(12 citation statements)

References 17 publications

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“…Duality quantum algorithm was proposed in 2002 [ 71 ] for the first time, and it developed fast [ 72 , 73 , 74 , 75 ]. Because both the products of unitary operations and linear combinations of unitary (LCU) operations can be realized by duality quantum algorithm, it has a lot of applications to investigate novel quantum systems [ 16 , 17 , 18 , 19 , 20 , 21 , 76 , 77 , 78 , 79 , 80 ], e.g., systems of large-scale silicon quantum photonics, efficient quantum simulations of open quantum systems, quantum secure computing, passive quantum error correction, etc.…”

Section: Duality Quantum Algorithmmentioning

confidence: 99%

Efficient Quantum Simulation of an Anti-P-Pseudo-Hermitian Two-Level System

Zheng

Tian

et al. 2020

Entropy

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Besides Hermitian systems, quantum simulation has become a strong tool to investigate non-Hermitian systems, such as PT-symmetric, anti-PT-symmetric, and pseudo-Hermitian systems. In this work, we theoretically investigate quantum simulation of an anti-P-pseudo-Hermitian two-level system in different dimensional Hilbert spaces. In an arbitrary phase, we find that six dimensions are the minimum to construct the anti-P-pseudo-Hermitian two-level subsystem, and it has a higher success probability than using eight dimensions. We find that the dimensions can be reduced further to four or two when the system is in the anti-PT-symmetric or Hermitian phase, respectively. Both qubit-qudit hybrid and pure-qubit systems are able to realize the simulation, enabling experimental implementations in the near future.

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Section: Duality Quantum Algorithmmentioning

confidence: 99%

Efficient Quantum Simulation of an Anti-P-Pseudo-Hermitian Two-Level System

Zheng

Tian

et al. 2020

Entropy

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“…Moreover, Gudder has proved that all linear bounded operators in a finite dimensional Hilbert space can be expressed as an element in the positive cone of generalized quantum gates 21 . Many recent studies about the mathematical theory of duality quantum computer have been made 19 20 21 22 23 24 25 26 27 28 29 30 31 34 36 .…”

Section: Resultsmentioning

confidence: 99%

“…The concept of duality quantum computers is first proposed by Long in 2002 based on the general principle of quantum interference 17 18 , which draw many attentions 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 . It is shown that any bounded linear operator can be expressed as a linear combinations of unitary operators in a duality quantum computer 21 .…”

mentioning

confidence: 99%

Duality quantum algorithm efficiently simulates open quantum systems

Wei

Ruan

Long

2016

Sci Rep

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Because of inevitable coupling with the environment, nearly all practical quantum systems are open system, where the evolution is not necessarily unitary. In this paper, we propose a duality quantum algorithm for simulating Hamiltonian evolution of an open quantum system. In contrast to unitary evolution in a usual quantum computer, the evolution operator in a duality quantum computer is a linear combination of unitary operators. In this duality quantum algorithm, the time evolution of the open quantum system is realized by using Kraus operators which is naturally implemented in duality quantum computer. This duality quantum algorithm has two distinct advantages compared to existing quantum simulation algorithms with unitary evolution operations. Firstly, the query complexity of the algorithm is O(d3) in contrast to O(d4) in existing unitary simulation algorithm, where d is the dimension of the open quantum system. Secondly, By using a truncated Taylor series of the evolution operators, this duality quantum algorithm provides an exponential improvement in precision compared with previous unitary simulation algorithm.

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“…For example, the zero-wave function paradox was pointed out firstly by Gudder [11], and two possible solutions were given in Refs. [13] and [14]. Long has actively participated in the work of QIP as a reviewer when Dr. Brandt was the editor-in-chief, and as a member of the editorial board from 2014.…”

mentioning

confidence: 99%

“…This also indicates that we can perform duality quantum computing in an ordinary quantum computer, in the so-called duality quantum computing mode [16,17]. There have been intensive interests in the theory of duality computer in recent years [10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30], and experimental studies have also been reported [31,32].…”

mentioning

confidence: 99%

Duality quantum computer and the efficient quantum simulations

Wei

Long

2016

Quantum Inf Process

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In this paper, we firstly briefly review the duality quantum computer. Distinctly, the generalized quantum gates, the basic evolution operators in a duality quantum computer are no longer unitary, and they can be expressed in terms of linear combinations of unitary operators. All linear bounded operators can be realized in a duality quantum computer, and unitary operators are just the extreme points of the set of generalized quantum gates. A d-slits duality quantum computer can be realized in an ordinary quantum computer with an additional qudit using the duality quantum computing mode. Duality quantum computer provides flexibility and clear physical picture in designing quantum algorithms, serving as a useful bridge between quantum and classical algorithms. In this review, we will show that duality quantum computer can simulate quantum systems more efficiently than ordinary quantum computers by providing descriptions of the recent efficient quantum simulation algorithms of Childs et al [Quantum Information & Computation, 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.

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Density matrix formalism of duality quantum computer and the solution of zero-wave-function paradox

Cited by 20 publications

References 17 publications

Efficient Quantum Simulation of an Anti-P-Pseudo-Hermitian Two-Level System

Efficient Quantum Simulation of an Anti-P-Pseudo-Hermitian Two-Level System

Duality quantum algorithm efficiently simulates open quantum systems

Duality quantum computer and the efficient quantum simulations

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