Quantum computational geodesics

Brandt, Howard E.

doi:10.1080/09500340903180517

Cited by 3 publications

(3 citation statements)

References 20 publications

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“…In addition to this, there was no contribution of I ⊗ I ⊗ I component in any linear combination due to traceless properties of the generator of SU (8). The results are especially important, as it shown that we could represent the Lie algebra su(8) one-to-one in Pauli coordinates resembling change of coordinates which greatly reduced the amount of terms used for representation [12,5,4].…”

Section: Change Of Basis From Generator Basis To Pauli Basismentioning

confidence: 99%

“…This is particularly useful in representing the evolution of the quantum states, U = e −iHt using Riemannian geometry tools. This is done by representing the Hamiltonian, H of the evolution of the quantum states in terms of Pauli coordinates where U is an element of SU (8) Lie group, and H is also the respective element for su (8) Lie algebra [4,5,12].…”

Section: Introductionmentioning

confidence: 99%

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Algebraic representation of Three Qubit Quantum Circuit Problems

Chew¹,

Shah²,

Chan³

2022

MJMS

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The evolution of quantum states serves as good fundamental studies in understanding the quantum information systems which finally lead to the research on quantum computation. To carry out such a study, mathematical tools such as the Lie group and their associated Lie algebra is of great importance. In this study, the Lie algebra of su(8) is represented in a tensor product operation between three Pauli matrices. This can be realized by constructing the generalized Gell-Mann matrices and comparing them to the Pauli bases. It is shown that there is a one-to-one correlation of the Gell-Mann matrices with the Pauli basis which resembled the change of coordinates. Together with the commutator relations and the frequency analysis of the structure constant via the algebra, the Lie bracket operation will be highlighted providing insight into relating quantum circuit model with Lie Algebra. These are particularly useful when dealing with three-qubit quantum circuit problems which involve quantum gates that is derived from the SU(8) Lie group.

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Section: Change Of Basis From Generator Basis To Pauli Basismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Algebraic representation of Three Qubit Quantum Circuit Problems

Chew¹,

Shah²,

Chan³

2022

MJMS

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“…One of us, Long, came to know Dr. Brandt first through his important works in quantum information [1,2,3,4,5,6,7,8,9] and later his role as editor-in-chief of the journal Quantum Information Processing(QIP). Long proposed a new type of quantum computer in 2002 [10], which employed the wave-particle duality principle to quantum information processing.…”

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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Duality quantum computer and the efficient quantum simulations

Wei¹,

Long²

2015

Preprint

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Quantum computational geodesics

Cited by 3 publications

References 20 publications

Algebraic representation of Three Qubit Quantum Circuit Problems

Algebraic representation of Three Qubit Quantum Circuit Problems

Duality quantum computer and the efficient quantum simulations

Duality quantum computer and the efficient quantum simulations

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