Exponential of a matrix, a nonlinear problem, and quantum gates

Steeb, Willi-Hans; Hardy, Yorick

doi:10.1063/1.4905382

Cited by 4 publications

(2 citation statements)

References 12 publications

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“…Next, we determine the Hamiltonian H V that generates the unitary U as U = e iH V by invoking the identity, [32], from which equivalent expressions for V a 's are obtained i.e., V l a = Z l a = e − iπ 2 (2r+1)Z la , from which we choose V l a = e iπ 2 V la . Then, the multi-spin Hamiltonian generator…”

Section: Hypergraph Hamiltonian Couplingmentioning

confidence: 99%

Operational Algorithms for Separable Qubit X States

Ellinas

2019

Condensed Matter

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This work motivates and applies operational methodology to simulation of quantum statistics of separable qubit X states. Three operational algorithms for evaluating separability probability distributions are put forward. Building on previous findings, the volume function characterizing the separability distribution is determined via quantum measurements of multi-qubit observables. Three measuring states, one for each algorithm are generated via (i) a multi-qubit channel map, (ii) a unitary operator generated by a Hamiltonian describing a non-uniform hypergraph configuration of interactions among 12 qubits, and (iii) a quantum walk CP map in a extended state space. Higher order CZ gates are the only tools of the algorithms hence the work associates itself computationally with the Instantaneous Quantum Polynomial-time Circuits (IQP), while wrt possible implementation the work relates to the Lechner-Hauke-Zoller (LHZ) architecture of higher order coupling. Finally some uncertainty aspects of the quantum measurement observables are discussed together with possible extensions to non-qubit separable bipartite systems.

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Section: Hypergraph Hamiltonian Couplingmentioning

confidence: 99%

Operational Algorithms for Separable Qubit X States

Ellinas

2019

Condensed Matter

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“…Thus an algorithm that can compute any branch is required. The matrix Lambert W function has been recently considered in a problem of quantum computing [31], where the matrix argument A is normal (A * A = AA * ).…”

Section: ) (O) the Colors Of The Curves That Separate Two Adjacent Rmentioning

confidence: 99%

An Algorithm for the Matrix Lambert $W$ Function

Fasi

Higham

Iannazzo³

2015

SIAM J. Matrix Anal. & Appl.

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Abstract. An algorithm is proposed for computing primary matrix Lambert W functions of a square matrix A, which are solutions of the matrix equation W e W = A. The algorithm employs the Schur decomposition and blocks the triangular form in such a way that Newton's method can be used on each diagonal block, with a starting matrix depending on the block. A natural simplification of Newton's method for the Lambert W function is shown to be numerically unstable. By reorganizing the iteration a new Newton variant is constructed that is proved to be numerically stable. Numerical experiments demonstrate that the algorithm is able to compute the branches of the matrix Lambert W function in a numerically reliable way.

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Verified computation for the matrix Lambert W function

Miyajima

2019

Applied Mathematics and Computation

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Exponential of a matrix, a nonlinear problem, and quantum gates

Abstract: Abstract. We describe solutions of the matrix equation exp(z(A − I n )) = A, where z ∈ C. Applications in quantum computing are given. Both normal and nonnormal matrices are studied. For normal matrices, the Lambert W-function plays a central role.

Cited by 4 publications

References 12 publications

Operational Algorithms for Separable Qubit X States

Operational Algorithms for Separable Qubit X States

An Algorithm for the Matrix Lambert $W$ Function

Verified computation for the matrix Lambert W function

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