Geometry and Dynamics of a Quantum Search Algorithm for an Ordered Tuple of Multi-Qubits

Uwano, Yoshio

doi:10.5772/53187

Cited by 2 publications

(5 citation statements)

References 27 publications

(59 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…A geometric study analogous to [7] about the projection of the Grover-type search on the QSS was however deferred to [5] because of another new interest in the gradient system on the QSS associated with the negative von-Neumann entropy. It is shown in [3] that the gradient system of interest is understood to be a very natural extension of the gradient system associated with the negative Shannon entropy on a classical statistical manifold which is studied by Nakamura [9].…”

Section: Introductionmentioning

confidence: 99%

“…In order to describe the motive of this paper, a brief history of the series of the author's works [1,3,4,5] is given below. As a departure point of the series of the author's works, Grover's quantum search algorithm [6] is worth touched on, which is well-known to be one of the milestones on the road of quantum computation [2]: For a large number, say N = 2 n , of randomly sorted data, the complexity of Grover's algorithm is of O( √ N ), which is lower than the theoretical boundary, O(N ), of any non-quantum searches.…”

Section: Introductionmentioning

confidence: 99%

“…After the papers [1,4] by the author and Yuya, the deferred task for a geometric study of the projection of the Grover-type search sequence for an ordered tuple of multi-qubits is made successfully by the author [5]: The projection of the Grover-type search sequence on the QSS is shown to be on an m-geodesic, an autoparallel curve with respect to the mixture-type parallel transport [13], on the QSS. This result strongly encourages the author to seek other dynamical systems whose trajectories realize geodesics on the QSS.…”

Section: Introductionmentioning

confidence: 99%

“…At the beginning of the outline, it should be remarked that the pair of sections, Section 2 and Section 3, among five sections in this paper are mostly for reviews of the QSS, the EAHLE and the e-geodesics, which are done according to the author's previous papers [1,3,5] and the literature [13] by Hayashi on quantum information. Although the review part seems to occupy rather large part of this paper, it is indispensable because a similarity between looks of the EAHLE and of the tangent vector along the e-geodesics play a key role to reach to the main theorem of this paper.…”

Section: Introductionmentioning

confidence: 99%

“…[1,3,4,5]. Equation(14) works effectively to derive a useful formula to the gradient equation on the QSS[1,3,4].…”

mentioning

confidence: 99%

See 4 more Smart Citations

All the trajectories of an extended averaged Hebbian learning equation on the quantum state space are the e-geodesics

Uwano¹

2016

Math. Model. Geom.

Self Cite

View full text Add to dashboard Cite

In this paper, two families of trajectories on the quantum state space (QSS) originating from a synaptic-neuron model and from quantum information geometry meet together. The extended averaged Hebbian learning equation (EAHLE) on the QSS developed by the author and Yuya [1] from a Hebbian synaptic-neuron model is studied from a quantum-informationgeometric point of view. It is shown that all the trajectories of the EAHLE are the egeodesics, the autoparallel curves with respect to the exponential-type parallel transport, on the QSS. As a secondary outcome, an explicit representation of solution of the averaged Hebbian learning equation, the origin of the EAHLE, is derived from that of the e-geodesics on the QSS.

show abstract