Theoretical analysis of a nearly optimal analog quantum search

Cafaro, Carlo; Alsing, Paul M.

doi:10.1088/1402-4896/ab111f

Cited by 14 publications

(23 citation statements)

References 43 publications

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“…Therefore, by minimizing the entropy production, we shall find the optimum paths on the manifold of state space parametrized by θ along which one drives the system. To be more specific, in view of the connection between analog quantum search and two-level quantum systems [16,17], we assume that the output of a continuous-time quantum search algorithm where the input is the normalized N = 2 n -dimensional n-qubit source state |s def = |ψ (θ 0 ) can be described as,…”

Section: A From Quantum Evolutions To Probability Pathsmentioning

confidence: 99%

Information geometry aspects of minimum entropy production paths from quantum mechanical evolutions

Cafaro

Alsing

2020

Phys. Rev. E

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We present an information geometric analysis of entropic speeds and entropy production rates in geodesic evolution on manifolds of parametrized quantum states. These pure states emerge as outputs of suitable su (2; C) time-dependent Hamiltonian operators used to describe distinct types of analog quantum search schemes. The Riemannian metrization on the manifold is specified by the Fisher information evaluated along the parametrized squared probability amplitudes obtained from analysis of the temporal quantum mechanical evolution of a spin-1/2 particle in an external timedependent magnetic field that specifies the su (2; C) Hamiltonian model. We employ a minimum action method to transfer a quantum system from an initial state to a final state on the manifold in a finite temporal interval. Furthermore, we demonstrate that the minimizing (optimum) path is the shortest (geodesic) path between the two states, and, in particular, minimizes also the total entropy production that occurs during the transfer. Finally, by evaluating the entropic speed and the total entropy production along the optimum transfer paths in a number of physical scenarios of interest in analog quantum search problems, we show in a clear quantitative manner that to a faster transfer there corresponds necessarily a higher entropy production rate. Thus, we conclude that lower entropic efficiency values appear to accompany higher entropic speed values in quantum transfer processes.

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Section: A From Quantum Evolutions To Probability Pathsmentioning

confidence: 99%

Information geometry aspects of minimum entropy production paths from quantum mechanical evolutions

Cafaro

Alsing

2020

Phys. Rev. E

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“…Finally, building upon our works presented in Refs. [7,17,18,20], we presented in Ref. [21] an information geometric analysis of geodesic speeds and entropy production rates in geodesic motion on manifolds of parametrized quantum states.…”

Section: Arxiv:200202248v1 [Quant-ph] 6 Feb 2020mentioning

confidence: 99%

Information Geometric Perspective on Off-Resonance Effects in Driven Two-Level Quantum Systems

2020

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We present an information geometric analysis of off-resonance effects on classes of exactly solvable generalized semi-classical Rabi systems. Specifically, we consider population transfer performed by four distinct off-resonant driving schemes specified by su (2; C) time-dependent Hamiltonian models. For each scheme, we study the consequences of a departure from the on-resonance condition in terms of both geodesic paths and geodesic speeds on the corresponding manifold of transition probability vectors. In particular, we analyze the robustness of each driving scheme against off-resonance effects. Moreover, we report on a possible tradeoff between speed and robustness in the driving schemes being investigated. Finally, we discuss the emergence of a different relative ranking in terms of performance among the various driving schemes when transitioning from on-resonant to off-resonant scenarios.

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“…In conclusion, our proposed analysis was partially inspired by some of our previous findings reported in Refs. [32,33] and can be improved in a number of ways in the immediate short term. For instance, it would be interesting to address the following question: How large should the nearly optimal fidelity value be chosen, given the finite precision of quantum measurements and the unavoidable presence of decoherence effects in physical implementations of quantum information processing tasks?…”

Section: B Limitations and Possible Future Developmentsmentioning

confidence: 99%

Transition probabilities in generalized quantum search Hamiltonian evolutions

Gassner

Cafaro

Capozziello

2019

Int. J. Geom. Methods Mod. Phys.

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A relevant problem in quantum computing concerns how fast a source state can be driven into a target state according to Schrödinger's quantum mechanical evolution specified by a suitable driving Hamiltonian. In this paper, we study in detail the computational aspects necessary to calculate the transition probability from a source state to a target state in a continuous time quantum search problem defined by a multi-parameter generalized time-independent Hamiltonian. In particular, quantifying the performance of a quantum search in terms of speed (minimum search time) and fidelity (maximum success probability), we consider a variety of special cases that emerge from the generalized Hamiltonian. In the context of optimal quantum search, we find it is possible to outperform, in terms of minimum search time, the well-known Farhi-Gutmann analog quantum search algorithm. In the context of nearly optimal quantum search, instead, we show it is possible to identify sub-optimal search algorithms capable of outperforming optimal search algorithms if only a sufficiently high success probability is sought. Finally, we briefly discuss the relevance of a tradeoff between speed and fidelity with emphasis on issues of both theoretical and practical importance to quantum information processing.

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Theoretical analysis of a nearly optimal analog quantum search

Cited by 14 publications

References 43 publications

Information geometry aspects of minimum entropy production paths from quantum mechanical evolutions

Information geometry aspects of minimum entropy production paths from quantum mechanical evolutions

Information Geometric Perspective on Off-Resonance Effects in Driven Two-Level Quantum Systems

Transition probabilities in generalized quantum search Hamiltonian evolutions

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