Time-optimal control with finite bandwidth

Hirose, Masashi; Cappellaro, Paola

doi:10.1007/s11128-018-1845-6

Cited by 16 publications

(12 citation statements)

References 69 publications

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“…One practically important issue we have not discussed here is the time optimality or time dependence of the operation on the system size. This problem has been studied quite actively (See, e.g., some recent studies [4,5,[26][27][28] and references therein). In addition, we still have very little insight into how to obtain the specific profile of the control pulses [21].…”

Section: Discussionmentioning

confidence: 99%

Hilbert Space Structure Induced by Quantum Probes

Kato

Owari

Maruyama

2019

11th Italian Quantum Information Science Conference (IQIS2018)

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In the general setting of quantum controls, it is unrealistic to control all of the degrees of freedom of a quantum system. We consider a scenario where our direct access is restricted to a small subsystem S that is constantly interacting with the rest of the system E. What we investigate here is the fundamental structure of the Hilbert space that is caused solely by the restrictedness of the direct control. We clarify the intrinsic space structure of the entire system and that of the operations which could be activated through S. The structures hereby revealed would help us make quantum control problems more transparent and provide a guide for understanding what we can implement. They can be deduced by considering an algebraic structure, which is the Jordan algebra formed from Hermitian operators, naturally induced by the setting of limited access. From a few very simple assumptions about direct operations, we elucidate rich structures of the operator algebras and Hilbert spaces that manifest themselves in quantum control scenarios.

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Section: Discussionmentioning

confidence: 99%

Hilbert Space Structure Induced by Quantum Probes

Kato

Owari

Maruyama

2019

11th Italian Quantum Information Science Conference (IQIS2018)

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“…where γ def = E /E in Eq. (32). Observe that for E = E , we recover from the expression of P (t; x, E, E ) in Eq.…”

Section: The Modified Farhi-gutmann Search Hamiltonianmentioning

confidence: 97%

Theoretical analysis of a nearly optimal analog quantum search

Cafaro

Alsing

2019

Phys. Scr.

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We analyze the possibility of modifying the original Farhi-Gutmann Hamiltonian algorithm in order to speed up the procedure for producing a suitably distributed unknown normalized quantum mechanical state. Such a modification is feasible provided only a nearly optimal fidelity is sought.We propose to select the lower bounds of the nearly optimal fidelity values such that their deviations from unit fidelity are less than the minimum error probability characterizing the optimum ambiguous discrimination scheme between the two nonorthogonal quantum states yielding the chosen nearly optimal fidelity values. Departing from the working assumptions of perfect state overlap and uniform distribution of the target state on the unit sphere in N -dimensional complex Hilbert space, we determine that the modified algorithm can indeed outperform the original analog counterpart of a quantum search algorithm. This performance enhancement occurs in terms of speed for a convenient choice of both the ratio γ = E /E between the energy eigenvalues E and E of the modified search Hamiltonian and the quantum mechanical overlap x between the source and the target states. Finally, we briefly discuss possible analytical improvements of our investigation together with its potential relevance in practical quantum engineering applications.

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“…46 ), they have not been used to address this problem to the best of our knowledge. An ad hoc method based on time-optimal control of a two-level system 47,48 was also proposed: it consists in realizing Bang-Bang control with imperfect square control fields 49 . However, to achieve a gate with a reasonably low error the imperfect square pulse must still have a relatively large bandwidth.…”

Section: Strong Driving Of a Two-level Systemmentioning

confidence: 99%

Engineering fast high-fidelity quantum operations with constrained interactions

2021

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Understanding how to tailor quantum dynamics to achieve the desired evolution is a crucial problem in almost all quantum technologies. Oftentimes an otherwise ideal quantum dynamics is corrupted by unavoidable interactions, and finding ways to mitigate the unwanted effects of such interactions on the dynamics is a very active field of research. Here, we present a very general method for designing high-efficiency control sequences that are fully compatible with experimental constraints on available interactions and their tunability. Our approach relies on the Magnus expansion to find order by order the necessary corrections that result in a high-fidelity operation. In the end finding, the control fields are reduced to solve a set of linear equations. We illustrate our method by applying it to a number of physically relevant problems: the strong-driving limit of a two-level system, fast squeezing in a parametrically driven cavity, the leakage problem in transmon qubit gates, and the acceleration of SNAP gates in a qubit-cavity system.

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Time-optimal control with finite bandwidth

Cited by 16 publications

References 69 publications

Hilbert Space Structure Induced by Quantum Probes

Hilbert Space Structure Induced by Quantum Probes

Theoretical analysis of a nearly optimal analog quantum search

Engineering fast high-fidelity quantum operations with constrained interactions

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