Quantum gate generation for systems with drift in U(<i>n</i>) using Lyapunov–LaSalle techniques

Silveira, Hector Bessa; Silva, Paulo Sérgio Pereira da; Rouchon, Pierre

doi:10.1080/00207179.2016.1161830

Cited by 6 publications

(12 citation statements)

References 10 publications

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“…In order to give a complete description of the FPA, it will be necessary to recall some results of [25].…”

Section: Description Of the Fixed-point Algorithm (Fpa)mentioning

confidence: 99%

“…It was shown in [25] that V( X) corresponds to a notion of distance between X ∈ W and the identity matrix I. This notion of distance then naturally defines a (not bounded) notion of distance between two matrices X 1 , X 2 of U(n) by considering the map dist :…”

Section: Consider the Lyapunov Functionmentioning

confidence: 99%

“…This fact justifies the need of new methods, like numerical optimal control, Lyapunov methods and so on. Lyapunov stabilization [6,7,11,12,15,[24][25][26][27] may be applicable for large n, but they generate slow solutions (in the sense that that the final time must be large) when compared to the ones that are generated by optimal control, when this last approach is applicable. Hence the study of numerical methods that can be applied for large n and also produces a fast solution is a relevant field of research, indeed.…”

Section: Introductionmentioning

confidence: 99%

“…However, this method is not iterative, and hence the solutions are slow, that is, a large final time T f that depends on the rate of convergence of the Lyapunov tracking control is needed. In [25], the method of [24] was generalized for systems with drift. However, it also generates slow solutions when compared for instance to GRAPE [8,9].…”

Section: Introductionmentioning

confidence: 99%

“…One first obtains, by right translation of the approximate solution, a new trajectory X(t) such that its final condition X(T f ) is exactly equal to X goal . The idea is then to consider the trajectory X(t) as a reference trajectory and to apply a stabilizing feedback of the corresponding tracking problem, as done in previous works of the authors [24,25]. The novelty of this work is that we consider the construction of an adequate right-translation R ∈ U(n) that corrects the action of the feedback in order to obtain an exact generation of quantum gate.…”

Section: Introductionmentioning

confidence: 99%

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A fixed point algorithm for improving fidelity of quantum gates

2021

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This work considers the problem of quantum gate generation for controllable quantum systems with drift. It is assumed that an approximate solution called seed is pre-computed by some known algorithm. This work presents a method, called Fixed-Point Algorithm (FPA) that is able to improve arbitrarily the fidelity of the given seed. When the infidelity of the seed is small enough and the approximate solution is attractive in the context of a tracking control problem (that is verified with probability one, in some sense), the Banach Fixed Point Theorem allows to prove the exponential convergence of the FPA. Even when the FPA does not converge, several iterated applications of the FPA may produce the desired fidelity. The FPA produces only small corrections in the control pulses and preserves the original bandwidth of the seed. The computational effort of each step of the FPA corresponds to the one of the numerical integration of a stabilized closed loop system. A piecewise-constant and a smooth numerical implementations are developed. Several numerical experiments with a N-qubit system illustrates the effectiveness of the method in several different applications including the conversion of piecewise-constant control pulses into smooth ones and the reduction of their bandwidth.

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“…In order to give a complete description of the FPA, it will be necessary to recall some results of [25].…”

Section: Description Of the Fixed-point Algorithm (Fpa)mentioning

confidence: 99%

Section: Consider the Lyapunov Functionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

A fixed point algorithm for improving fidelity of quantum gates

2021

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Optimal control methods for quantum gate preparation: a comparative study

Riaz

Cong

Qamar

2019

Quantum Inf Process

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Quantum Lyapunov control with machine learning

Hou

2019

Quantum Inf Process

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Quantum state engineering is a central task in Lyapunov-based quantum control. Given different initial states, better performance may be achieved if the control parameters, such as the Lyapunov function, are individually optimized for each initial state, however, at the expense of computing resources. To tackle this issue, we propose an initial-state-adaptive Lyapunov control strategy with machine learning, specifically, artificial neural networks trained through supervised learning. Two designs are presented and illustrated where the feedforward neural network and the general regression neural network are used to select control schemes and design Lyapunov functions, respectively. Since the sample generation and the training of neural networks are carried out in advance, the initial-state-adaptive Lyapunov control can be implemented without much increase of computational resources.

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Quantum gate generation for systems with drift in U(n) using Lyapunov–LaSalle techniques

Cited by 6 publications

References 10 publications

A fixed point algorithm for improving fidelity of quantum gates

A fixed point algorithm for improving fidelity of quantum gates

Optimal control methods for quantum gate preparation: a comparative study

Quantum Lyapunov control with machine learning

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