Quantum Control at the Boundary

Balmaseda, Aitor; Pérez-Pardo, Juan Manuel

doi:10.1007/978-3-030-24748-5_5

Cited by 7 publications

(7 citation statements)

References 38 publications

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“…We will prove now Theorem 2.15, i.e., weak approximate controllability of quantum induction control systems; this is a stronger version of a theorem proven in [6] in the case of Quantum Graphs. In order to do that, we rely on Theorem 5.5 and the stability proven in Theorem 2.9 and Corollary 5.3.…”

Section: 3mentioning

confidence: 84%

Quantum controllability on graph-like manifolds through magnetic potentials and boundary conditions

Balmaseda¹,

Lonigro²,

Pérez-Pardo³

2021

Preprint

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We investigate the controllability of an infinite-dimensional quantum system by modifying the boundary conditions instead of applying external fields. We analyse the existence of solutions of the Schrödinger equation for a time-dependent Hamiltonian with time-dependent domain, but constant form domain. A stability theorem for such systems, which improves known results, is proven. We study magnetic systems on Quantum Circuits, a higherdimensional generalisation of Quantum Graphs whose edges are allowed to be manifolds of arbitrary dimension. We consider a particular class of boundary conditions (quasi-δ boundary conditions) compatible with the graph structure. By applying the stability theorem, we prove that these systems are approximately controllable. Smooth control functions are allowed in this framework.

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Section: 3mentioning

confidence: 84%

Quantum controllability on graph-like manifolds through magnetic potentials and boundary conditions

Balmaseda¹,

Lonigro²,

Pérez-Pardo³

2021

Preprint

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“…As a final remark, let us stress the role played by the group Z as a symmetry of the quantum system. Indeed, using symmetry considerations, we have been able to identify a wide class of self-adjoint extensions, which preserves the topology of the graph (these self-adjoint extensions are obtained by imposing boundary conditions already known in the literature as quasi-δ boundary conditions [9]). Notice that the family of self-adjoint extensions obtained is more general than a merely periodic repetition of the parameters defining the self-adjoint extension at each unit cell.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

“…However, one of the sources of decoherence in the description of superconducting qubits arises precisely because of the aforementioned truncation to the lowest orders. Hence, it is worth addressing the system in its full generality and try, for instance, to achieve general controllability results, as was done in [9].…”

Section: Introductionmentioning

confidence: 99%

On Z -Invariant Self-Adjoint Extensions of the Laplacian on Quantum Circuits

2019

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An analysis of the invariance properties of self-adjoint extensions of symmetric operators under the action of a group of symmetries is presented. For a given group G, criteria for the existence of G-invariant self-adjoint extensions of the Laplace–Beltrami operator over a Riemannian manifold are illustrated and critically revisited. These criteria are employed for characterising self-adjoint extensions of the Laplace–Beltrami operator on an infinite set of intervals, Ω , constituting a quantum circuit, which are invariant under a given action of the group Z . A study of the different unitary representations of the group Z on the space of square integrable functions on Ω is performed and the corresponding Z -invariant self-adjoint extensions of the Laplace–Beltrami operator are introduced. The study and characterisation of the invariance properties allows for the determination of the spectrum and generalised eigenfunctions in particular examples.

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“…Results in this direction have been found for a quantum particle in a one-dimensional cavity with moving walls, which can be transformed into a fixed-boundary problem [20][21][22][23]. More recently, time-dependent boundary conditions in a graph-like manifold, potentially relevant in quantum control theory, have been investigated [24,25].…”

Section: Introductionmentioning

confidence: 99%

On the Schrödinger Equation for Time-Dependent Hamiltonians with a Constant Form Domain

2022

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We study two seminal approaches, developed by B. Simon and J. Kisyński, to the well-posedness of the Schrödinger equation with a time-dependent Hamiltonian. In both cases, the Hamiltonian is assumed to be semibounded from below and to have a constant form domain, but a possibly non-constant operator domain. The problem is addressed in the abstract setting, without assuming any specific functional expression for the Hamiltonian. The connection between the two approaches is the relation between sesquilinear forms and the bounded linear operators representing them. We provide a characterisation of the continuity and differentiability properties of form-valued and operator-valued functions, which enables an extensive comparison between the two approaches and their technical assumptions.

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Quantum Control at the Boundary

Cited by 7 publications

References 38 publications

Quantum controllability on graph-like manifolds through magnetic potentials and boundary conditions

Quantum controllability on graph-like manifolds through magnetic potentials and boundary conditions

On Z -Invariant Self-Adjoint Extensions of the Laplacian on Quantum Circuits

On the Schrödinger Equation for Time-Dependent Hamiltonians with a Constant Form Domain

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