Differential topology of adiabatically controlled quantum processes

Jonckheere, Edmond; Rezakhani, A. T.; Farooq, Ahmad

doi:10.1007/s11128-012-0445-0

Cited by 7 publications

(5 citation statements)

References 17 publications

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“…Securing stability of the eigenstructure of H (and V ) requires N = N , an assumption that can be justified invoking genericity. Such issue specialized to energy landscape traces back to von Neumann and Wigner [10] and was further developed in [11], [12].…”

Section: Genericity and Stability Of Hamiltonian Eigenstructurementioning

confidence: 99%

Robust Control Performance for Open Quantum Systems

Schirmer,

Langbein,

Weidner

et al. 2020

Preprint

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Section: Genericity and Stability Of Hamiltonian Eigenstructurementioning

confidence: 99%

Robust Control Performance for Open Quantum Systems

Schirmer,

Langbein,

Weidner

et al. 2020

Preprint

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“…We found that the algorithm's precision requirements increase with problem size if its quadratic speedup is to be maintained. In this context, it is also useful to note again that obtaining the quantum speedup for the Roland and Cerf algorithm requires an 'exponentially precise' annealing schedule, as the minimum gap is exponentially localized [33,35,45], and that further digitization of the algorithm into a circuit by Trotterization [27,36,37] does not preserve the quadratic quantum speedup [46]. Nonetheless, it should be noted that newer algorithms for simulating Hamiltonian evolutions using quantum circuits offer more efficient digitization techniques [47][48][49][50].…”

Section: Conclusion and Discussionmentioning

confidence: 99%

How quantum is the speedup in adiabatic unstructured search?

Hen¹

2019

Quantum Inf Process

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In classical computing, analog approaches have sometimes appeared to be more powerful than they really are. This occurs when resources, particularly precision, are not appropriately taken into account. While the same should also hold for analog quantum computing, precision issues are often neglected from the analysis. In this work we present a classical analog algorithm for unstructured search that can be viewed as analogous to the quantum adiabatic unstructured search algorithm devised by Roland and Cerf [Phys. Rev. A 65, 042308 (2002)]. We show that similarly to its quantum counterpart, the classical construction may also provide a quadratic speedup over standard digital unstructured search. We discuss the meaning and the possible implications of this result in the context of adiabatic quantum computing.

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“…Securing stability of the eigenstructure of H (and V ) requires N = N , which can be justified invoking genericity. See also [33], [35].…”

Section: A Multiple Eigenvaluesmentioning

confidence: 99%

Robust Control Performance for Open Quantum Systems

Schirmer

Langbein

Weidner

et al. 2022

IEEE Trans. Automat. Contr.

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Robust performance of control schemes for open quantum systems is investigated under classical uncertainties in the generators of the dynamics and nonclassical uncertainties due to decoherence and initial state preparation errors. A formalism is developed to measure performance based on the transmission of a dynamic perturbation or initial state preparation error to the quantum state error. This makes it possible to apply tools from classical robust control such as structured singular value analysis. A difficulty arising from the singularity of the closedloop Bloch equations for the quantum state is overcome by introducing the #-inversion lemma, a specialized version of the matrix inversion lemma. Under some conditions, this guarantees continuity of the structured singular value at s = 0. Additional difficulties occur when symmetry gives rise to multiple open-loop poles, which under symmetrybreaking unfold into single eigenvalues. The concepts are applied to systems subject to pure decoherence and a general dissipative system example of two qubits in a leaky cavity under laser driving fields and spontaneous emission. A nonclassical performance index, steady-state entanglement quantified by the concurrence, a nonlinear function of the system state, is introduced. Simulations confirm a conflict between entanglement, its log-sensitivity and stability margin under decoherence.

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Differential topology of adiabatically controlled quantum processes

Cited by 7 publications

References 17 publications

Robust Control Performance for Open Quantum Systems

Robust Control Performance for Open Quantum Systems

How quantum is the speedup in adiabatic unstructured search?

Robust Control Performance for Open Quantum Systems

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