Control aspects of holonomic quantum computation

Lucarelli, Dennis

doi:10.1063/1.1888028

Cited by 12 publications

(14 citation statements)

References 44 publications

(86 reference statements)

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“…In holonomic quantum computation [2,3], the Wilson loops are used to perform quantum logic gates. The non-abelian adiabatic curvature is…”

Section: Propertymentioning

confidence: 99%

“…If the target state is an eigenstate of the quantum system, an adiabatic approach [1] is a good strategy to solve quantum control problems, since external parameters are usually slowly varied with respect to the response of the quantum system and since the adiabatic approximation predicts that the wave function remains projected onto an eigenstate during the dynamics. Adiabatic schemes of quantum control have been proposed for quantum computation by holonomic approaches [2,3] or by quantum annealing [4], and for atomic control by strong laser fields [5]. Real quantum systems are never isolated.…”

Section: Introductionmentioning

confidence: 99%

“…The goal of the present paper is the characterization of these defects. Some adiabatic quantum control methods are based on geometric approaches (geometry of fiber bundles [3] or topology of eigensurfaces [5]). We want a geometric characterization of the defects induced by the entanglement.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Adiabatic quantum control hampered by entanglement

Viennot¹

2014

J. Phys. A: Math. Theor.

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Abstract. We study the defects in adiabatic control of a quantum system caused by the entanglement of the system with its environment. Such defects can be assimilated to decoherence processes due to perturbative couplings between the system and the environment. To analyse these effects, we propose a geometric approach, based on a field theory on the control manifold issued from the higher gauge theory associated with the C * -geometric phases. We study a visualization method to analyse the defects of the adiabatic control based on the drawing of the field strengths of the gauge theory. To illustrate the present methodology we consider the example of the atomic STIRAP (stimulated Raman adiabatic passage) where the controlled atom is entangled with another atom. We study the robustness of the STIRAP effect when the controlled atom is entangled with another one.

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“…In holonomic quantum computation [2,3], the Wilson loops are used to perform quantum logic gates. The non-abelian adiabatic curvature is…”

Section: Propertymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Adiabatic quantum control hampered by entanglement

Viennot¹

2014

J. Phys. A: Math. Theor.

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“…An adiabatic approach [1] can be used to describe quantum control since the variations of the control parameters are often slow. Quantum control schemes based on adiabatic approximation have been proposed for different closed systems [2,3,4,5]. For open quantum systems, adiabatic approaches based on non-hermitian Hamiltonians have been studied [6,7,8].…”

Section: Introductionmentioning

confidence: 99%

Adiabatic theorem for bipartite quantum systems in weak coupling limit

Viennot¹,

Aubourg²

2014

J. Phys. A: Math. Theor.

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Abstract. We study the adiabatic approximation of the dynamics of a bipartite quantum system with respect to one of the components, when the coupling between its two components is perturbative. We show that the density matrix of the considered component is described by adiabatic transport formulae exhibiting operator-valued geometric and dynamical phases. The present results can be used to study the quantum control of the dynamics of qubits and of open quantum systems where the two components are the system and its environment. We treat two examples, the control of an atomic qubit interacting with another one and the control of a spin in the middle of a Heisenberg spin chain.

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“…[26]. Moreover some approaches of quantum computation based on the geometrization of the quantum dynamics and on the geometric phases have been proposed [27,28,29,30], usually called holonomic quantum computation (HQC). These approaches are based on the geometric properties of fiber bundles modelizing the dynamics of closed quantum systems.…”

Section: Introductionmentioning

confidence: 99%

Purification of Lindblad dynamics, geometry of mixed states and geometric phases

Viennot

2018

Journal of Geometry and Physics

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We propose a nonlinear Schrödinger equation in a Hilbert space enlarged with an ancilla such that the partial trace of its solution obeys to the Lindblad equation of an open quantum system. The dynamics involved by this nonlinear Schrödinger equation constitutes then a purification of the Lindblad dynamics. We study the (non adiabatic) geometric phases involved by this purification and show that our theory unifies several definitions of geometric phases for open systems which have been previously proposed. We study the geometry involved by this purification and show that it is a complicated geometric structure related to an higher gauge theory, i.e. a categorical bibundle with a connective structure.

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Control aspects of holonomic quantum computation

Cited by 12 publications

References 44 publications

Adiabatic quantum control hampered by entanglement

Adiabatic quantum control hampered by entanglement

Adiabatic theorem for bipartite quantum systems in weak coupling limit

Purification of Lindblad dynamics, geometry of mixed states and geometric phases

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