Scattering theory in relation to quantum computing

Myers, John M.; Wu, Tai Tsun

doi:10.1117/12.721693

Cited by 2 publications

(2 citation statements)

References 11 publications

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“…It is tempting to study rigorously successive scatterings from a quantum memory modeled by point interactions. This case is discussed for small impurities in [26] where it is concluded that impurities add up over a sequence of scatterings. The incoming states may not be pure but incoming quaternions are successively rotated in an appropriate sense in the frequency domain.…”

Section: Discussionmentioning

confidence: 99%

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Impurity and quaternions in nonrelativistic scattering from a quantum memory

Margetis

Grillakis

2008

J. Phys. A: Math. Theor.

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Models of quantum computing rely on transformations of the states of a quantum memory. We study mathematical aspects of a model proposed by Wu in which the memory state is changed via the scattering of incoming particles. This operation causes the memory content to deviate from a pure state, i.e. induces impurity. For nonrelativistic particles scattered from a two-state memory and sufficiently general interaction potentials in (1+1) dimensions, we express impurity in terms of quaternionic commutators. In this context, pure memory states correspond to null hyperbolic quaternions. In the case with point interactions, the scattering process amounts to appropriate rotations of quaternions in the frequency domain. Our work complements previous analyses by Margetis and Myers (2006 J. Phys. A 39 11567).

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Section: Discussionmentioning

confidence: 99%

“…where r(x, ω) is the quaternion corresponding to the frequency-domain density matrix φ(x, ω) φ † (x, ω) by ( 9), i.e., r(x, ω) := i φ(x, ω) φ † (x, ω), (26) assuming that the signals have only positive-frequency content. Thus, we have the formula…”

Section: Impuritymentioning

confidence: 99%

Impurity and quaternions in nonrelativistic scattering from a quantum memory

Margetis

Grillakis

2008

J. Phys. A: Math. Theor.

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Superlattice model for quantum gates

Anzaldo-Meneses

2019

EPL

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Probability electronic current conservation in superlattices leads to a natural connection with the qubit and quantum gate concepts of quantum information and the introduction of Bloch spheres and Hopf bundles. Superlattices or multilayer devices with coupled channels are described by sectionally constant potentials in the longitudinal direction and arbitrary lateral dependency, which allow the explicit analytic calculation of the scattering amplitudes connecting ingoing with outgoing wave functions. A superlattice with n open channels and two terminals can be seen as a quantum gate, since both can be viewed as quantum systems with n components, each of which can have two states given by input and output. Taking into account the dimensionality of the respective Hilbert spaces, it results that the one-channel or mode superlattice corresponds to a single qubit; the two-channels case to two qubits, and the three-and four-channels cases to three qubits. The coupling of modes or channels corresponds to the entanglement of qubits. As shown in this work, superlattices with interacting energy modes constitute physical systems which allow to understand and evaluate explicitly the main features used to describe entangled qubits through the study of Hopf fiber bundles on spheres. Explicit examples for superlattice gate models with coupled channels are provided.

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Scattering theory in relation to quantum computing

Cited by 2 publications

References 11 publications

Impurity and quaternions in nonrelativistic scattering from a quantum memory

Impurity and quaternions in nonrelativistic scattering from a quantum memory

Superlattice model for quantum gates

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