Generalized Schrödinger cat states and their classical emulation

Pérez-Leija, Armando; Szameit, Alexander; Ramos-Prieto, Irán; Moya‐Cessa, H.; Christodoulides, Demetrios N.

doi:10.1103/physreva.93.053815

Cited by 9 publications

(7 citation statements)

References 46 publications

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“…Here, it is important to note that in contrast to the Fock states, the coherent states are the quantum states whose statistical behavior most resemble the classical one, this has generated considerable interest in using micro-mirrors for the generation of coherent mechanical states or even superposition of them if such micro-mirrors can be cooled to their quantum ground states [ 43 , 44 , 45 , 46 , 47 , 48 ].…”

Section: Theorymentioning

confidence: 99%

Approximate Evolution for A Hybrid System—An Optomechanical Jaynes-Cummings Model

Medina-Dozal

Ramos-Prieto

Récamier

2020

Entropy

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In this work, we start from a phenomenological Hamiltonian built from two known systems: the Hamiltonian of a pumped optomechanical system and the Jaynes-Cummings Hamiltonian. Using algebraic techniques we construct an approximate time evolution operator U^(t) for the forced optomechanical system (as a product of exponentials) and take the JC Hamiltonian as an interaction. We transform the later with U^(t) to obtain a generalized interaction picture Hamiltonian which can be linearized and whose time evolution operator is written in a product form. The analytic results are compared with purely numerical calculations using the full Hamiltonian and the agreement between them is remarkable.

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Section: Theorymentioning

confidence: 99%

Approximate Evolution for A Hybrid System—An Optomechanical Jaynes-Cummings Model

Medina-Dozal

Ramos-Prieto

Récamier

2020

Entropy

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“…Even though, to the authors' best knowledge, no realization of such an operation with optical means has been presented so far, the theory of f -deformed oscillators has been investigated quite thoroughly (see, for example, Refs. [27][28][29][30]). It thus seems much more reasonable to assume that an operation like C(gβ) will be available at some point, compared to that defined by Eq.…”

Section: Continuous-variable Gate Teleportationmentioning

confidence: 99%

Teleportation-assisted optical controlled-sign gates

Ewert

Loock

2019

Phys. Rev. A

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Reliable entangling gates for qubits encoded in single-photon states represent a major challenge on the road to scalable quantum computing architectures based on linear optics. In this work, we present two approaches to develop high-fidelity, near-deterministic controlled-sign-shift gates based on the techniques of quantum gate teleportation. On the one hand, teleportation in a discrete-variable setting, i.e., for qubits, offers unit-fidelity operations but suffers from low success probabilities. Here, we apply recent results on advanced linear optical Bell measurements to reach a near-deterministic regime. On the other hand, in the setting of continuous variables, associated with coherent states, squeezing, and, typically, Gaussian states, teleportation can be performed in a deterministic fashion, but the finite amount of squeezing implies an inevitable deformation of a teleported single-mode state. Using a new generalized form of the nonlinear-sign-shift gate for gate teleportation, we are able to achieve fidelities of the resulting csign gate above 90%. A special focus is also put on a comparison of the two approaches, not only with respect to fidelity and success probability, but also in terms of resource consumption.

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“…Experimental realizations of Laguerre type generalized coherent states using the behavior of a beamsplitter with a specific geometry are explored in [23]. They also appear in the realization of a quantum oscillator consisting of a trapped ion in [27].The realization of generalized coherent states have also been investigated in photonic lattices [28,29].…”

Section: Xmentioning

confidence: 99%

Generalized Coherent States, Reproducing Kernels, and Quantum Support Vector Machines

Chatterjee,

2016

Preprint

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The support vector machine (SVM) is a popular machine learning classification method which produces a nonlinear decision boundary in a feature space by constructing linear boundaries in a transformed Hilbert space. It is well known that these algorithms when executed on a classical computer do not scale well with the size of the feature space both in terms of data points and dimensionality. One of the most significant limitations of classical algorithms using non-linear kernels is that the kernel function has to be evaluated for all pairs of input feature vectors which themselves may be of substantially high dimension. This can lead to computationally excessive times during training and during the prediction process for a new data point. Here, we propose using both canonical and generalized coherent states to rapidly calculate specific nonlinear kernel functions.The key link will be the reproducing kernel Hilbert space (RKHS) property for SVMs that naturally arise from canonical and generalized coherent states. Specifically, we discuss the fast evaluation of radial kernels through a positive operator valued measure (POVM) on a quantum optical system based on canonical coherent states. A similar procedure may also lead to fast calculations of kernels not usually used in classical algorithms such as those arising from generalized coherent states.

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Generalized Schrödinger cat states and their classical emulation

Cited by 9 publications

References 46 publications

Approximate Evolution for A Hybrid System—An Optomechanical Jaynes-Cummings Model

Approximate Evolution for A Hybrid System—An Optomechanical Jaynes-Cummings Model

Teleportation-assisted optical controlled-sign gates

Generalized Coherent States, Reproducing Kernels, and Quantum Support Vector Machines

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