CNOT Quantum Gate Based on Spatial Photonic Qubits Under Resonant Electro-Optical Control

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Abstract

A theoretical model of a quantum node that implements the two-qubit CNOT operation with use of photonic qubits with spatial encoding is considered. Each qubit is represented by a pair of modes supporting an arbitrary superposition of single-photon states. The active element of the node is a single or double quantum dot with a tunable frequency, which coherently exchanges an energy quantum with the modes. The spectral characteristics of the quantum node elements are simulated. The probability of implementation of a controlled inversion of the qubit state is calculated depending on the system parameters.

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About the authors

A. V. Tsukanov

Valiev Institute of Physics and Technology of the Russian Academy of Sciences

Author for correspondence.
Email: tsukanov@ftian.ru
Russian Federation, Moscow

I. Yu. Kateev

Valiev Institute of Physics and Technology of the Russian Academy of Sciences

Email: ikateyev@mail.ru
Russian Federation, Moscow

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Supplementary files

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2. Fig. 1. Schematic of a quantum node that implements a two-qubit CNOT operation on photonic qubits. The controlling (controlled) qubit is represented by two waveguides, each supporting a single mode with x(y) polarisation. Their interaction energies J0, x(y) are assumed to be small. The quantum points of QT A and QT B are located at the mode bunches Ex(y),1 and Ex(y),2 of the microresonators MR 1 and MR 2. Both MRs exchange photons with each other, the waveguides of the controlled qubit and the waveguide of the controlling qubit with velocities J, Jy and Jx, respectively. The electronic transitions between g and px(y) states in each of the CTs are indirectly coupled to the corresponding waveguide modes through the MRs. Direct energy exchange between the CTs occurs under the influence of the Ferster interaction with the rate ΩF

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3. Fig. 2. Time dependence plots of the population dependences of the ground states for the scheme of indirect photon transfer between the waveguides of the controlled qubit through CT A. The undesirable effect of direct photon tunnelling with small (a) and intermediate (b) J velocities is taken into account. All parameters are given in units of the frequency of the optical transition in CTs

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4. Fig. 3. Time dependence plots of the population dependences of the basis states for the scheme of indirect photon transfer between waveguides through CT A with regard to small (a) and large (b) detunings of the subsystem frequencies. A weak direct tunnelling coupling between the single-photon states of the modes is assumed. All parameters are given in units of the frequency of the optical transition in CTs

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5. Fig. 4. Time dependence plots of the population dependences of the ground states for the scheme of indirect photon transfer between waveguides through DCTs in resonant (a) and non-resonant (b) modes. A strong Förster coupling between the one-electron states of the CTs is assumed. All parameters are given in units of the frequency of the optical transition in CTs

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6. Fig. 5. Plots of the two-dimensional electric field distribution of two waveguides with thickness h = 1.77 μm and width b = 1.7 μm at L = 9.5 μm (top) and b = 3 μm at L = 8.5 μm (bottom) for odd (left) and even (right) x-modes. The horizontal lines indicate the boundaries of the waveguides

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7. Fig. 6. Plots of dependences of the optical interaction coefficient J of two waveguides with thickness h = 1.77 μm on the distance L between them at different values of the width b for the x-mode (a) and y-mode (b)

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8. Fig. 7. Plots of the two-dimensional electric field distribution of the x-mode of a system consisting of a microdisk with radius R and a waveguide with width b. The waveguide is at a distance d from the microdisk. Top: R = 30 µm, b = 3 µm, d = 6.5 µm, bottom: R = 27 µm, b = 1.9 µm, d = 8 µm

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9. Fig. 8. Plots of dependences of the maximum value of Ex of the single-photon electric field for x-mode MR on the distance d between the waveguide and the microdisk for a thin waveguide (a) and a moderate-width waveguide (b)

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10. Fig. 9. Plots of dependences of the emissivity of the microdisk for the x-mode at R = 30 μm, h = 1.77 μm (a) and for the y-mode at R = 27 μm, h = 1.89 μm (b) on the distance d between the waveguide and the microdisk at different values of the waveguide width b

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