Universal quantum gates for hybrid systems assisted by quantum dots inside double-sided optical microcavities

Hai-Rui Wei and Fu-Guo Deng

Phys. Rev. A 87, 022305 – Published 6 February 2013

Abstract

We present some deterministic schemes to construct universal quantum gates, that is, controlled- not, three-qubit Toffoli, and Fredkin gates, between flying photon qubits and stationary electron-spin qubits assisted by quantum dots inside double-sided optical microcavities. The control qubit of our gates is encoded on the polarization of the moving single photon and the target qubits are encoded on the confined electron spins in quantum dots inside optical microcavities. Our schemes for these universal quantum gates on a hybrid system have some advantages. First, all the gates are accomplished with a success probability of 100 $%$ in principle. Second, our schemes require no additional qubits. Third, the control qubits of the gates are easily manipulated and the target qubits are perfect for storage and processing. Fourth, the gates do not require that the transmission for the uncoupled cavity is balanceable with the reflectance for the coupled cavity, in order to get a high fidelity. Fifth, the devices for the three universal gates work in both the weak coupling and the strong coupling regimes, and they are feasible in experiment.

Received 5 November 2012

DOI:https://doi.org/10.1103/PhysRevA.87.022305

Authors & Affiliations

Hai-Rui Wei and Fu-Guo Deng^*

Department of Physics, Applied Optics Beijing Area Major Laboratory, Beijing Normal University, Beijing 100875, China

^*Corresponding author: fgdeng@bnu.edu.cn

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Issue

Vol. 87, Iss. 2 — February 2013

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Images

Figure 1
(a) A schematic diagram for a singly charged QD inside a double-sided optical microcavity. (b) Schematic description of the relevant exciton energy levels and the spin selection rules for optical transition of negatively charged excitons. The symbols $⇑$ ( $⇓$ ) and $↑$ ( $↓$ ) represent a hole and an excess electron with $z$ -direction spin projections $| + \frac{3}{2} 〉$ ( $| - \frac{3}{2} 〉$ ) and $| + \frac{1}{2} 〉$ ( $| - \frac{1}{2} 〉$ ), respectively. $| R^{↑} 〉$ ( $| R^{↓} 〉$ ) denotes a right-circularly polarized photon propagating along (against) the normal direction of the cavity $z$ axis (the quantization axis) and $| L^{↑} 〉$ ( $| L^{↓} 〉$ ) denotes a left-circularly polarized photon propagating along (against) the $z$ axis.Reuse & Permissions
Figure 2
The quantum circuit for constructing a deterministic cnot gate with a flying photon polarization as the control qubit and a confined electron spin as the target qubit. PBS $_{i}$ ( $i = 1, 2, 3$ ) is a polarizing beam splitter in the circular basis, which transmits the right-circular polarization photon $| R 〉$ and reflects the left-circular polarization photon $| L 〉$ , respectively. HWP represents a half-wave plate which is set to $22 . 5^{\circ}$ to induce the Hadamard transformations on the polarizations of photons. $P_{π}$ is a phase shifter that contributes a $π$ phase shift to the photon passing through it. DL is the time-delay device for making the photons from modes 1 and 5 reach PBS $_{3}$ simultaneously. Before and after the photon interacts with the electron spin in the QD inside the double-side optical microcavity, a Hadamard ( $H_{e}$ ) operation is performed on the electron spin by using a $π / 2$ microwave pulse or an optical pulse.Reuse & Permissions
Figure 3
Scheme for implementing a three-qubit Toffoli gate with a flying photon polarization and a confined electron-spin qubit as the two control qubits and another confined electron-spin qubit as the target qubit.Reuse & Permissions
Figure 4
Schematic setup for a deterministic three-qubit Fredkin gate with a flying photon polarization as the control qubit and two confined electron spins as the target qubits. $S_{1}$ and $S_{2}$ are two optical switches.Reuse & Permissions
Figure 5
The fidelities of our three-qubit gates vs the side leakage rate $κ_{s} / κ$ and the coupling strength $g / κ$ . (a) The fidelity of our Toffoli gate ( $F_{T}$ ). (b) The fidelity of our Fredkin gate ( $F_{F}$ ). The solid (red), dashed-dotted (green), large-dashed (blue), and dashed (brown) lines correspond to $g = 0.5 κ$ , $g = 0.75 κ$ , $g = 1.0 κ$ , and $g = 2.4 κ$ , respectively. $γ = 0.1 κ$ , which is experimentally achievable, and $ω_{X^{-}} = ω_{c} = ω$ are taken here.Reuse & Permissions
Figure 6
The efficiencies of our universal quantum gates vs the side leakage rate $κ_{s} / κ$ and the coupling strength $g / κ$ . (a) The efficiency of our cnot gate ( $η_{CNOT}$ ). (b) The efficiency of our Toffoli gate ( $η_{T}$ ). (c) The efficiency of our Fredkin gate ( $η_{F}$ ). The solid (red), dashed-dotted (green), large-dashed (blue), and dashed (brown) lines correspond to $g = 0.5 κ$ , $g = 0.75 κ$ , $g = 1.0 κ$ , and $g = 2.4 κ$ , respectively. We take $γ = 0.1 κ$ and $ω_{X^{-}} = ω_{c} = ω$ for panels (a), (b), and (c).Reuse & Permissions

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