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Implementation of quantum logic gates using polar molecules in pendular states
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Figures

Image of FIG. 1.

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FIG. 1.

The configuration of two polar molecules. μ 1 and μ 2 are permanent dipole moments for molecules 1 and 2; r 12 is the distance vector from molecules 1 to 2. ε is the external electric field and α is the angle between r 12 and the external field. θ12) is the angle between μ 1 ( μ 2 ) and ε .

Image of FIG. 2.

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FIG. 2.

Ratio of frequency shift, Δω, to the dipole-dipole interaction parameter, , as a function of reduced field strength, x = μ ε /B and x′ = μ ε ′/B at sites of the two dipoles.

Image of FIG. 3.

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FIG. 3.

Converged laser pulses for NOT gate. The upper panel is the laser pulses for realizing the NOT gate for dipole 1, on the left and dipole 2 on the right. The initial and target states are listed in Table I . The lower panel shows the evolution of all populations driven by NOT pulses. The left panel exhibits the population evolution under the NOT pulse for dipole 1. The initial state is and the final populations are 0.733 for |00⟩ and 0.265 for |11⟩. The right panel shows the population evolution via the NOT pulse for dipole 2. It has the same initial condition as the left panel and the converged population is 0.216 for |00⟩ and 0.781 for |11⟩. Both pulses perform the corresponding NOT gates nicely.

Image of FIG. 4.

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FIG. 4.

Optimized laser pulses for Hadamard gates. The left panel pertains to performing the Hadamard gate on dipole 1 and the right one to performing that on dipole 2. The lower panels show the population evolution under the Hadamard laser pulse. In order to exhibit the curves clearly, we chose |01⟩ as the initial state; the final populations of |01⟩ and |11⟩ are 0.429 and 0.566, respectively. For the case of the Hadamard gate on dipole 2, the |00⟩ qubit was chosen as the initial state. The populations at the end of the evolution are 0.528 for |00⟩ and 0.470 for |01⟩. The functions of these gates are realized very well by these two pulses.

Image of FIG. 5.

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FIG. 5.

Optimized laser pulse for realizing the CNOT gate. The initial and target states are listed in Table III . In the lower panel, the population evolution is driven by the CNOT pulse. The initial state is . After population oscillations due to the effect of the laser pulse, the final qubit populations are 0.00363 (|00⟩), 0.25807 (|01⟩), 0.00273 (|10⟩), and 0.73546 (|11⟩). The populations of state |10⟩ and |11⟩ are switched, which confirms the correctness of the converged laser pulse.

Image of FIG. 6.

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FIG. 6.

Optimized laser pulse for realizing the CNOT gate when the distance between two dipoles is 75 nm. The initial and target states are listed in Table III . The optimized laser pulse, which is shown in the upper panel, lasts 110 ns. The lower panel shows the population evolution driven by the pulse. The initial state is the same as Fig. 5 . The final converged populations for state |01⟩ and |10⟩ are 0.22 and 0.73, respectively.

Tables

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Table I.

The initial and target states of the NOT gate. The final fidelities for both NOT gates are 0.967 and 0.985, respectively.

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Table II.

The initial and target states of the Hadmard gate. The yield fidelities are 0.944 and 0.902.

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Table III.

The initial and target states of the CNOT gate. The converged fidelity is 0.975.

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Table IV.

Comparison with other polar molecular systems.

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/content/aip/journal/jcp/138/2/10.1063/1.4774058
2013-01-10
2014-04-16

Abstract

We present a systematic approach to implementation of basic quantum logic gates operating on polar molecules in pendular states as qubits for a quantum computer. A static electric field prevents quenching of the dipole moments by rotation, thereby creating the pendular states; also, the field gradient enables distinguishing among qubit sites. Multi-target optimal control theory is used as a means of optimizing the initial-to-target transition probability via a laser field. We give detailed calculations for the SrO molecule, a favorite candidate for proposed quantum computers. Our simulation results indicate that NOT, Hadamard and CNOT gates can be realized with high fidelity, as high as 0.985, for such pendular qubit states.

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Scitation: Implementation of quantum logic gates using polar molecules in pendular states
http://aip.metastore.ingenta.com/content/aip/journal/jcp/138/2/10.1063/1.4774058
10.1063/1.4774058
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