Research ArticleEXPERIMENTAL PHYSICS

Versatile microwave-driven trapped ion spin system for quantum information processing

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Science Advances  08 Jul 2016:
Vol. 2, no. 7, e1600093
DOI: 10.1126/sciadv.1600093

Figures

  • Fig. 1 Conditional quantum dynamics in a fully coupled three-spin system.

    (A) Ramsey fringes from the first spin after different conditional evolution times (1 and 4 ms). The phase shift reveals the coupling to other spins. Each data point represents the result of 50 repetitions of the experiment. (B) For different initial states of the second and third spin and different conditional evolution times, the acquired phase shift is plotted. From the slope, information about the couplings can be deduced. Error bars represent SDs.

  • Fig. 2 Different experimentally realized spin-1/2 systems.

    Spins are symbolized by dots, and the base in which each spin is encoded is denoted by σ± and π, respectively. A line connecting two dots represents a J-coupling between them, whereas ± indicates the sign of this interaction. Experimental results are summarized in the right column. (A) All spins are encoded in the same basis; hence, their coupling has a positive sign. (B and C) One of the spins is encoded in a different base, which results in different interactions. (D) It is also possible to decouple a selected spin while the remaining spins are left coupled. (E) If the coupling of all spins is suppressed, their states are preserved.

  • Fig. 3 Circuit for the QFT.

    The circuit that realizes the QFT in our experiments consists of single-qubit rotations [R(θ, φ)] and conditional evolutions [U(T)] of different duration. For technical reasons, single-qubit operations on different qubits are applied one after another, and the Hadamard gate (H) is realized by two rotations [R(π/2, −π/2)R(π, 0)]. The additional SWAP gate that completes the QFT is realized by relabeling qubits 1 and 3 after the projective measurement. During the optimization of the sequence, the conditional evolution time, T2 = 0.22 ms, was neglected. The whole sequence takes 8.6 ms as a result of the conditional evolution times. The duration of the single-qubit rotations can be neglected because the Rabi frequency is about 2π × 50 kHz.

  • Fig. 4 Exemplary results of a QFT.

    After the QFT with input state |010〉, additional Ramsey π/2 pulses reveal interference fringes from every single qubit. The experimental results (solid lines) are compared with the predicted outcomes (dashed lines). Each data point represents 50 repetitions and error bars denote SDs.

  • Fig. 5 Estimating the period of quantum states.

    (A to D) After application of the QFT for different input states, a projective measurement takes place. The measured probability of finding each possible output state is shown (blue bars) along with the ideal results (gray bars) and with simulations that take into account experimental imperfections of the setup (yellow bars). The SSO S and distinguishability D are measures of the performance. Each experiment is repeated 1250 times. The statistical error is too small to be shown.

Tables

  • Table 1 State fidelities after application of the QFT.

    The single-qubit state fidelities F1, F2, and F3 are estimated from Ramsey fringes and excitation probabilities after applying the QFT. From correlation measurements, the three-qubit state fidelities F are deduced.

    Initial stateF1F2F3F1 × F2 × F3F
    |000〉0.74(5)0.88(5)0.82(5)0.53(6)0.59(2)
    |001〉0.77(4)0.81(2)0.86(4)0.53(4)0.54(2)
    |010〉0.76(7)0.86(4)0.84(4)0.55(4)0.55(2)
    |011〉0.77(5)0.84(2)0.83(4)0.54(5)0.54(2)
    |100〉0.74(5)0.89(5)0.88(5)0.58(6)0.59(2)
    |101〉0.73(4)0.85(2)0.90(4)0.56(4)0.66(2)
    |110〉0.70(4)0.78(4)0.90(3)0.49(4)0.57(2)
    |111〉0.68(4)0.79(3)0.89(4)0.48(4)0.63(2)
    |+00〉0.84(2)0.78(5)0.86(5)0.56(5)0.65(2)
    |+01〉0.83(2)0.84(3)0.81(4)0.56(4)
    |+10〉0.81(2)0.77(4)0.76(4)0.47(3)
    |+11〉0.82(2)0.81(2)0.80(4)0.54(3)
    |++0〉0.79(2)0.74(2)0.88(4)0.51(3)
    |++1〉0.84(2)0.73(2)0.75(4)0.46(3)
    |+++〉0.86(2)0.79(2)0.77(2)0.52(3)0.54(2)

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