Experimentally Realizable Controlled-NOT Gate in a Flux-qubit / Resonator System

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Shiro Saito, Todd Tilma*, Simon J. Devitt*, Kae Nemoto*, and Kouichi Semba
Physical Science Laboratory, *National Institute of Informatics

@Superconducting qubits have attracted increasing interest in the context of quantum computing and quantum information processing [1]. We are focusing on a superconducting flux qubit/resonator system [see Fig. 1(a)] where the resonator works as a quantum bus (qubus). Using the qubus concept we can perform any two-qubit operation between any two qubits that are coupled to the quantum bus without using multiple swap gates, which are required in other systems that use direct qubit-qubit coupling. We present an experimentally realizable microwave pulse sequence that effects the controlled-NOT (C-NOT) gate operation in a qubit/resonator system [2]. From numerical simulations, we obtained a process fidelity FP [3] of 98.8 % (98.0 %) for a two-(three-)qubit/resonator system under ideal conditions.
@Figure 1(a) is a schematic of our system. Each qubit couples to the resonator through a mutual inductance M. Because of the fixed coupling, the qubit transition frequency depends slightly on the resonator state. We utilize this frequency difference to realize the C-NOT gate in cooperation with a two-photon blue side band (BSB) transition, which can create an entanglement between the control qubit and the resonator. Figure 1(b) shows a basic operational sequence of pulses on our two-qubit/resonator system. The pulse characteristics are represented by a frequency (C: carrier frequency, BSB: BSB frequency), a length (/2, ) and a phase (0, , ) from the top to the bottom. We obtained an FP of 98.8 % by optimizing the free evolution time T and the phase of the second BSB pulse . Here we set the frequencies of the control, target qubit and resonator at 6, 5 and 10 GHz, respectively, and the coupling between the qubit and the resonator at 0.1 GHz. Moreover, we obtained a high FP of 98.0 % even when we added a third qubit with a frequency of 7 GHz, which means that our proposal is scalable. The total gate time is 200 ns, which is much shorter than the coherence time of a flux qubit (4 µs). We estimated FP under decoherence (see Fig. 2). We obtained an FP of 90.3 % under the best conditions yet achieved experimentally: Q=106 and 1=2=0.25 MHz. Even with this realistic decoherence model, FP still exceeds 90 %, showing that our gate remains robust against this type of loss.
@This work was supported by KAKENHI.

[1] J. Clarke and F. K. Wilhelm, Nature 453 (2008) 1031.
[2] S. Saito, T. Tilma, S. J. Devitt, K. Nemoto, and K. Semba, Phys. Rev. B 80 (2009) 224509.
[3] I. L. Chuang and M. A. Nielsen, J. Mod. Opt. 44 (1997) 2455.
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Fig. 1. (a) Superconducting flux-qubit/resonator system.
(b) Pulse sequence of C-NOT gate.
Fig. 2. Process fidelity under decoherence.

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