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

Shiro Saito, Todd Tilma ^{*}, Simon J. Devitt^{*}, Kae Nemoto^{*}, and Kouichi Semba

Physical Science Laboratory,^{*}National Institute of InformaticsSuperconducting 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

F_{P}[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 inductanceM. 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 (π/2, π) and a phase (0, π,φ) from the top to the bottom. We obtained anF_{P}of 98.8 % by optimizing the free evolution time T and the phase of the second BSB pulseφ. 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 highF_{P}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 estimatedF_{P}under decoherence (see Fig. 2). We obtained anF_{P}of 90.3 % under the best conditions yet achieved experimentally: Q=10^{6}and Γ_{1}=Γ_{2}=0.25 MHz. Even with this realistic decoherence model,F_{P}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. B80(2009) 224509.

[3] I. L. Chuang and M. A. Nielsen, J. Mod. Opt.44(1997) 2455.

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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