Fast generation of multiparticle entangled state for flux qubits in a circle array of transmission line resonators with tunable coupling

Z. H. Peng, Yu-xi Liu, Y. Nakamura, and J. S. Tsai

Phys. Rev. B 85, 024537 – Published 30 January 2012

Abstract

We study a one-step approach to the fast generation of Greenberger-Horne-Zeilinger (GHZ) states in a circuit QED system with superconducting flux qubits. The GHZ state can be generated in about 10 ns, which is much shorter than the coherence time of flux qubits and comparable with the time of single-qubit operation. In our proposal a time-dependent microwave field is applied to a superconducting transmission line resonator (TLR) and displaces the resonator in a controlled manner, thus inducing indirect qubit-qubit coupling without residual entanglement between the qubits and the resonator. The design of a tunably coupled TLR circle array provides us with the potential for extending this one-step scheme to the case of many qubits coupled via several TLRs.

Received 21 November 2011

DOI:https://doi.org/10.1103/PhysRevB.85.024537

Authors & Affiliations

Z. H. Peng^1,*, Yu-xi Liu^2,3, Y. Nakamura^1,4, and J. S. Tsai^1,4

¹Advanced Science Institute, RIKEN, Wako, Saitama 351-0198, Japan
²Institute of Microelectronics, Tsinghua University, Beijing 100084, China
³Tsinghua National Laboratory for Information Science and Technology (TNList), Tsinghua University, Beijing 100084, China
⁴NEC Green Innovation Research Laboratories, Tsukuba, Ibaraki 305-8501, Japan

^*zhihui_peng@riken.jp

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Vol. 85, Iss. 2 — 1 January 2012

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Images

Figure 1
Schematic description of our setup. (a) The flux qubits are placed around current antinode of the TLR (half wavelength or full wavelength). The red dashed curve illustrates the amplitude of the magnetic field of the half-wavelength TLR. (b) Schematic description of the tunable gap gradiometric flux qubits. The crosses denote Josephson junctions. The qubit is controlled by the bias lines $I_{ɛ}$ and $I_{α}$ . (c) Energy-level diagram of the system. $Δ, ω_{d}, ω_{r}$ are energy gap of the qubits, driving microwave frequency, and fundamental frequency of the cavity mode, respectively. The strong classical driving field denoted by the large arrow resonantly interacts with the flux qubits. We assume that all qubits have the same Rabi frequency $Ω_{R}$ .Reuse & Permissions
Figure 2
Time dependence of the fidelity of the generated entangled state in two flux qubits coupled to one TLR. The following parameters were used: $ω_{r} = 2 π \times$ 10GHz, $Δ = 2 π \times 10.1$ GHz, $g = 2 π \times 50$ MHz, $δ = - 2 π \times 100$ MHz. The target EPR state is $(| + + 〉 + i | - - 〉) / \sqrt{2}$ . (a) The blue solid, red solid, and red dashed curves are simulated using the effective Hamiltonians in Eq. (11) and in Eq. (10) and the full Hamiltonian in Eq. (17), respectively, with the optimized driving strength $Ω = 20 δ$ . (b) Simulation using the full Hamiltonian in Eq. (17) for different driving strengths around the time $t = 2 π / δ = 10$ ns.Reuse & Permissions
Figure 3
Schematic description of flux qubits coupled to two tunably coupled TLRs (half-wavelength or full-wavelength TLRs). $N$ qubits are coupled to the current antinode of the two resonators. A dc-SQUID is placed at the current antinode of the two resonators. The inductive coupling between two resonators could be tuned by changing the biased flux $φ_{e}$ in the symmetric dc-SQUID loop. Two classical microwave fields resonantly interact with $N$ qubits by driving the TLRs. $L_{c}$ , $M_{CA}$ , and $M_{CB}$ are self-inductance of the dc-SQUID coupler loop, mutual inductance between the coupler and Resonator A, and mutual inductance between the coupler and Resonator B, respectively.Reuse & Permissions
Figure 4
Schematic description of a circle array of TLRs coupled by a dc-SQUID. $M$ TLRs are placed as the current antinodes around the coupler. Flux qubits are coupled to the current antinodes of the TLRs.Reuse & Permissions
Figure 5
Time dependence of the fidelity of the generated entangled state for two flux qubits, which are coupled by two coupled TLRs. Here the two qubits are separately coupled to the two TRLs. We set the following parameters for our numerical calculations: $ω_{r} = 2 π \times 10$ GHz, $Δ = 2 π \times 10.12$ GHz, $J = 2 π \times 40$ MHz, $g_{k} = \sqrt{2} J$ , and $δ^{'} = - 3 J$ . The target state is $(| + + 〉 + i | - - 〉) / \sqrt{2}$ . (a) The blue solid and red dashed curves are simulated using the effective Hamiltonian Eq. (30) and the full Hamiltonian in Eq. (34), respectively, with optimized driving strength $Ω_{R} = 42 J$ . (b) Simulation using the full Hamiltonian in Eq. (34) with different driving strengths around the time $t = 2 π / J = 25$ ns.Reuse & Permissions

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