Measurement of the Entanglement of Two Superconducting Qubits via State Tomography

Steffen, Matthias; Ansmann, M.; Bialczak, Radoslaw C.; Katz, Nadav; Lucero, Erik; McDermott, Robert; Neeley, M.; Weig, Eva M.; Cleland, A. N.; Martinis, John M.

doi:10.1126/science.1130886

Cited by 483 publications

(509 citation statements)

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“…For the bipartite entanglement, capacitively coupled phase qubits showed high fidelity in a recent experiment, 9 while for charge qubits, only partial entanglement was observed. The interactions between phase qubits are XY-type interactions, which describe simultaneous two-qubit flipping processes.…”

Section: ͑5͒mentioning

confidence: 99%

“…The quantification of entanglement can be done by using the state tomography measurement. 9,25 Recently, for capacitively coupled phase qubits, the tomography measurement has been done, 9 where they simultaneously measure the state of coupled qubits. For present coupling, we expect that the similar tomography measurement can also be performed.…”

Section: ͑5͒mentioning

confidence: 99%

“…Indeed, the entanglements between two charges, 7 phase, 8,9 and flux qubits 10,11 have been reported. While the timely evolving states in the experiments of charge qubits 7 exhibit a partial entanglement, the excited level ͑eigenstate͒ of capacitively coupled two phase qubits 9 shows higher fidelity for the entanglement. The experiments in Ref.…”

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confidence: 99%

“…Actually, the higher fidelity in the capacitively coupled two phase qubits is caused by the two-qubit tunneling processes. 9 In a very recent study, the two-qubit tunneling process was theoretically shown to play an important role in generating the Bell states, maximally entangled, in the ground and excited states. 12 For multipartite entanglements in superconducting qubit systems, there have been few studies.…”

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Macroscopic Greenberger-Horne-Zeilinger andWstates in flux qubits

Kim

Cho

2008

Phys. Rev. B

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We investigate two types of genuine three-qubit entanglement, known as the Greenberger-Horne-Zeilinger ͑GHZ͒ and W states, in a macroscopic quantum system. Superconducting flux qubits are theoretically considered in order to generate such states. A phase coupling is proposed to offer enough strength of interactions between qubits. While an excited state can be the W state, the GHZ state is formed at the ground state of the three flux qubits. The GHZ and W states are shown to be robust against external flux fluctuations for feasible experimental realizations. As a macroscopic quantum system, superconducting qubit systems have been investigated intensively in experiments because their system parameters can be controlled to manipulate quantum states coherently. Indeed, the entanglements between two charges, 7 phase, 8,9 and flux qubits 10,11 have been reported. While the timely evolving states in the experiments of charge qubits 7 exhibit a partial entanglement, the excited level ͑eigenstate͒ of capacitively coupled two phase qubits 9 shows higher fidelity for the entanglement. The experiments in Ref. 10 show a possibility that two flux qubits can be entangled by a macroscopic quantum tunneling between two-qubit states, flipping both qubits. Actually, the higher fidelity in the capacitively coupled two phase qubits is caused by the two-qubit tunneling processes. 9 In a very recent study, the two-qubit tunneling process was theoretically shown to play an important role in generating the Bell states, maximally entangled, in the ground and excited states. 12 For multipartite entanglements in superconducting qubit systems, there have been few studies. To produce the GHZ state in three charge qubits, only a way of doing a local qubit operation via time evolutions was suggested. 13 As one of the possible directions to produce such multipartite entanglements, then it is natural to ask how to create the W state as well as the GHZ state in the eigenstates of superconducting three-qubit systems. Here, we consider three flux qubits. Normally, the interaction strength between inductively coupled flux qubits 14 is not so strong that the controllable range of interaction is not sufficiently wide. To control a wide range of interaction strengths in the qubits, we use the phase-coupling scheme [15][16][17][18][19] for three qubit ͓see Fig. 1͑a͔͒ which enables one to generate the GHZ and W states and to keep them robust against external flux fluctuations for feasible experimental realizations.We start with the model shown in Fig. 1͑a͒. The Hamiltonian is written by Ĥ = 1 2 P i T M ij −1 P j + U eff ͑ˆ͒, where The periodic boundary conditions involved in the qubit loops and the connecting loops can be written aswhere q = a, b, and c is qubit index and r, s, and n q integers. Here, f q ϵ ⌽ q / ⌽ 0 with external flux ⌽ q and the superconducting unit flux quantum ⌽ 0 = h / 2e. Two independent conditions in Eqs. ͑2͒ and ͑3͒ are the boundary conditions for connecting loops. For simplicity, we consider E J2 = E J3 = E J and C 2 = C 3 = C,...

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Section: ͑5͒mentioning

confidence: 99%

Section: ͑5͒mentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

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Macroscopic Greenberger-Horne-Zeilinger andWstates in flux qubits

Kim

Cho

2008

Phys. Rev. B

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“…Superconducting qubits utilize charge [5][6][7] or flux [8] degrees of freedom, or energy levels quantization in a single current-biased Josephson junction [9,10]. Inter-qubit coupling [15][16][17][18][19][20] and also quantum logic gates [21][22][23] have been reported later. Further progress in the field slowed down due to obvious decoherence issues that are still to be overcome in order to implement a working quantum computer.…”

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Josephson charge qubits: a brief review

Pashkin

Astafiev

Yamamoto

et al. 2009

Quantum Inf Process

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The field of solid-state quantum computation is expanding rapidly initiated by our original charge qubit demonstrations. Various types of solid-state qubits are being studied, and their coherent properties are improving. The goal of this review is to summarize achievements on Josephson charge qubits. We cover the results obtained in our joint group of NEC Nano Electronics Research Laboratories and RIKEN Advanced Science Institute, also referring to the works done by other groups. Starting from a short introduction, we describe the principle of the Josephson charge qubit, its manipulation and readout. We proceed with coupling of two charge qubits and implementation of a logic gate. We also discuss decoherence issues. Finally, we show how a charge qubit can be used as an artificial atom coupled to a resonator to demonstrate lasing action.

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Superconducting Qubits

Il’ichev

Oelsner

2018

Wiley Encyclopedia of Electrical and Electronics Engineering

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Superconducting qubits were initially developed with the goal of realizing a superposition of macroscopically distinct quantum states by exploiting superconducting circuits. This basic idea resulted from the quantum mechanical description of the Josephson junction, the key element for producing superconducting qubits. Because the phase across a Josephson junction and its charge are canonical conjugates, there are two alternative realizations of superconducting qubits. The first one is based on the charge degree of freedom, termed charge qubit. The second utilizes the phase (or flux) degree of freedom and correspondingly are called phase (flux) qubits. Nowadays, the most robust superconducting qubit is the transmon. In practical applications, quantum state initialization and manipulations are heavily restricted by the quantum coherence of the qubit itself and of the qubit‐based systems. The main source of decoherence is interactions with the environment. Their relatively large values result from the macroscopic size of the quantum bits. Still, their circuit architecture enables the implementation of different types of coupling schemes between superconducting qubits and qubit‐resonator systems. The handling of superconducting quantum structures requires special experimental methods, including qubit fabrication, cooling to milliKelvin temperatures, experimental characterization, and readout. Concerning applications, superconducting qubits are promising candidates for both quantum simulators and universal quantum computing. This article covers a description of basic types of superconducting qubits and gives a general description of their use that includes dissipation and decoherence, coupling schemes, experimental realization, and basic measurement techniques. Finally, their use as building blocks for the realization of quantum computation is discussed.

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Measurement of the Entanglement of Two Superconducting Qubits via State Tomography

Cited by 483 publications

References 18 publications

Macroscopic Greenberger-Horne-Zeilinger andWstates in flux qubits

Macroscopic Greenberger-Horne-Zeilinger andWstates in flux qubits

Josephson charge qubits: a brief review

Superconducting Qubits

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