Superconducting persistent-current qubit

Orlando, Terry P.; Mooij, J. E.; Tian, Lin; Wal, Caspar H. van der; Levitov, L. S.; Lloyd, Seth; Mazo, J. J.

doi:10.1103/physrevb.60.15398

Cited by 707 publications

(900 citation statements)

References 57 publications

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“…12 To illustrate the form of the solutions to the time independent Schrödinger equation for a SQUID ring, using the Hamiltonian ͑2͒, we show in Fig. 2͑a͒ the first four eigenenergies ͑ = 0,1,2,3͒ as a function of external flux ⌽ x for a typical mesoscopic quantum SQUID ring with parameters 12 C s =5ϫ 10 −15 F, ⌳ s =3ϫ 10 −10 H ͑giving a characteristic SQUID ring oscillator frequency of 130 GHz, this is much smaller than the superconducting energy gap in, for example, niobium, that is often used to fabricate SQUID circuits͒ and ប = 0.035⌽ 0 2 / ⌳ s equivalent to a Josephson frequency of 700 GHz, which is not unrealistic when compared to those used by Friedman et al 6 ͑2 THz͒ and Orlando et al 28 ͑2.12 THz͒. These frequencies should be sufficient to avoid thermal excitations for any experiments performed at 40 mK, a temperature easily obtainable in modern dilution refrigerators.…”

Section: Theoretical Modelmentioning

confidence: 92%

Quantum downconversion and multipartite entanglement via a mesoscopic superconducting quantum interference device ring

et al. 2005

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In this paper we study, by analogy with quantum optics, the superconducting quantum interference device ͑SQUID͒ ring mediated quantum mechanical interaction of an input electromagnetic field oscillator mode with two or more output oscillator modes at subintegers of the input frequency. We show that through the nonlinearity of the SQUID ring multiphoton downconversion can take place between the input and output modes with the resultant output photons being created in an entangled state. We also demonstrate that the degree of this entanglement can be adjusted by means of a static magnetic flux which controls the strength of the interaction between these modes via the SQUID ring.

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Section: Theoretical Modelmentioning

confidence: 92%

Quantum downconversion and multipartite entanglement via a mesoscopic superconducting quantum interference device ring

et al. 2005

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“…The WKB approximation allows us to calculate the three-qubit tunneling t 3 a through this doublewell potential. 21,22 Other tunnelings such as single-qubit tunnelings, t 1 a and t 1 b , and two-qubit tunnelings, t 2 a and t 2 b can also be calculated. The tight-binding approximation based on the eight states of three qubits gives the effective Hamiltonian,…”

Section: ͑5͒mentioning

confidence: 99%

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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“…19 Generally, the macroscopic tunneling processes between any two many-qubit states are possible due to the quantum fluctuation originating from the kinetic energy. The offdiagonal components are the macroscopic quantum tunneling amplitudes, i.e., …”

Section: ͑3͒mentioning

confidence: 99%

Macroscopic many-qubit interactions in superconducting flux qubits

Cho¹,

Kim²

2008

Phys. Rev. B

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Superconducting flux qubits are considered to investigate macroscopic many-qubit interactions. Many-qubit states based on current states can be manipulated through the current-phase relation in each superconducting loop. For flux qubit systems comprised of N-qubit loops, a general expression of low-energy Hamiltonian is presented in terms of low-energy levels of qubits and macroscopic quantum tunnelings between the many-qubit states. Many-qubit interactions classified by Ising-type or tunnel exchange interactions can be observable experimentally. Flux qubit systems can provide various artificial-spin systems to study many-body systems that cannot be found naturally. DOI: 10.1103/PhysRevB.77.212506 PACS number͑s͒: 74.50.ϩr, 03.67.Lx, 85.25.Cp It is believed that electrons are interacting in a pair. The interaction is called two-body interaction. Understanding the many-electron effects is one of the most important researches in condensed-matter physics. Normally, rich many-electron physics has been revealed by the two-body interactions of spin pairs in solid-state materials. In a strongly correlated electronic system, however, a low-energy Hamiltonian can involve more than three spin interactions. 1-4 Such multiplespin interactions are known to play a significant role in strongly correlated systems. Some examples include the magnetism of solid 3 He, the high T c superconductivity, and so on. 2,3 Moreover, it is well known theoretically that higher dimensional systems can be mapped to the multiple-spin interaction Hamiltonian of one-dimensional chain unlikely found naturally. 5 The last decade has seen rapidly developing advanced material technologies that make it possible to investigate previously inaccessible quantum systems for quantum information and computation in solid-state systems. Especially, coherent manipulation of quantum states in tunable superconducting devices has enabled to demonstrate macroscopic qubits 6-8 and entangled states of qubits. 9-11 Experimentally, it has been shown that, in terms of pseudospins, different types of exchange interactions between two artificial spins such as an Ising interaction for charge qubits 9 and flux qubits 10,12 and an XY interaction for phase qubits 11 can be realized and controlled by the system parameters. Although different types of solid-state qubit systems have revealed such artificial-spin exchange interactions, multiple artificial-spin interactions have not been demonstrated yet. This Brief Report aims to discuss, in a general framework, how artificial-multiple-spin interactions are possible and realizable in superconducting qubit systems. Flux qubit systems are shown to have an intrinsic property which is multiple artificial-spin interactions. Moreover, controllable system parameters in the flux qubit systems enable to create various types of artificial-spin systems even though a flux qubit system is fabricated experimentally. Then, the manmade superconducting structures of flux qubits can offer experimental simulators for many-body physics in associat...

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Superconducting persistent-current qubit

Cited by 707 publications

References 57 publications

Quantum downconversion and multipartite entanglement via a mesoscopic superconducting quantum interference device ring

Quantum downconversion and multipartite entanglement via a mesoscopic superconducting quantum interference device ring

Macroscopic Greenberger-Horne-Zeilinger andWstates in flux qubits

Macroscopic many-qubit interactions in superconducting flux qubits

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