Here we report on the production and tomography of genuinely entangled Greenberger-Horne-Zeilinger states with up to ten qubits connecting to a bus resonator in a superconducting circuit, where the resonator-mediated qubit-qubit interactions are used to controllably entangle multiple qubits and to operate on different pairs of qubits in parallel. The resulting 10-qubit density matrix is probed by quantum state tomography, with a fidelity of 0.668±0.025. Our results demonstrate the largest entanglement created so far in solid-state architectures and pave the way to large-scale quantum computation.

A rf-superconducting quantum interference device ͑SQUID͒ flux qubit that is robust against fabrication variations in Josephson-junction critical currents and device inductance has been implemented. Measurements of the persistent current and of the tunneling energy between the two lowest-lying states, both in the coherent and incoherent regimes, are presented. These experimental results are shown to be in agreement with predictions of a quantum-mechanical Hamiltonian whose parameters were independently calibrated, thus justifying the identification of this device as a flux qubit. In addition, measurements of the flux and critical current noise spectral densities are presented that indicate that these devices with Nb wiring are comparable to the best Al wiring rf SQUIDs reported in the literature thus far, with a 1 / f flux noise spectral density at 1 Hz of 1.3 −0.5 +0.7 ⌽ 0 / ͱ Hz. An explicit formula for converting the observed flux noise spectral density into a freeinduction-decay time for a flux qubit biased to its optimal point and operated in the energy eigenbasis is presented. I. MOTIVATIONExperimental efforts to develop useful solid-state quantum information processors have encountered a host of practical problems that have substantially limited progress. While the desire to reduce noise in solid-state qubits appears to be the key factor that drives much of the recent work in this field, it must be acknowledged that there are formidable challenges related to architecture, circuit density, fabrication variation, calibration, and control that also deserve attention. For example, a qubit that is inherently exponentially sensitive to fabrication variations with no recourse for in situ correction holds little promise in any large-scale architecture, even with the best of modern fabrication facilities. Likewise, a qubit that requires an inordinate number of custom-tuned time-dependent control signals to be launched onto the chip, in order to correct for fabrication variations or to compensate for unintended on-chip crosstalk, would also not be useful in a large-scale processor. Thus, a qubit designed in the absence of information concerning its ultimate use in a larger-scale system may prove to be of little utility in the future. In what follows, we present an experimental demonstration of a superconducting flux qubit 1 that has been specifically designed to address several issues that pertain to the implementation of a large-scale quantum information processor. While noise is not the central focus of this paper, we nonetheless present experimental evidence that, despite its physical size and relative complexity, the observed flux noise in this flux qubit is comparable to the quietest such devices reported on in the literature to date.It has been well established that rf superconducting quantum interference devices ͑SQUIDs͒ can be used as qubits given an appropriate choice of device parameters. Such devices can be operated as a flux-biased phase qubit using two intrawell energy levels 2 or as a flux qubit using...

We report the first observation of resonant tunneling of a system between two macroscopically distinct states: energy levels in different Auxoid wells of a weakly damped superconducting quantum interference device which differ in mean current by approximately 6 p, A. Near 50 mK, the tunneling rate I (4,) from the metastable well vs applied Ilux &9, is found to exhibit a series of local maxima where the levels (spaced by =1.9 K) in the two wells cross. The positions of these maxima agree well with the level crossings calculated using independently determined system parameters. PACS numbers: 74.50.+r, 73.40.Gk Throughout the history of quantum mechanics, there have been a series of paradoxes resulting from attempts to reconcile the description of nature at the microscopic level with everyday observations of macroscopic objects. While many explanations have been proposed, the dilemma remains in the minds of many [1,2]. It is of some interest then to try to observe quantum effects, familiar in the microscopic world, in variables describing macroscopically distinct states. Josephson junctions, along with the superconducting quantum interference device (SQUID), have proven to be excellent systems for such investigations. The IIux 4 linking the SQUID (or the phase difference across a current biased junction) describes the collective motion of a macroscopic number of particles and yet manifests quantum behavior at accessible temperatures. Further, it is possible to characterize these systems very well, permitting quantitative comparison with theory. Tunneling of these macroscopic variables to the continuum (MQT) [3 -7] has been widely studied and generally found to be in excellent agreement with theory. Level quantization within a well has been observed [8], again agreeing with theory [9,10]. However, answers to more fundamental questions (including macroscopic quantum coherence [1]) require measurements of the behavior of systems involving transitions between macroscopically distinct, discrete final and initial states. Extensive theoretical analysis of such transitions has been done using the two state approximation to the SQUID [11,12].These predict that, under conditions of low damping and temperature, 4 should display the quantum interference behavior familiar for microscopic systems. The limited experimental work on such systems has tended to confirm these predictions in the higher damping regime where evidence for discrete final states is indirect [13]. Recently reported results on magnetic systems have been interpreted in terms of macroscopic quantum behavior [14]. However, there is currently substantial controversy as to the interpretation of the results that, it is argued, differ markedly from theory [15]. In this Letter, we report the observation of resonances in the tunneling rate of the fiux between two macroscopically distinct Iluxoid wells of a SQUID when the ground state of the upper well is aligned with an excited state in the lower well. We refer to this phenomenon, in which the quantized final and in...

We investigate the experimental feasibility of realizing quantum information transfer (QIT) and entanglement with SQUID qubits in a microwave cavity via dark states. Realistic system parameters are presented. Our results show that QIT and entanglement with two-SQUID qubits can be achieved with a high fidelity. The present scheme is tolerant to device parameter nonuniformity. We also show that the strong coupling limit can be achieved with SQUID qubits in a microwave cavity. Thus, cavity-SQUID systems provide a new way for production of nonclassical microwave source and quantum communication. DOI: 10.1103/PhysRevLett.92.117902 PACS numbers: 03.67.Lx, 03.67.Mn, 42.50.Dv, 85.25.Dq Superconducting devices including single Cooper pair boxes, Josephson junctions, and superconducting quantum interference devices (SQUIDs) [1][2][3][4][5][6][7][8][9][10] have appeared to be among the most promising candidates for quantum information processing. Superconducting qubits are relatively easy to scale up and have been demonstrated to have a long decoherence time [10 -12]. In past years, many methods for demonstrating macroscopic coherence in SQUIDs [5] or performing a single-''SQUID qubit'' operation [6 -10] have been presented. Recently, spectroscopy evidence of entanglement in two charge qubits or Josephson junctions has also been reported [13,14]. However, how to obtain a two-SQUID qubit operation, which is the key ingredient for any quantum computing algorithms, has not been thoroughly investigated.In this Letter, we discuss how quantum information transfer (QIT) and entanglement can be achieved with two-SQUID qubits in cavity QED via dark states, and then we give a detailed analysis on the experimental feasibility. This proposal has advantages: (i) Because the population in the level jai (defined below) is minimized, spontaneous emission from this level is greatly suppressed and thus QIT and entanglement can be realized with a high fidelity. (ii) No tunneling between the SQUID qubit levels j0i and j1i is required; therefore decay from the level j1i can be made negligibly small during the operation, via adjusting the potential barrier. (iii) Since the cavity mode acts as a ''bus'' and can mediate long range, fast interaction between distant SQUID qubits, the cavity-based scheme is simpler than the noncavity schemes where significant resources may be needed to couple distant SQUID qubits. (iv) SQUIDs are sensitive to environment. By placing SQUIDs into a superconducting cavity, decoherence caused by external environment is greatly suppressed because the cavity can be doubled as a magnetic shield for SQUIDs. (v) Level structure of each individual SQUID qubit can be adjusted by either design variations and/or changing local bias field. Hence, coupling between microwave pulse and any particular SQUID qubit can be obtained selectively via frequency matching. (vi) The position of SQUID qubits in a cavity is fixed while for cavity-atom systems it remains a significant technical challenge to control the center of mass motion o...

We present a way to teleport multiqubit quantum information from a sender to a distant receiver via the control of many agents in a network. We show that the original state of each qubit can be restored by the receiver as long as all the agents collaborate. However, even if one agent does not cooperate, the receiver cannot fully recover the original state of each qubit. The method operates essentially through entangling quantum information during teleportation, in such a way that the required auxiliary qubit resources, local operation, and classical communication are considerably reduced for the present purpose.

We present a scheme to achieve maximally entangled states, controlled phase-shift gate, and SWAP gate for two superconducting-quantum-interference-device ͑SQUID͒ qubits, by placing SQUIDs in a microwave cavity. We also show how to transfer quantum information from one SQUID qubit to another. In this scheme, no transfer of quantum information between the SQUIDs and the cavity is required, the cavity field is only virtually excited and thus the requirement on the quality factor of the cavity is greatly relaxed.

An improved tunable coupling element for building networks of coupled rf-superconducting quantum interference device ͑rf-SQUID͒ flux qubits has been experimentally demonstrated. This new form of coupler, based on the compound Josephson-junction rf-SQUID, provides a sign and magnitude tunable mutual inductance between qubits with minimal nonlinear crosstalk from the coupler tuning parameter into the qubits. Quantitative agreement is shown between an effective one-dimensional model of the coupler's potential and measurements of the coupler persistent current and susceptibility. The choice of architecture of a prototype solid-state quantum information processor is primarily driven by the algorithm that the designer wishes to implement. Within the field of superconducting quantum devices at least two distinct architectures have arisen. Gate model algorithms require qubits with long-lived excited states and dynamic couplings. Recent efforts have focused upon chargelike 1 and phase 2 qubits coupled to microwave resonators. Adiabatic quantum algorithms 3,4 require qubits whose ground state encode binary variables and static couplings. One implementation involves a network of inductively coupled flux qubits. 5 The Hamiltonian for this architecture is that of a quantum Ising spin glass,where ⑀ i ϵ 2͉I i p ͉⌽ i x and ⌬ i are the bias and tunneling energy of qubit i, respectively, and J ij ϵ M ij ͉I i p ͉͉I j p ͉ is the coupling energy between qubits i and j. Here, ͉I i p ͉ represents the magnitude of the qubit persistent current, ⌽ i x is an external flux bias and M ij is a mutual inductance. A programmable processor would require in situ tunable ⌽ i x and M ij . Inductive coupling could also be useful in other quantum computation schemes in which the flux qubit's persistent current basis is nearly concurrent with the computation basis. 6 More involved parametric coupling schemes are needed if the flux qubits are biased to their optimal points where the energy and persistent current bases are orthogonal. 7 Maassen van den Brink et al. 8 proposed the use of an rf-superconducting quantum interference device ͑rf-SQUID͒ to implement tunable M ij . Experiments on systems of coupled flux qubits verified that such couplers did perform as anticipated. 9 However, additional work not reported in the literature revealed two serious deficiencies: first, the tuning mechanism involves threading flux through the rf-SQUID loop, thus inducing a large persistent current I p that, in turn, biases the qubits. This is a significant problem if the qubit biases need to be controlled to high precision atop what can be a very large nonlinear crosstalk imparted by the coupler. Second, M ij = 0 can only be achieved if ␤ ϵ 2 LI c / ⌽ 0 Ͻ 1, where L and I c are the rf-SQUID inductance and critical current, respectively. On the other hand, in order to achieve appreciable nonzero coupling it proved necessary to design devices with ␤ տ 0.9. Such devices were acutely sensitive to fabrication variations, where higher than expected I c could make M ij = 0 ...

A three-level scheme for implementing single-qubit operations in superconducting quantum interference devices is proposed and analyzed. We show that, compared with the conventional two-level scheme, the proposed three-level qubit scheme is much faster and has a much lower intrinsic error rate.