Article

# Measurement of the entanglement of two superconducting qubits via state tomography.

Department of Physics and California Nano Systems Institute, University of California, Santa Barbara, CA 93106, USA.

Science (Impact Factor: 31.48). 10/2006; 313(5792):1423-5. DOI: 10.1126/science.1130886 Source: PubMed

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**ABSTRACT:**Majorana fermions are long-sought exotic particles that are their own antiparticles. Here we propose to utilize superconducting circuits to construct two superconducting-qubit arrays where Majorana modes can occur. A so-called Majorana qubit is encoded by using the unpaired Majorana modes, which emerge at the left and right ends of the chain in the Majorana-fermion representation. We also show this Majorana qubit in the spin representation and its advantage, over a single superconducting qubit, regarding quantum coherence. Moreover, we propose to use four superconducting qubits as the smallest system to demonstrate the braiding of Majorana modes and show how the states before and after braiding Majoranas can be discriminated.Scientific reports. 01/2014; 4:5535. - [Show abstract] [Hide abstract]

**ABSTRACT:**We propose a superconducting phase qubit on the basis of the radio-frequency SQUID with the screening parameter value βL ≡ (2π/Φ0)LIc ≈ 1, biased by a half flux quantum Φe = Φ0/2. Significant anharmonicity (> 30%) can be achieved in this system due to the interplay of the cosine Josephson potential and the parabolic magnetic-energy potential that ultimately leads to the quartic polynomial shape of the well. The two lowest eigenstates in this global minimum perfectly suit for the qubit which is insensitive to the charge variable, biased in the optimal point and allows an efficient dispersive readout. Moreover, the transition frequency in this qubit can be tuned within an appreciable range allowing variable qubit-qubit coupling. The superconducting qubits based on the Josephson tunnel junctions (see, e.g., the reviews in Refs. [1, 2]) have already demonstrated their great potential for the quantum computation [3]. The so-called phase qubits present the class of devices which are particularly suitable for integration with microwave on-chip transmission lines and resonators, i.e. the elements which significantly ex-tend the scope of the quantum circuit designs [4]. These qubits are based on the energy quantization in the shal-low wells of the inclined cosine Josephson potential [5]. This shape is ensured either by finite bias current I s with the value slightly below the critical current of the Joseph-son junction I c or a finite flux bias Φ e applied to the qubit loop (in the case of a loop configuration of the circuit) [6]. In both cases, the energy potential can be approximated by the cubic parabola with a smooth energy barrier iso-lating the well from one side and allowing escape out of this well enabling a simple readout. The low depth of the cubic parabola well leads to an-harmonicity, viz. successive reduction of the transition energies ∆E n = (E n+1 − E n), n = 0, 1, ..., from bottom to top, necessary for the qubit operation within the basis states |n = 0 and |n = 1 excluding unwanted excitation of the higher energy states (n > 1). Usually the phase qubit is designed such that for appropriate phase bias the cubic potential well includes three-four energy levels with anharmonicity of a few per cent [2, 6]. This is achieved by adjusting the plasma frequency of the Josephson junction both by designing appropriate parameters of the junction and, possibly, by applying external capacitor shunting. The lowering of the energy barrier by applying the so-called measuring pulse, makes possible the reduction of the number of the levels to two (n = 0 and 1), with no-tably different rates of escape to a running-phase state (in the case of current bias), or to the lower-energy state in the adjacent well (in the case of the loop configuration of the qubit). The large (but finite) difference of these tun-neling rates sets the maximum theoretical value for the fidelity of such measurement to 96.6%. In the carefullyPhysical Review B 12/2009; 80(21):214535. · 3.66 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**We suggest that experiments based on Josephson junctions, SQUIDS, and coupled Josephson qubits may be used to construct a resonant environment for dark matter axions. We propose experimental setups in which axionic interaction strengths in a Josephson junction environment can be tested, similar in nature to recent experiments that test for quantum entanglement of two coupled Josephson qubits. We point out that the parameter values relevant for early-universe axion cosmology are accessible with present day's achievements in nanotechnology. We work out how typical dark matter and dark energy signals would look like in a novel detector that exploits this effect.Modern Physics Letters A 01/2012; 26(38). · 1.34 Impact Factor

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