Superconducting Quantum Circuits, Qubits and Computing

This paper gives an introduction to the physics and principles of operation of quantized superconducting electrical circuits for quantum information processing.Comment: 59 pages 68 figures. Prepared for Handbook of Theoretical and Computational Nanotechnolog

Selective coupling of superconducting qubits via tunable stripline cavity

We theoretically investigate selective coupling of superconducting charge qubits mediated by a superconducting stripline cavity with a tunable resonance frequency. The frequency control is provided by a flux biased dc-SQUID attached to the cavity. Selective entanglement of the qubit states is achieved by sweeping the cavity frequency through the qubit-cavity resonances. The circuit is scalable, and allows to keep the qubits at their optimal points with respect to decoherence during the whole operation. We derive an effective quantum Hamiltonian for the basic, two-qubit-cavity system, and analyze appropriate circuit parameters. We present a protocol for performing Bell inequality measurements, and discuss a composite pulse sequence generating a universal control-phase gate

Current-voltage characteristics of asymmetric double-barrier Josephson junctions

We develop a theory for the current-voltage characteristics of diffusive superconductor-normal metal-superconductor Josephson junctions with resistive interfaces and the distance between the electrodes smaller than the superconducting coherence length. The theory allows for a quantitative analytical and numerical analysis in the whole range of the interface transparencies and asymmetry. We focus on the regime of large interface resistance compared to the resistance of the normal region, when the electron-hole dephasing in the normal region is significant and the finite length of the junction plays a role. In the limit of strong asymmetry we find pronounced current structures at the combination subharmonics of $\Delta+\Delta_g$, where $\Delta_g$ is the proximity minigap in the normal region, in addition to the subharmonics of the energy gap $2\Delta$ in the electrodes. In the limit of rather transparent interfaces, our theory recovers a known formula for the current in a short mesoscopic connector - a convolution of the current through a single-channel point contact with the transparency distribution for an asymmetric double-barrier potential.Comment: 10 pages, 3 figure

Scattering theory of superconductive tunneling in quantum junctions

We present a consistent theory of superconductive tunneling in single-mode junctions within a scattering formulation of Bogoliubov-de Gennes quantum mechanics. Both dc Josephson effect and dc quasiparticle transport in voltage biased junctions are considered. Elastic quasiparticle scattering by the junction determines equilibrium Josephson current. We discuss the origin of Andreev bound states in tunnel junctions and their role in equilibrium Josephson transport. In contrast, quasiparticle tunneling in voltage biased junctions is determined by inelastic scattering. We derive a general expression for inelastic scattering amplitudes and calculate the quasiparticle current at all voltages with emphasis on a discussion of the properties of subgap tunnel current and the nature of subharmonic gap structure.Comment: 47 pages, 9 figures, [preprint,eqsecnum,aps]{revtex

Coherent multiple Andreev reflections and current resonances in SNS junctions

We study coherent multiple Andreev reflections in quantum SNS junctions of finite length and arbitrary transparency. The presence of superconducting bound states in these junctions gives rise to great enhancement of the subgap current. The effect is most pronounced in low-transparency junctions, $D\ll1$, and in the interval of applied voltage $\Delta/2<eV<\Delta$, where the amplitude of the current structures is proportional to the first power of the junction transparency $D$. The resonant current structures consist of steps and oscillations of the two-particle current and also of multiparticle resonance peaks. The positions of the two-particle current structures have pronounced temperature dependence which scales with $\Delta(T)$, while the positions of the multiparticle resonances have weak temperature dependence, being mostly determined by the junction geometry. Despite the large resonant two-particle current, the excess current at large voltage is small and proportional to $D^2$. Pacs: 74.50.+r, 74.80.Fp, 74.20.Fg, 73.23.AdComment: 23 pages, 16 figure

Readout methods and devices for Josephson-junction-based solid-state qubits

We discuss the current situation concerning measurement and readout of Josephson-junction based qubits. In particular we focus attention of dispersive low-dissipation techniques involving reflection of radiation from an oscillator circuit coupled to a qubit, allowing single-shot determination of the state of the qubit. In particular we develop a formalism describing a charge qubit read out by measuring its effective (quantum) capacitance. To exemplify, we also give explicit formulas for the readout time.Comment: 20 pages, 7 figures. To be published in J. Phys.: Condensed Matter, 18 (2006) Special issue: Quantum computin

Circuit Quantum Electrodynamics with a Superconducting Quantum Point Contact

We consider a superconducting quantum point contact in a circuit quantum electrodynamics setup. We study three different configurations, attainable with current technology, where a quantum point contact is coupled galvanically to a coplanar waveguide resonator. Furthermore, we demonstrate that the strong and ultrastrong coupling regimes can be achieved with realistic parameters, allowing the coherent exchange between a superconducting quantum point contact and a quantized intracavity field.Comment: 5 pages, 4 figures. Updated version, accepted for publication as a Rapid Communication in Physical Review

Andreev Level Qubit

We investigate the dynamics of a two-level Andreev bound state system in a transmissive quantum point contact embedded in an rf-SQUID. Coherent coupling of the Andreev levels to the circulating supercurrent allows manipulation and read out of the level states. The two-level Hamiltonian for the Andreev levels is derived, and the effect of interaction with the quantum fluctuations of the induced flux is studied. We also consider an inductive coupling of qubits, and discuss the relevant SQUID parameters for qubit operation and read out.Comment: 4 pages, 1 figur

Non-Makovian decoherence of a two-level system weakly coupled to a bosonic bath

Bloch-Redfield equation is a common tool for studying evolution of qubit systems weakly coupled to environment. We investigate the accuracy of the Born approximation underlying this equation. We find that the high order terms in the perturbative expansion contain accumulating divergences that make straightforward Born approximation inappropriate. We develop diagrammatic technique to formulate, and solve the improved self-consistent Born approximation. This more accurate treatment reveals an exponential time dependent prefactor in the non-Markovian contribution dominating the qubit long-time relaxation found in Phys. Rev. B 71, 035318 (2005). At the same time, the associated dephasing is not affected and is described by the Born-Markov approximation.Comment: To appear in EuroPhys. Let