The formation of bound states at surfaces materials with an energy gap in the bulk electron spectrum is a well known physical phenomenon. At superconductor surfaces, quasiparticles energies inside superconducting Δ may be trapped quantum wells, formed by total reflection against vacuum and Andreev superconductor. Since reflects as hole sends Cooper pair into superconductor, surface give rise to resonant transport quasiparticle currents, observed tunnelling spectra. In junctions these...

We have fabricated and characterized tunable superconducting transmission line resonators. To change the resonance frequency, we modify boundary condition at one end of resonator through Josephson inductance a quantum interference device. demonstrate large tuning range (several hundred megahertz), high quality factors (104), that can frequency few-photon field on time scale orders magnitude faster than photon lifetime resonator. This demonstration has implications in variety applications.

Recent demonstrations of macroscopic quantum coherence in Josephson junction based electronic circuits have opened an entirely new dimension for research and applications the established field electronics. In this article we discuss basic qubit applications, methods description these circuits, circuit solutions couplings. Principles manipulation readout superconducting qubits are reviewed illustrated with recent experiments using various types.

We discuss the implementation of an iterative quantum phase estimation algorithm with a single ancillary qubit. suggest using this as benchmark for multiqubit implementations. Furthermore, we describe in detail smallest possible realization, only two qubits, and exemplify superconducting circuit. robustness presence gate errors, show that seven bits precision is obtainable, even very limited accuracies.

We develop a theory of subharmonic gap structure (SGS) in superconducting one-mode tunnel junction. The subgap current is attributed to inelastic multichannel quasiparticle tunneling assisted by the time-dependent phase difference at contact. Opening scattering channels manifested onsets and peaks forming SGS. An explicit analytical expansion found for powers small contact transparency.

We report the observation of photon generation in a microwave cavity with time-dependent boundary condition. Our system is microfabricated quarter-wave coplanar waveguide cavity. The electrical length varied by using tunable inductance superconducting quantum interference device. It measured at temperature significantly less than resonance frequency. When modulated approximately twice static frequency, spontaneous parametric oscillations field are observed. Time-resolved measurements...

We develop a theory of parametric resonance in tunable superconducting cavities. The nonlinearity introduced by the quantum interference device (SQUID) attached to cavity and damping due connection transmission line are taken into consideration. study detail nonlinear classical dynamics field below above threshold for degenerate resonance, featuring regimes multistability radiation. investigate phase-sensitive amplification external signals on as well detuned signals, relate amplifier...

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

We theoretically investigate selective coupling of superconducting charge qubits mediated by a stripline cavity with tunable resonance frequency. The frequency control is provided flux-biased dc quantum interference device attached to the cavity. Selective entanglement qubit states achieved sweeping through qubit-cavity resonances. circuit able accommodate several and allows one keep at their optimal points respect decoherence during whole operation. derive an effective Hamiltonian for...

Abstract We propose and demonstrate a read-out technique for superconducting qubit by dispersively coupling it with Josephson parametric oscillator. employ tunable quarter wavelength resonator modulate its resonant frequency at twice value an amplitude surpassing the threshold instability. map states onto two distinct of classical oscillation: one oscillating state, 185±15 photons in resonator, zero oscillation amplitude. This high contrast obviates following quantum-limited amplifier....

We have developed and measured a high-gain quantum-limited microwave parametric amplifier based on superconducting lumped LC resonator with the inductor L including an array of eight quantum interference devices (SQUIDs). This is parametrically pumped by modulating flux threading SQUIDs at twice frequency. Around 5 GHz, maximum gain 31 dB, product amplitude $\ifmmode\times\else\texttimes\fi{}$ bandwidth above 60 MHz, 1 dB compression point $\ensuremath{-}123$ dBm 20 are obtained in...

We present an extensive experimental and theoretical study of the proximity effect in InAs nanowires connected to superconducting electrodes. fabricate investigate devices with suspended gate-controlled nonsuspended nanowires, a broad range lengths normal-state resistances. analyze main features current-voltage characteristics: Josephson current, excess subgap current as functions length, temperature, magnetic field, gate voltage, compare them theory. The critical for short-length device, L...

Exploiting multiple modes in a quantum acoustic device could enable applications information hardware-efficient setup, including simulation synthetic dimension and continuous-variable computing with cluster states.We develop multimode surface wave (SAW) resonator superconducting interference (SQUID) integrated one of the Bragg reflectors. The interaction SQUID-shunted mirror gives rise to coupling between more than 20 accessible modes. We exploit this demonstrate two-mode squeezing SAW...

We report on the implementation of a near-quantum-limited, traveling-wave parametric amplifier that uses three-wave mixing (3WM). To favor amplification by 3WM, we use superconducting nonlinear asymmetric inductive element (SNAIL) loops, biased with dc magnetic flux. In addition, equip device dispersion engineering features to create stopband at second harmonic pump and suppress propagation higher harmonics otherwise degrade amplification. With chain 440 SNAILs, provides up 20 dB gain 3-dB...

We present the first measurements of viscosity superfluid ${}^{3}\mathrm{He}$ in magnetic fields up to $15\mathrm{T}$, at temperatures down $2\mathrm{mK}$ along melting curve, using an assumption for temperature dependence normal density. At higher than $4\mathrm{T}$, shows a minimum ${A}_{1}$ phase, and reaches local maximum ${A}_{2}$ transition which becomes global $14.6\mathrm{T}$. The sharp decrease just below can be understood within Ginzburg-Landau framework is consistent with both...

In highly resistive superconducting tunnel junctions, excess subgap current is usually observed and often attributed to microscopic pinholes in the barrier. We have studied superconductor--insulator--superconductor (SIS) superconductor--insulator--normal-metal (SIN) junctions. $\mathrm{Al}/{\mathrm{AlO}}_{x}/\mathrm{Al}$ we a decrease of 2 orders magnitude upon transition from SIS SIN regime, where it then matched theory. $\mathrm{Al}/{\mathrm{AlO}}_{x}/\mathrm{Cu}$ also generic features...

We review recent advances in the research on quantum parametric phenomena superconducting circuits with Josephson junctions. discuss physical processes parametrically driven tunable cavity and outline theoretical foundations for their description. Amplification frequency conversion are discussed detail degenerate nondegenerate resonance, including noise squeezing photon entanglement. Experimental this area played decisive role successful development of limited amplifiers information...

Near-term quantum computers are limited by the decoherence of qubits to only being able run low-depth circuits with acceptable fidelity. This severely restricts what algorithms can be compiled and implemented on such devices. One way overcome these limitations is expand available gate set from single- two-qubit gates multi-qubit gates, which entangle three or more in a single step. Here, we show that realized simultaneous application multiple group where at least one qubit involved two...

Single-atom junctions between superconducting niobium leads are produced using the mechanically controllable break junction technique. The current-voltage characteristics of these analyzed an exact formulation for a quantum point contact. For tunneling two single atoms with sufficiently large vacuum barrier, it is found that channel dominates current, and characteristic described by theory, without adjustable parameters. contact Nb atom shown five conductance channels contribute to...

We experimentally study the behavior of a parametrically pumped nonlinear oscillator, which is based on superconducting \lambda /4 resonator, and terminated by flux-tunable SQUID. extract parameters for two devices. In particular, we effect nonlinearities in system compare to theory. The Duffing nonlinearity, \alpha, determined from probe-power dependent frequency shift \beta, related parametric flux pumping, pump amplitude onset oscillations. Both depend device can be tuned in-situ applied...

We report on the experimental observation of period multiplication in parametrically driven tunable superconducting resonators. modulate magnetic flux through a quantum interference device, attached to quarter-wavelength resonator, with frequencies nω close multiples, n = 2, 3, 4, and 5, resonator fundamental mode observe intense output radiation at ω. The field manifests n-fold degeneracy respect phase, states are phase shifted by 2π/n each other. Our demonstration verifies theoretical...

We have observed period-tripling subharmonic oscillations, in a superconducting coplanar waveguide resonator operated the quantum regime, $k_B T \ll \hbarω$. The is terminated by tunable inductance that provides Kerr-type nonlinearity. detected output field quadratures at frequencies near fundamental mode, $ω/2π\sim 5\,$GHz, when was driven current $3ω$ with an amplitude exceeding instability threshold. radiation red-detuned from mode. three stable radiative states equal amplitudes and...

We present a detailed theory for the Andreev level qubit, system consisting of highly transmissive quantum point contact embedded in superconducting loop. The two-level Hamiltonian levels interacting with phase fluctuations is derived by using path integral method. also derive kinetic equation describing qubit decoherence due to interaction acoustic phonons. collision terms are nonlinear fermionic nature states, leading slow nonexponential relaxation and dephasing at temperatures smaller...

We report conductance and supercurrent of InAs nanowires coupled to Al-superconducting electrodes with short channel lengths good Ohmic contacts. The are suspended 15 nm above a local gate electrode. charge density in the can be controlled by small change voltage. For large negative voltages, number conducting channels is reduced gradually, we observe stepwise decrease both critical current before vanishes completely.

We characterize a novel Josephson parametric amplifier based on flux-tunable quarter-wavelength resonator. The fundamental resonance frequency is ~1GHz, but we use higher modes of the resonator for our measurements. An on-chip tuning line allows magnetic flux pumping amplifier. investigate and compare degenerate amplification, involving single mode, nondegenerate using pair modes. show that reach quantum-limited noise performance in both cases, added can be less than 0.5 photons case low gain.