A simple all-microwave entangling gate for fixed-frequency superconducting qubits

We demonstrate an all-microwave two-qubit gate on superconducting qubits which are fixed in frequency at optimal bias points. The gate requires no additional subcircuitry and is tunable via the amplitude of microwave irradiation on one qubit at the transition frequency of the other. We use the gate to generate entangled states with a maximal extracted concurrence of 0.88 and quantum process tomography reveals a gate fidelity of 81%

Response of thin-film SQUIDs to applied fields and vortex fields: Linear SQUIDs

In this paper we analyze the properties of a dc SQUID when the London penetration depth \lambda is larger than the superconducting film thickness d. We present equations that govern the static behavior for arbitrary values of \Lambda = \lambda^2/d relative to the linear dimensions of the SQUID. The SQUID's critical current I_c depends upon the effective flux \Phi, the magnetic flux through a contour surrounding the central hole plus a term proportional to the line integral of the current density around this contour. While it is well known that the SQUID inductance depends upon \Lambda, we show here that the focusing of magnetic flux from applied fields and vortex-generated fields into the central hole of the SQUID also depends upon \Lambda. We apply this formalism to the simplest case of a linear SQUID of width 2w, consisting of a coplanar pair of long superconducting strips of separation 2a, connected by two small Josephson junctions to a superconducting current-input lead at one end and by a superconducting lead at the other end. The central region of this SQUID shares many properties with a superconducting coplanar stripline. We calculate magnetic-field and current-density profiles, the inductance (including both geometric and kinetic inductances), magnetic moments, and the effective area as a function of \Lambda/w and a/w.Comment: 18 pages, 20 figures, revised for Phys. Rev. B, the main revisions being to denote the effective flux by \Phi rather than

The Use of Resources in Resource Acquisition

The author considers the processes through which a firm can acquire resources and argues that its current stock of resources create asymmetries in competition for new resources. Two simple models illustrate how this can work through linkages on the demand and/or cost side. The normative implication is that firms should expand their resource portfolios by building on their existing resources; different firms will then acquire different new resources, and small initial heterogeneities will amplify over time

Efficient measurement of quantum gate error by interleaved randomized benchmarking

We describe a scalable experimental protocol for obtaining estimates of the error rate of individual quantum computational gates. This protocol, in which random Clifford gates are interleaved between a gate of interest, provides a bounded estimate of the average error of the gate under test so long as the average variation of the noise affecting the full set of Clifford gates is small. This technique takes into account both state preparation and measurement errors and is scalable in the number of qubits. We apply this protocol to a superconducting qubit system and find gate errors that compare favorably with the gate errors extracted via quantum process tomography.Comment: 5 pages, 2 figures, published versio

Self-aligned nanoscale SQUID on a tip

A nanometer-sized superconducting quantum interference device (nanoSQUID) is fabricated on the apex of a sharp quartz tip and integrated into a scanning SQUID microscope. A simple self-aligned fabrication method results in nanoSQUIDs with diameters down to 100 nm with no lithographic processing. An aluminum nanoSQUID with an effective area of 0.034 $\mu$m$^2$ displays flux sensitivity of 1.8$\cdot 10^{-6}$ $\Phi_0/\mathrm{Hz}^{1/2} and operates in fields as high as 0.6 T. With projected spin sensitivity of 65$\mu_B/\mathrm{Hz}^{1/2}$ and high bandwidth, the SQUID on a tip is a highly promising probe for nanoscale magnetic imaging and spectroscopy.Comment: 14 manuscript pages, 5 figure

Theory of Type-II Superconductors with Finite London Penetration Depth

Previous continuum theory of type-II superconductors of various shapes with and without vortex pinning in an applied magnetic field and with transport current, is generalized to account for a finite London penetration depth lambda. This extension is particularly important at low inductions B, where the transition to the Meissner state is now described correctly, and for films with thickness comparable to or smaller than lambda. The finite width of the surface layer with screening currents and the correct dc and ac responses in various geometries follow naturally from an equation of motion for the current density in which the integral kernel now accounts for finite lambda. New geometries considered here are thick and thin strips with applied current, and `washers', i.e. thin film squares with a slot and central hole as used for SQUIDs.Comment: 14 pages, including 15 high-resolution figure