18,786 research outputs found
A superconducting qubit with Purcell protection and tunable coupling
We present a superconducting qubit for the circuit quantum electrodynamics
architecture that has a tunable coupling strength g. We show that this coupling
strength can be tuned from zero to values that are comparable with other
superconducting qubits. At g = 0 the qubit is in a decoherence free subspace
with respect to spontaneous emission induced by the Purcell effect. Furthermore
we show that in the decoherence free subspace the state of the qubit can still
be measured by either a dispersive shift on the resonance frequency of the
resonator or by a cycling-type measurement.Comment: 4 pages, 3 figure
Global analysis of piecewise linear systems using impact maps and surface Lyapunov functions
This paper presents an entirely new constructive global analysis methodology for a class of hybrid systems known as piecewise linear systems (PLS). This methodology infers global properties of PLS solely by studying the behavior at switching surfaces associated with PLS. The main idea is to analyze impact maps, i.e., maps from one switching surface to the next switching surface. Such maps are known to be "unfriendly" maps in the sense that they are highly nonlinear, multivalued, and not continuous. We found, however, that an impact map induced by an linear time-invariant flow between two switching surfaces can be represented as a linear transformation analytically parametrized by a scalar function of the state. This representation of impact maps allows the search for surface Lyapunov functions (SuLF) to be done by simply solving a semidefinite program, allowing global asymptotic stability, robustness, and performance of limit cycles and equilibrium points of PLS to be efficiently checked. This new analysis methodology has been applied to relay feedback, on/off and saturation systems, where it has shown to be very successful in globally analyzing a large number of examples. In fact, it is still an open problem whether there exists an example with a globally stable limit cycle or equilibrium point that cannot be successfully analyzed with this new methodology. Examples analyzed include systems of relative degree larger than one and of high dimension, for which no other analysis methodology could be applied. This success in globally analyzing certain classes of PLS has shown the power of this new methodology, and suggests its potential toward the analysis of larger and more complex PLS
Differential invariants of generic hyperbolic Monge--Amp\`ere equations
In this paper basic differential invariants of generic hyperbolic
Monge--Amp\`ere equations with respect to contact transformations are
constructed and the equivalence problem for these equations is solved.Comment: 25 page
Concatenated dynamical decoupling with virtual pulses
The loss of quantum information due to interaction with external degrees of
freedom, which is known as decoherence, remains one of the main obstacles for
large-scale implementations of quantum computing. Accordingly, different
measures are being explored for reducing its effect. One of them is dynamical
decoupling (DD) which offers a practical solution because it only requires the
application of control pulses to the system qubits. Starting from basic DD
sequences, more sophisticated schemes were developed that eliminate
higher-order terms of the system-environment interaction and are also more
robust against experimental imperfections. A particularly successful scheme,
called concatenated DD (CDD), gives a recipe for generating higher order
sequences by inserting lower order sequences into the delays of a generating
sequence. Here, we show how this scheme can be improved further by converting
some of the pulses to virtual (and thus ideal) pulses. The resulting scheme,
called vCDD, has lower power deposition and is more robust against pulse
imperfections than the original CDD scheme.Comment: 9 pages, 9 figure
Tunable coupling of superconducting qubits
We study an LC-circuit implemented using a current-biased Josephson junction
(CBJJ) as a tunable coupler for superconducting qubits. By modulating the bias
current, the junction can be tuned in and out of resonance and entangled with
the qubits coupled to it. One can thus implement two-qubit operations by
mediating entanglement. We consider the examples of CBJJ and charge--phase
qubits. A simple recoupling scheme leads to a generalization to arbitrary qubit
designs.Comment: To appear in Phys. Rev. Lett., 3 figure
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