6,653 research outputs found
Higher-order CIS codes
We introduce {\bf complementary information set codes} of higher-order. A
binary linear code of length and dimension is called a complementary
information set code of order (-CIS code for short) if it has
pairwise disjoint information sets. The duals of such codes permit to reduce
the cost of masking cryptographic algorithms against side-channel attacks. As
in the case of codes for error correction, given the length and the dimension
of a -CIS code, we look for the highest possible minimum distance. In this
paper, this new class of codes is investigated. The existence of good long CIS
codes of order is derived by a counting argument. General constructions
based on cyclic and quasi-cyclic codes and on the building up construction are
given. A formula similar to a mass formula is given. A classification of 3-CIS
codes of length is given. Nonlinear codes better than linear codes are
derived by taking binary images of -codes. A general algorithm based on
Edmonds' basis packing algorithm from matroid theory is developed with the
following property: given a binary linear code of rate it either provides
disjoint information sets or proves that the code is not -CIS. Using
this algorithm, all optimal or best known codes where and are shown to be -CIS for all
such and , except for with and with .Comment: 13 pages; 1 figur
Engineering Fast High-Fidelity Quantum Operations With Constrained Interactions
Understanding how to tailor quantum dynamics to achieve a desired evolution is a crucial problemin almost all quantum technologies. We present a very general method for designing high-efficiencycontrol sequences that are always fully compatible with experimental constraints on available inter-actions and their tunability. Our approach reduces in the end to finding control fields by solvinga set of time-independent linear equations. We illustrate our method by applying it to a numberof physically-relevant problems: the strong-driving limit of a two-level system, fast squeezing in aparametrically driven cavity, the leakage problem in transmon qubit gates, and the acceleration ofSNAP gates in a qubit-cavity system
Measuring a transmon qubit in circuit QED: dressed squeezed states
Using circuit QED, we consider the measurement of a superconducting transmon
qubit via a coupled microwave resonator. For ideally dispersive coupling,
ringing up the resonator produces coherent states with frequencies matched to
transmon energy states. Realistic coupling is not ideally dispersive, however,
so transmon-resonator energy levels hybridize into joint eigenstate ladders of
the Jaynes-Cummings type. Previous work has shown that ringing up the resonator
approximately respects this ladder structure to produce a coherent state in the
eigenbasis (a dressed coherent state). We numerically investigate the validity
of this coherent state approximation to find two primary deviations. First,
resonator ring-up leaks small stray populations into eigenstate ladders
corresponding to different transmon states. Second, within an eigenstate ladder
the transmon nonlinearity shears the coherent state as it evolves. We then show
that the next natural approximation for this sheared state in the eigenbasis is
a dressed squeezed state, and derive simple evolution equations for such states
using a hybrid phase-Fock-space description.Comment: 18 pages, 8 figures; v2 published versio
Complete elimination of information leakage in continuous-variable quantum communication channels
In all lossy communication channels realized to date, information is
inevitably leaked to a potential eavesdropper. Here we present a communication
protocol that does not allow for any information leakage to a potential
eavesdropper in a purely lossy channel. By encoding information into a
restricted Gaussian alphabet of squeezed states we show, both theoretically and
experimentally, that the Holevo information between the eavesdropper and the
intended recipient can be exactly zero in a purely lossy channel while
minimized in a noisy channel. This result is of fundamental interest, but might
also have practical implications in extending the distance of secure quantum
key distribution.Comment: 9 pages, 5 figure
Leak-rate of seals: comparison of theory with experiment
Seals are extremely useful devices to prevent fluid leakage. We present
experimental results for the leak-rate of rubber seals, and compare the results
to a novel theory, which is based on percolation theory and a recently
developed contact mechanics theory. We find good agreement between theory and
experiment.Comment: 6 pages, 10 figure
Steady-state phase diagram of a driven QED-cavity array with cross-Kerr nonlinearities
We study the properties of an array of QED-cavities coupled by nonlinear
elements in the presence of photon leakage and driven by a coherent source. The
main effect of the nonlinear couplings is to provide an effective cross-Kerr
interaction between nearest-neighbor cavities. Additionally, correlated photon
hopping between neighboring cavities arises. We provide a detailed mean-field
analysis of the steady-state phase diagram as a function of the system
parameters, the leakage, and the external driving, and show the emergence of a
number of different quantum phases. A photon crystal associated to a spatial
modulation of the photon blockade appears. The steady state can also display
oscillating behavior and bistability. In some regions the crystalline ordering
may coexist with the oscillating behavior. Furthermore we study the effect of
short-range quantum fluctuations by employing a cluster mean-field analysis.
Focusing on the corrections to the photon crystal boundaries, we show that,
apart for some quantitative differences, the cluster mean field supports the
findings of the simple single-site analysis. In the last part of the paper we
concentrate on the possibility to build up the class of arrays introduced here,
by means of superconducting circuits of existing technology. We consider a
realistic choice of the parameters for this specific implementation and discuss
some properties of the steady-state phase diagram.Comment: 11 pages, 12 figure
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