723 research outputs found
Robust Quantum Error Correction via Convex Optimization
We present a semidefinite program optimization approach to quantum error
correction that yields codes and recovery procedures that are robust against
significant variations in the noise channel. Our approach allows us to optimize
the encoding, recovery, or both, and is amenable to approximations that
significantly improve computational cost while retaining fidelity. We
illustrate our theory numerically for optimized 5-qubit codes, using the
standard [5,1,3] code as a benchmark. Our optimized encoding and recovery
yields fidelities that are uniformly higher by 1-2 orders of magnitude against
random unitary weight-2 errors compared to the [5,1,3] code with standard
recovery. We observe similar improvement for a 4-qubit decoherence-free
subspace code.Comment: 4 pages, including 3 figures. v2: new example
Phase Diagrams for the = 1/2 Fractional Quantum Hall Effect in Electron Systems Confined to Symmetric, Wide GaAs Quantum Wells
We report an experimental investigation of fractional quantum Hall effect
(FQHE) at the even-denominator Landau level filling factor = 1/2 in very
high quality wide GaAs quantum wells, and at very high magnetic fields up to 45
T. The quasi-two-dimensional electron systems we study are confined to GaAs
quantum wells with widths ranging from 41 to 96 nm and have variable
densities in the range of to cm. We present several experimental phase diagrams for the
stability of the FQHE in these quantum wells. In general, for a given
, the 1/2 FQHE is stable in a limited range of intermediate densities where
it has a bilayer-like charge distribution; it makes a transition to a
compressible phase at low densities and to an insulating phase at high
densities. The densities at which the FQHE is stable are larger for
narrower quantum wells. Moreover, even a slight charge distribution asymmetry
destabilizes the FQHE and turns the electron system into a
compressible state. We also present a plot of the symmetric-to-antisymmetric
subband separation (), which characterizes the inter-layer
tunneling, vs density for various . This plot reveals that at
the boundary between the compressible and FQHE phases increases
\textit{linearly} with density for all the samples. Finally, we summarize the
experimental data in a diagram that takes into account the relative strengths
of the inter-layer and intra-layer Coulomb interactions and . We
conclude that, consistent with the conclusions of some of the previous studies,
the FQHE observed in wide GaAs quantum wells with symmetric charge
distribution is stabilized by a delicate balance between the inter-layer and
intra-layer interactions, and is very likely described by a two-component
() state.Comment: Accepted for publication in Phys. Rev.
Anisotropic low-temperature piezoresistance in (311)A GaAs two-dimensional holes
We report low-temperature resistance measurements in a modulation-doped,
(311)A GaAs two-dimensional hole system as a function of applied in-plane
strain. The data reveal a strong but anisotropic piezoresistance whose
magnitude depends on the density as well as the direction along which the
resistance is measured. At a density of cm and for a
strain of about applied along [01], e.g., the
resistance measured along this direction changes by nearly a factor of two
while the resistance change in the [33] direction is less than 10% and
has the opposite sign. Our accurate energy band calculations indicate a
pronounced and anisotropic deformation of the heavy-hole dispersion with
strain, qualitatively consistent with the experimental data. The extremely
anisotropic magnitude of the piezoresistance, however, lacks a quantitative
explanation.Comment: 4 pages. Submitted to Applied Physics Letter
Correlated errors can lead to better performance of quantum codes
A formulation for evaluating the performance of quantum error correcting
codes for a general error model is presented. In this formulation, the
correlation between errors is quantified by a Hamiltonian description of the
noise process. We classify correlated errors using the system-bath interaction:
local versus nonlocal and two-body versus many-body interactions. In
particular, we consider Calderbank-Shor-Steane codes and observe a better
performance in the presence of correlated errors depending on the timing of the
error recovery. We also find this timing to be an important factor in the
design of a coding system for achieving higher fidelities.Comment: 5 pages, 3 figures. Replaced by the published version. Title change
Multicomponent fractional quantum Hall states with subband and spin degrees of freedom
In wide GaAs quantum wells where two electric subbands are occupied we apply
a parallel magnetic field or increase the electron density to cause a crossing
of the two Landau levels of these subbands and with opposite spins. Near
the crossing, the fractional quantum Hall states in the filling factor range
exhibit a remarkable sequence of pseudospin polarization transitions
resulting from the interplay between the spin and subband degrees of freedom.
The field positions of the transitions yield a new and quantitative measure of
the composite Fermions' discrete energy level separations. Surprisingly, the
separations are smaller when the electrons have higher spin-polarization
Local Estimates for the Koornwinder Jacobi-Type Polynomials
In this paper we give some local estimates for the Koornwinder Jacobi-type polynomials by using asymptotic properties of Jacobi orthogonal polynomials
Superconducting, Insulating, and Anomalous Metallic Regimes in a Gated Two-Dimensional Semiconductor-Superconductor Array
The superconductor-insulator transition in two dimensions has been widely
investigated as a paradigmatic quantum phase transition. The topic remains
controversial, however, because many experiments exhibit a metallic regime with
saturating low-temperature resistance, at odds with conventional theory. Here,
we explore this transition in a novel, highly controllable system, a
semiconductor heterostructure with epitaxial Al, patterned to form a regular
array of superconducting islands connected by a gateable quantum well. Spanning
nine orders of magnitude in resistance, the system exhibits regimes of
superconducting, metallic, and insulating behavior, along with signatures of
flux commensurability and vortex penetration. An in-plane magnetic field
eliminates the metallic regime, restoring the direct superconductor-insulator
transition, and improves scaling, while strongly altering the scaling exponent
Jump-diffusion unravelling of a non Markovian generalized Lindblad master equation
The "correlated-projection technique" has been successfully applied to derive
a large class of highly non Markovian dynamics, the so called non Markovian
generalized Lindblad type equations or Lindblad rate equations. In this
article, general unravellings are presented for these equations, described in
terms of jump-diffusion stochastic differential equations for wave functions.
We show also that the proposed unravelling can be interpreted in terms of
measurements continuous in time, but with some conceptual restrictions. The
main point in the measurement interpretation is that the structure itself of
the underlying mathematical theory poses restrictions on what can be considered
as observable and what is not; such restrictions can be seen as the effect of
some kind of superselection rule. Finally, we develop a concrete example and we
discuss possible effects on the heterodyne spectrum of a two-level system due
to a structured thermal-like bath with memory.Comment: 23 page
Efficient estimation of nearly sparse many-body quantum Hamiltonians
We develop an efficient and robust approach to Hamiltonian identification for
multipartite quantum systems based on the method of compressed sensing. This
work demonstrates that with only O(s log(d)) experimental configurations,
consisting of random local preparations and measurements, one can estimate the
Hamiltonian of a d-dimensional system, provided that the Hamiltonian is nearly
s-sparse in a known basis. We numerically simulate the performance of this
algorithm for three- and four-body interactions in spin-coupled quantum dots
and atoms in optical lattices. Furthermore, we apply the algorithm to
characterize Hamiltonian fine structure and unknown system-bath interactions.Comment: 8 pages, 2 figures. Title is changed. Detailed error analysis is
added. Figures are updated with additional clarifying discussion
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