11,074 research outputs found
Some Remarks on the Question of Charge Densities in Stationary-Current-Carrying Conductors
Recently, some discussions arose as to the definition of charge and the value
of the density of charge in stationary-current-carrying conductors. We stress
that the problem of charge definition comes from a misunderstanding of the
usual definition. We provide some theoretical elements which suggest that
positive and negative charge densities are equal in the frame of the positive
ions.Comment: 14 pages, TeX, macro newsym.tex include
Ultrahigh Error Threshold for Surface Codes with Biased Noise
We show that a simple modification of the surface code can exhibit an
enormous gain in the error correction threshold for a noise model in which
Pauli Z errors occur more frequently than X or Y errors. Such biased noise,
where dephasing dominates, is ubiquitous in many quantum architectures. In the
limit of pure dephasing noise we find a threshold of 43.7(1)% using a tensor
network decoder proposed by Bravyi, Suchara and Vargo. The threshold remains
surprisingly large in the regime of realistic noise bias ratios, for example
28.2(2)% at a bias of 10. The performance is in fact at or near the hashing
bound for all values of the bias. The modified surface code still uses only
weight-4 stabilizers on a square lattice, but merely requires measuring
products of Y instead of Z around the faces, as this doubles the number of
useful syndrome bits associated with the dominant Z errors. Our results
demonstrate that large efficiency gains can be found by appropriately tailoring
codes and decoders to realistic noise models, even under the locality
constraints of topological codes.Comment: 6 pages, 5 figures, comments welcome; v2 includes minor improvements
to the numerical results, additional references, and an extended discussion;
v3 published version (incorporating supplementary material into main body of
paper
Tailored codes for small quantum memories
We demonstrate that small quantum memories, realized via quantum error
correction in multi-qubit devices, can benefit substantially by choosing a
quantum code that is tailored to the relevant error model of the system. For a
biased noise model, with independent bit and phase flips occurring at different
rates, we show that a single code greatly outperforms the well-studied Steane
code across the full range of parameters of the noise model, including for
unbiased noise. In fact, this tailored code performs almost optimally when
compared with 10,000 randomly selected stabilizer codes of comparable
experimental complexity. Tailored codes can even outperform the Steane code
with realistic experimental noise, and without any increase in the experimental
complexity, as we demonstrate by comparison in the observed error model in a
recent 7-qubit trapped ion experiment.Comment: 6 pages, 2 figures, supplementary material; v2 published versio
Degradation of a quantum directional reference frame as a random walk
We investigate if the degradation of a quantum directional reference frame
through repeated use can be modeled as a classical direction undergoing a
random walk on a sphere. We demonstrate that the behaviour of the fidelity for
a degrading quantum directional reference frame, defined as the average
probability of correctly determining the orientation of a test system, can be
fit precisely using such a model. Physically, the mechanism for the random walk
is the uncontrollable back-action on the reference frame due to its use in a
measurement of the direction of another system. However, we find that the
magnitude of the step size of this random walk is not given by our classical
model and must be determined from the full quantum description.Comment: 5 pages, no figures. Comments are welcome. v2: several changes to
clarify the key results. v3: journal reference added, acknowledgements and
references update
Toric codes and quantum doubles from two-body Hamiltonians
We present here a procedure to obtain the Hamiltonians of the toric code and Kitaev quantum double models as the low-energy limits of entirely two-body Hamiltonians. Our construction makes use of a new type of perturbation gadget based on error-detecting subsystem codes. The procedure is motivated by a projected entangled pair states (PEPS) description of the target models, and reproduces the target models' behavior using only couplings that are natural in terms of the original Hamiltonians. This allows our construction to capture the symmetries of the target models
Tailoring surface codes for highly biased noise
The surface code, with a simple modification, exhibits ultra-high error
correction thresholds when the noise is biased towards dephasing. Here, we
identify features of the surface code responsible for these ultra-high
thresholds. We provide strong evidence that the threshold error rate of the
surface code tracks the hashing bound exactly for all biases, and show how to
exploit these features to achieve significant improvement in logical failure
rate. First, we consider the infinite bias limit, meaning pure dephasing. We
prove that the error threshold of the modified surface code for pure dephasing
noise is , i.e., that all qubits are fully dephased, and this threshold
can be achieved by a polynomial time decoding algorithm. We demonstrate that
the sub-threshold behavior of the code depends critically on the precise shape
and boundary conditions of the code. That is, for rectangular surface codes
with standard rough/smooth open boundaries, it is controlled by the parameter
, where and are dimensions of the surface code lattice. We
demonstrate a significant improvement in logical failure rate with pure
dephasing for co-prime codes that have , and closely-related rotated
codes, which have a modified boundary. The effect is dramatic: the same logical
failure rate achievable with a square surface code and physical qubits can
be obtained with a co-prime or rotated surface code using only
physical qubits. Finally, we use approximate maximum likelihood decoding to
demonstrate that this improvement persists for a general Pauli noise biased
towards dephasing. In particular, comparing with a square surface code, we
observe a significant improvement in logical failure rate against biased noise
using a rotated surface code with approximately half the number of physical
qubits.Comment: 18+4 pages, 24 figures; v2 includes additional coauthor (ASD) and new
results on the performance of surface codes in the finite-bias regime,
obtained with beveled surface codes and an improved tensor network decoder;
v3 published versio
Airloads research study. Volume 2: Airload coefficients derived from wind tunnel data
The development of B-1 aircraft rigid wind tunnel data for use in subsequent tasks of the Airloads Research Study is described. Data from the Rockwell International external structural loads data bank were used to generate coefficients of rigid airload shear, bending moment, and torsion at specific component reference stations or both symmetric and asymmetric loadings. Component stations include the movable wing, horizontal and vertical stabilizers, and forward and aft fuselages. The coefficient data cover a Mach number range from 0.7 to 2.2 for a wing sweep position of 67.5 degree
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