11,372 research outputs found
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
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
Quantum computational renormalization in the Haldane phase
Single-spin measurements on the ground state of an interacting spin lattice
can be used to perform a quantum computation. We show how such measurements can
mimic renormalization group transformations and remove the short-ranged
variations of the state that can reduce the fidelity of a computation. This
suggests that the quantum computational ability of a spin lattice could be a
robust property of a quantum phase. We illustrate our idea with the ground
state of a spin-1 chain, which can serve as a quantum computational wire not
only at the Affleck-Kennedy-Lieb-Tasaki point, but within the
rotationally-invariant Haldane phase.Comment: v2: 4 pages, 3 figures; improved description of buffering scheme and
connection to string operators. v3: final published versio
Relativistically invariant quantum information
We show that quantum information can be encoded into entangled states of
multiple indistinguishable particles in such a way that any inertial observer
can prepare, manipulate, or measure the encoded state independent of their
Lorentz reference frame. Such relativistically invariant quantum information is
free of the difficulties associated with encoding into spin or other degrees of
freedom in a relativistic context.Comment: 5 pages, published versio
A molecular perspective on the limits of life: Enzymes under pressure
From a purely operational standpoint, the existence of microbes that can grow
under extreme conditions, or "extremophiles", leads to the question of how the
molecules making up these microbes can maintain both their structure and
function. While microbes that live under extremes of temperature have been
heavily studied, those that live under extremes of pressure have been
neglected, in part due to the difficulty of collecting samples and performing
experiments under the ambient conditions of the microbe. However, thermodynamic
arguments imply that the effects of pressure might lead to different organismal
solutions than from the effects of temperature. Observationally, some of these
solutions might be in the condensed matter properties of the intracellular
milieu in addition to genetic modifications of the macromolecules or repair
mechanisms for the macromolecules. Here, the effects of pressure on enzymes,
which are proteins essential for the growth and reproduction of an organism,
and some adaptations against these effects are reviewed and amplified by the
results from molecular dynamics simulations. The aim is to provide biological
background for soft matter studies of these systems under pressure.Comment: 16 pages, 8 figure
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
Universal continuous-variable quantum computation: Requirement of optical nonlinearity for photon counting
Although universal continuous-variable quantum computation cannot be achieved
via linear optics (including squeezing), homodyne detection and feed-forward,
inclusion of ideal photon counting measurements overcomes this obstacle. These
measurements are sometimes described by arrays of beam splitters to distribute
the photons across several modes. We show that such a scheme cannot be used to
implement ideal photon counting and that such measurements necessarily involve
nonlinear evolution. However, this requirement of nonlinearity can be moved
"off-line," thereby permitting universal continuous-variable quantum
computation with linear optics.Comment: 6 pages, no figures, replaced with published versio
Measurement-based quantum computation in a 2D phase of matter
Recently it has been shown that the non-local correlations needed for
measurement based quantum computation (MBQC) can be revealed in the ground
state of the Affleck-Kennedy-Lieb-Tasaki (AKLT) model involving nearest
neighbor spin-3/2 interactions on a honeycomb lattice. This state is not
singular but resides in the disordered phase of ground states of a large family
of Hamiltonians characterized by short-range-correlated valence bond solid
states. By applying local filtering and adaptive single particle measurements
we show that most states in the disordered phase can be reduced to a graph of
correlated qubits that is a scalable resource for MBQC. At the transition
between the disordered and Neel ordered phases we find a transition from
universal to non-universal states as witnessed by the scaling of percolation in
the reduced graph state.Comment: 8 pages, 6 figures, comments welcome. v2: published versio
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