4 research outputs found
The XYZ hexagonal stabilizer code
We consider a topological stabilizer code on a honeycomb grid, the "XYZ"
code. The code is inspired by the Kitaev honeycomb model and is a simple
realization of a "matching code" discussed by Wootton [J. Phys. A: Math. Theor.
48, 215302 (2015)], with a specific implementation of the boundary. It utilizes
weight-six () plaquette stabilizers and weight-two () link
stabilizers on a planar hexagonal grid composed of qubits for code
distance , with weight-three stabilizers at the boundary, stabilizing one
logical qubit. We study the properties of the code using maximum-likelihood
decoding, assuming perfect stabilizer measurements. For pure , , or
noise, we can solve for the logical failure rate analytically, giving a
threshold of 50%. In contrast to the rotated surface code and the XZZX code,
which have code distance only for pure noise, here the code distance
is for both pure and pure noise. Thresholds for noise with
finite bias are similar to the XZZX code, but with markedly lower
sub-threshold logical failure rates. The code possesses distinctive syndrome
properties with unidirectional pairs of plaquette defects along the three
directions of the triangular lattice for isolated errors, which may be useful
for efficient matching-based or other approximate decoding.Comment: 15 pages, 7 figure
Data-driven decoding of quantum error correcting codes using graph neural networks
To leverage the full potential of quantum error-correcting stabilizer codes
it is crucial to have an efficient and accurate decoder. Accurate, maximum
likelihood, decoders are computationally very expensive whereas decoders based
on more efficient algorithms give sub-optimal performance. In addition, the
accuracy will depend on the quality of models and estimates of error rates for
idling qubits, gates, measurements, and resets, and will typically assume
symmetric error channels. In this work, instead, we explore a model-free,
data-driven, approach to decoding, using a graph neural network (GNN). The
decoding problem is formulated as a graph classification task in which a set of
stabilizer measurements is mapped to an annotated detector graph for which the
neural network predicts the most likely logical error class. We show that the
GNN-based decoder can outperform a matching decoder for circuit level noise on
the surface code given only simulated experimental data, even if the matching
decoder is given full information of the underlying error model. Although
training is computationally demanding, inference is fast and scales
approximately linearly with the space-time volume of the code. We also find
that we can use large, but more limited, datasets of real experimental data
[Google Quantum AI, Nature {\bf 614}, 676 (2023)] for the repetition code,
giving decoding accuracies that are on par with minimum weight perfect
matching. The results show that a purely data-driven approach to decoding may
be a viable future option for practical quantum error correction, which is
competitive in terms of speed, accuracy, and versatility.Comment: 15 pages, 12 figure
Error-rate-agnostic decoding of topological stabilizer codes
Efficient high-performance decoding of topological stabilizer codes has the
potential to crucially improve the balance between logical failure rates and
the number and individual error rates of the constituent qubits. High-threshold
maximum-likelihood decoders require an explicit error model for Pauli errors to
decode a specific syndrome, whereas lower-threshold heuristic approaches such
as minimum weight matching are "error agnostic". Here we consider an
intermediate approach, formulating a decoder that depends on the bias, i.e.,
the relative probability of phase-flip to bit-flip errors, but is agnostic to
error rate. Our decoder is based on counting the number and effective weight of
the most likely error chains in each equivalence class of a given syndrome. We
use Metropolis-based Monte Carlo sampling to explore the space of error chains
and find unique chains, that are efficiently identified using a hash table.
Using the error-rate invariance the decoder can sample chains effectively at an
error rate which is higher than the physical error rate and without the need
for "thermalization" between chains in different equivalence classes. Applied
to the surface code and the XZZX code, the decoder matches maximum-likelihood
decoders for moderate code sizes or low error rates. We anticipate that,
because of the compressed information content per syndrome, it can be taken
full advantage of in combination with machine-learning methods to extrapolate
Monte Carlo-generated data.Comment: 15 pages, 9 figures; V2 Added analysis of low error-rate performanc
Longlasting insecticidal nets for prevention of Leishmania donovani infection in India and Nepal: paired cluster randomised trial
Objective To test the effectiveness of large scale distribution of longlasting nets treated with insecticide in reducing the incidence of visceral leishmaniasis in India and Nepal