3,713 research outputs found
Topological quantum memory
We analyze surface codes, the topological quantum error-correcting codes
introduced by Kitaev. In these codes, qubits are arranged in a two-dimensional
array on a surface of nontrivial topology, and encoded quantum operations are
associated with nontrivial homology cycles of the surface. We formulate
protocols for error recovery, and study the efficacy of these protocols. An
order-disorder phase transition occurs in this system at a nonzero critical
value of the error rate; if the error rate is below the critical value (the
accuracy threshold), encoded information can be protected arbitrarily well in
the limit of a large code block. This phase transition can be accurately
modeled by a three-dimensional Z_2 lattice gauge theory with quenched disorder.
We estimate the accuracy threshold, assuming that all quantum gates are local,
that qubits can be measured rapidly, and that polynomial-size classical
computations can be executed instantaneously. We also devise a robust recovery
procedure that does not require measurement or fast classical processing;
however for this procedure the quantum gates are local only if the qubits are
arranged in four or more spatial dimensions. We discuss procedures for
encoding, measurement, and performing fault-tolerant universal quantum
computation with surface codes, and argue that these codes provide a promising
framework for quantum computing architectures.Comment: 39 pages, 21 figures, REVTe
Fault-Tolerance of "Bad" Quantum Low-Density Parity Check Codes
We discuss error-correction properties for families of quantum low-density
parity check (LDPC) codes with relative distance that tends to zero in the
limit of large blocklength. In particular, we show that any family of LDPC
codes, quantum or classical, where distance scales as a positive power of the
block length, , , can correct all errors with
certainty if the error rate per (qu)bit is sufficiently small. We specifically
analyze the case of LDPC version of the quantum hypergraph-product codes
recently suggested by Tillich and Z\'emor. These codes are a finite-rate
generalization of the toric codes, and, for sufficiently large quantum
computers, offer an advantage over the toric codes.Comment: 4.5 pages, 1 figur
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
Deep Q-learning decoder for depolarizing noise on the toric code
We present an AI-based decoding agent for quantum error correction of
depolarizing noise on the toric code. The agent is trained using deep
reinforcement learning (DRL), where an artificial neural network encodes the
state-action Q-values of error-correcting , , and Pauli operations,
occurring with probabilities , , and , respectively. By learning
to take advantage of the correlations between bit-flip and phase-flip errors,
the decoder outperforms the minimum-weight-perfect-matching (MWPM) algorithm,
achieving higher success rate and higher error threshold for depolarizing noise
(), for code distances . The decoder trained on
depolarizing noise also has close to optimal performance for uncorrelated noise
and provides functional but sub-optimal decoding for biased noise (). We argue that the DRL-type decoder provides a promising framework
for future practical error correction of topological codes, striking a balance
between on-the-fly calculations, in the form of forward evaluation of a deep
Q-network, and pre-training and information storage. The complete code, as well
as ready-to-use decoders (pre-trained networks), can be found in the repository
https://github.com/mats-granath/toric-RL-decoder.Comment: 8+10 pages, 10+8 figure
A single-system account of the relationship between priming, recognition, and fluency.
A single-system computational model of priming and recognition was applied to studies that have looked at the relationship between priming, recognition, and fluency in continuous identification paradigms. The model was applied to 3 findings that have been interpreted as evidence for a multiple-systems account: (a) priming can occur for items not recognized; (b) the pattern of identification reaction times (RTs) to hits, misses, correct rejections, and false alarms can change as a function of recognition performance; and (c) fluency effects (shorter RTs to words judged old vs. judged new) and priming effects (shorter RTs to old vs. new words) can be observed in amnesic patients at levels comparable with healthy adults despite impaired or near-chance recognition. The authors' simulations suggest, contrary to previous interpretations, that these results are consistent with a single-system account
Spin glass reflection of the decoding transition for quantum error correcting codes
We study the decoding transition for quantum error correcting codes with the
help of a mapping to random-bond Wegner spin models.
Families of quantum low density parity-check (LDPC) codes with a finite
decoding threshold lead to both known models (e.g., random bond Ising and
random plaquette gauge models) as well as unexplored earlier generally
non-local disordered spin models with non-trivial phase diagrams. The decoding
transition corresponds to a transition from the ordered phase by proliferation
of extended defects which generalize the notion of domain walls to non-local
spin models. In recently discovered quantum LDPC code families with finite
rates the number of distinct classes of such extended defects is exponentially
large, corresponding to extensive ground state entropy of these codes.
Here, the transition can be driven by the entropy of the extended defects, a
mechanism distinct from that in the local spin models where the number of
defect types (domain walls) is always finite.Comment: 15 pages, 2 figure
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