14,652 research outputs found
Multi-path Summation for Decoding 2D Topological Codes
Fault tolerance is a prerequisite for scalable quantum computing.
Architectures based on 2D topological codes are effective for near-term
implementations of fault tolerance. To obtain high performance with these
architectures, we require a decoder which can adapt to the wide variety of
error models present in experiments. The typical approach to the problem of
decoding the surface code is to reduce it to minimum-weight perfect matching in
a way that provides a suboptimal threshold error rate, and is specialized to
correct a specific error model. Recently, optimal threshold error rates for a
variety of error models have been obtained by methods which do not use
minimum-weight perfect matching, showing that such thresholds can be achieved
in polynomial time. It is an open question whether these results can also be
achieved by minimum-weight perfect matching. In this work, we use belief
propagation and a novel algorithm for producing edge weights to increase the
utility of minimum-weight perfect matching for decoding surface codes. This
allows us to correct depolarizing errors using the rotated surface code,
obtaining a threshold of . This is larger than the threshold
achieved by previous matching-based decoders (), though
still below the known upper bound of .Comment: 19 pages, 13 figures, published in Quantum, available at
https://quantum-journal.org/papers/q-2018-10-19-102
Density-matrix simulation of small surface codes under current and projected experimental noise
We present a full density-matrix simulation of the quantum memory and
computing performance of the distance-3 logical qubit Surface-17, following a
recently proposed quantum circuit and using experimental error parameters for
transmon qubits in a planar circuit QED architecture. We use this simulation to
optimize components of the QEC scheme (e.g., trading off stabilizer measurement
infidelity for reduced cycle time) and to investigate the benefits of feedback
harnessing the fundamental asymmetry of relaxation-dominated error in the
constituent transmons. A lower-order approximate calculation extends these
predictions to the distance- Surface-49. These results clearly indicate
error rates below the fault-tolerance threshold of surface code, and the
potential for Surface-17 to perform beyond the break-even point of quantum
memory. At state-of-the-art qubit relaxation times and readout speeds,
Surface-49 could surpass the break-even point of computation.Comment: 10 pages + 8 pages appendix, 12 figure
Subminimal Paths on a Stochastic Graph
A simple model of a frustrated disordered system is presented. Apart from the
(very different) physical interpretation, the model shares many features with
that of Sherrington-Kirkpatrick for spin glasses, but, as a consequence of its
relative simplicity, its ground state can be exactly determined by numerical
methods. This fact allows us to test experimentally some theoretical
predictions, based on a specialization of the ``cavity method'' developed for
the SK model, which is presently limited to a ``non-frustrated'' approximation,
corresponding to some extent to the replica-symmetric one for the SK model.Comment: 24 pages, Plain TeX with macros included, 10 PostScript figures in a
separate file, included via EPSF and ROTATE macro packages for DVIPS driver,
internal report Dipartimento di Fisica dell'Univ. di Roma La Sapienza e INFN
sezione di Roma n. 104
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