10 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
Multi-Qubit Joint Measurements in Circuit QED: Stochastic Master Equation Analysis
We derive a family of stochastic master equations describing homodyne
measurement of multi-qubit diagonal observables in circuit quantum
electrodynamics. In the regime where qubit decay can be neglected, our approach
replaces the polaron-like transformation of previous work, which required a
lengthy calculation for the physically interesting case of three qubits and two
resonator modes. The technique introduced here makes this calculation
straightforward and manifestly correct. Using this technique, we are able to
show that registers larger than one qubit evolve under a non-Markovian master
equation. We perform numerical simulations of the three-qubit, two-mode case
from previous work, obtaining an average post-measurement state fidelity of
, limited by measurement-induced decoherence and dephasing.Comment: 22 pages, 9 figures. Comments welcom
Tractable Simulation of Error Correction with Honest Approximations to Realistic Fault Models
In previous work, we proposed a method for leveraging efficient classical
simulation algorithms to aid in the analysis of large-scale fault tolerant
circuits implemented on hypothetical quantum information processors. Here, we
extend those results by numerically studying the efficacy of this proposal as a
tool for understanding the performance of an error-correction gadget
implemented with fault models derived from physical simulations. Our approach
is to approximate the arbitrary error maps that arise from realistic physical
models with errors that are amenable to a particular classical simulation
algorithm in an "honest" way; that is, such that we do not underestimate the
faults introduced by our physical models. In all cases, our approximations
provide an "honest representation" of the performance of the circuit composed
of the original errors. This numerical evidence supports the use of our method
as a way to understand the feasibility of an implementation of quantum
information processing given a characterization of the underlying physical
processes in experimentally accessible examples.Comment: 34 pages, 9 tables, 4 figure
Code deformation and lattice surgery are gauge fixing
International audienceThe large-scale execution of quantum algorithms requires basic quantum operations to be implemented fault-tolerantly. The most popular technique for accomplishing this, using the devices that can be realized in the near term, uses stabilizer codes which can be embedded in a planar layout. The set of fault-tolerant operations which can be executed in these systems using unitary gates is typically very limited. This has driven the development of measurement-based schemes for performing logical operations in these codes, known as lattice surgery and code deformation. In parallel, gauge fixing has emerged as a measurement-based method for performing universal gate sets in subsystem stabilizer codes. In this work, we show that lattice surgery and code deformation can be expressed as special cases of gauge fixing, permitting a simple and rigorous test for fault-tolerance together with simple guiding principles for the implementation of these operations. We demonstrate the accuracy of this method numerically with examples based on the surface code, some of which are novel