Error correction for encoded quantum annealing

@article{Pastawski2016ErrorCF,
  title={Error correction for encoded quantum annealing},
  author={Fernando Pastawski and John Preskill},
  journal={Physical Review A},
  year={2016},
  volume={93},
  pages={052325}
}
Recently, W. Lechner, P. Hauke, and P. Zoller [Sci. Adv. 1, e1500838 (2015)] have proposed a quantum annealing architecture, in which a classical spin glass with all-to-all pairwise connectivity is simulated by a spin glass with geometrically local interactions. We interpret this architecture as a classical error-correcting code, which is highly robust against weakly correlated bit-flip noise, and we analyze the code's performance using a belief-propagation decoding algorithm. Our observations… 

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References

SHOWING 1-10 OF 14 REFERENCES
Error Correcting Codes For Adiabatic Quantum Computation
Mathematics Department, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139(Dated: February 1, 2008)Recently, there has been growing interest in using adiabatic quantum computation
A Quantum Adiabatic Evolution Algorithm Applied to Random Instances of an NP-Complete Problem
TLDR
For the small examples that the authors could simulate, the quantum adiabatic algorithm worked well, providing evidence that quantum computers (if large ones can be built) may be able to outperform ordinary computers on hard sets of instances of NP-complete problems.
Error suppression and error correction in adiabatic quantum computation I: techniques and challenges
TLDR
It is suggested that error suppression by itself is insufficient for large-scale, fault-tolerant AQC and that a form of error correction is needed.
A quantum annealing architecture with all-to-all connectivity from local interactions
TLDR
This work presents a scalable architecture with full connectivity, which can be implemented with local interactions only, and can be understood as a lattice gauge theory, where long-range interactions are mediated by gauge constraints.
Evidence for quantum annealing with more than one hundred qubits
Quantum annealing is expected to solve certain optimization problems more efficiently, but there are still open questions regarding the functioning of devices such as D-Wave One. A numerical and
Low-density parity-check codes
TLDR
A simple but nonoptimum decoding scheme operating directly from the channel a posteriori probabilities is described and the probability of error using this decoder on a binary symmetric channel is shown to decrease at least exponentially with a root of the block length.
An introduction to factor graphs
  • H. Loeliger
  • Computer Science
    IEEE Signal Processing Magazine
  • 2004
TLDR
This work uses Forney-style factor graphs, which support hierarchical modeling and are compatible with standard block diagrams, and uses them to derive practical detection/estimation algorithms in a wide area of applications.
Reverend Bayes on Inference Engines: A Distributed Hierarchical Approach
This paper presents generalizations of Bayes likelihood-ratio updating rule which facilitate an asynchronous propagation of the impacts of new beliefs and/or new evidence in hierarchically organized
Architectural Considerations in the Design of a Superconducting Quantum Annealing Processor
TLDR
A new ultralow-power embedded superconducting digital-to-analog flux converter (DAC) is developed used to program the processor with zero static power dissipation, optimized to achieve maximum flux storage density per unit area.
Towards fault tolerant adiabatic quantum computation.
  • D. Lidar
  • Physics
    Physical review letters
  • 2008
I show how to protect adiabatic quantum computation (AQC) against decoherence and certain control errors, using a hybrid methodology involving dynamical decoupling, subsystem and stabilizer codes,
...
...