Error correction for encoded quantum annealing

  title={Error correction for encoded quantum annealing},
  author={Fernando Pastawski and John Preskill},
  journal={Physical Review A},
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… 

Figures from this paper

Universal Parity Quantum Computing

A universal gate set for quantum computing with all-to-all connectivity and intrinsic robustness to bit-flip errors based on the parity encoding is proposed and a method to switch between different encoding variants via partial on-the- fly encoding and decoding is presented.

Quantum Approximate Optimization With Parallelizable Gates

  • W. Lechner
  • Computer Science, Physics
    IEEE Transactions on Quantum Engineering
  • 2020
A scheme to parallelize the quantum approximate optimization algorithm for arbitrary all-to-all connected problem graphs in a layout of quantum bits (qubits) with nearest-neighbor interactions in a lattice gauge model.

Embedding Overhead Scaling of Optimization Problems in Quantum Annealing

This work investigates the embedding penalty of established planar embedding schemes such as square lattice embedding, embedding on a Chimera lattice, and the Lechner-Hauke-Zoller scheme using simulated quantum annealing on classical hardware to demonstrate standard analog quantumAnnealing hardware is at a disadvantage in comparison to classical digital annealers.

Scaling overhead of embedding optimization problems in quantum annealing

The results demonstrate that standard analog quantum annealing hardware is at a disadvantage in comparison to classical digital annealers, as well as gate-model quantum anNEalers and could also serve as benchmark for improvements of the standard quantumAnnealing protocol.

Scalable effective temperature reduction for quantum annealers via nested quantum annealing correction

Nested quantum annealing correction (NQAC) is an error correcting scheme for quantum annealing that allows for the encoding of a logical qubit into an arbitrarily large number of physical qubits. The

Applications of Universal Parity Quantum Computation

We demonstrate the applicability of a universal gate set in the parity encoding, which is a dual to the standard gate model, by exploring several quantum gate algorithms such as the Quantum Fourier

Quantum annealing with a network of all-to-all connected, two-photon driven Kerr nonlinear oscillators

Quantum annealing aims to solve combinatorial optimization problems mapped on to Ising interactions between quantum spins. A critical factor that limits the success of a quantum annealer is its

Assessing the performance of quantum annealing with nonlinear driving

Current-generation quantum annealers have already proven to be successful problem solvers. Yet quantum annealing is still very much in its infancy, with suboptimal applicability. For instance, to

Simulated-quantum-annealing comparison between all-to-all connectivity schemes

Quantum annealing aims to exploit quantum mechanics to speed up the search for the solution to optimization problems. Most problems exhibit complete connectivity between the logical spin variables

A transmon quantum annealer: decomposing many-body Ising constraints into pair interactions

An implementation of a parity annealer with Transmon qubits with a specifically tailored Ising interaction from Josephson ring modulators is presented.



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

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,

A Quantum Adiabatic Evolution Algorithm Applied to Random Instances of an NP-Complete Problem

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

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

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

Architectural Considerations in the Design of a Superconducting Quantum Annealing Processor

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.

Low-density parity-check codes

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.

Survey propagation: An algorithm for satisfiability

A new type of message passing algorithm is introduced which allows to find efficiently a satisfying assignment of the variables in this difficult region of randomly generated formulas.

An introduction to factor graphs

  • H. Loeliger
  • Computer Science
    IEEE Signal Processing Magazine
  • 2004
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.