# 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…

## 21 Citations

### Universal Parity Quantum Computing

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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.

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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.

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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.

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- Physics
- 2017

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

- Computer Science
- 2022

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…

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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…

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- PhysicsPhysical Review A
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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

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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…

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

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