# 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

- Computer Science, Physics
- 2022

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

- Computer Science, PhysicsIEEE 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

- Computer SciencePRX Quantum
- 2021

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

- Computer Science
- 2021

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.

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…

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

- Physics
- 2016

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…

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

- Physics
- 2016

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

- Physics, Computer Science
- 2016

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

Boosting quantum annealer performance via quantum persistence

- Computer ScienceArXiv
- 2016

A novel method using a quantum annealer to fix the value of a large portion of the variables to values that have a high probability of being optimal in quadratic unconstrained binary optimization problems, which results in a considerable improvement in success metrics even for problems with high-precision couplers and biases.

Three phases of quantum annealing: Fast, slow, and very slow

- PhysicsPhysical Review A
- 2022

Currently, existing quantum annealers have proven themselves as viable technology for the ﬁrst practical applications in the noisy-intermediate-scale-quantum era. However, to fully exploit their…

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