# Error Correcting Codes For Adiabatic Quantum Computation

@article{Jordan2006ErrorCC, title={Error Correcting Codes For Adiabatic Quantum Computation}, author={Stephen P. Jordan and Edward Farhi and Peter W. Shor}, journal={Physical Review A}, year={2006}, volume={74}, pages={052322} }

Mathematics Department, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139(Dated: February 1, 2008)Recently, there has been growing interest in using adiabatic quantum computation as an architec-ture for experimentally realizable quantum computers. One of the reasons for this is the idea thatthe energy gap should provide some inherent resistance to noise. It is now known that universalquantum computation can be achieved adiabatically using 2-local Hamiltonians. The energy gap…

## 114 Citations

A Study of Error-Correcting Codes for Quantum Adiabatic Computation CS 252 Course Project { Spring 2007

- Computer Science, Physics
- 2007

This project simulates an adiabatic computation to solve the MAX-2SAT problem, and implements a recently proposed error- correcting code that is tolerant against 1-local errors and shows that the system can tolerate higher error rates using error-correction.

Error-corrected quantum annealing with hundreds of qubits.

- PhysicsNature communications
- 2014

A substantial improvement over the performance of the processors in the absence of error correction is demonstrated, paving the way towards large-scale noise-protected adiabatic quantum optimization devices, although a threshold theorem such as has been established in the circuit model of quantum computing remains elusive.

Arbitrary-time error suppression for Markovian adiabatic quantum computing using stabilizer subspace codes

- PhysicsPhysical Review A
- 2019

Adiabatic quantum computing (AQC) can be protected against thermal excitations via an encoding into error detecting codes, supplemented with an energy penalty formed from a sum of commuting…

Topological Code Architectures for Quantum Computation

- Computer Science
- 2014

This dissertation describes novel state distillation protocols that are naturally suited for topological architectures and show that they provide resource savings in terms of the number of required ancilla states when compared to more traditional approaches to quantum gate approximation.

Error suppression in Hamiltonian-based quantum computation using energy penalties

- Physics
- 2015

We consider the use of quantum error detecting codes, together with energy penalties against leaving the codespace, as a method for suppressing environmentally induced errors in Hamiltonian based…

Stability of quantum concatenated-code Hamiltonians

- Physics, Computer Science
- 2008

A class of Hamiltonians whose ground states are concatenated quantum codes and whose energy landscape naturally causes quantum error correction is defined, which is analyzed for robustness and suggested methods for implementing these highly unnatural Hamiltonians are suggested.

Physical implementation of protected qubits

- PhysicsReports on progress in physics. Physical Society
- 2012

It is shown that topological protection can be viewed as a Hamiltonian realization of error correction: for a quantum code for which the minimal number of errors that remain undetected is N, the corresponding Hamiltonian model of the effects of the environment noise appears only in the Nth order of the perturbation theory.

Environment-assisted analog quantum search

- PhysicsPhysical Review A
- 2018

Two main obstacles for observing quantum advantage in noisy intermediate-scale quantum computers (NISQ) are the finite precision effects due to control errors, or disorders, and decoherence effects…

Performance of two different quantum annealing correction codes

- Computer ScienceQuantum Inf. Process.
- 2016

There exists an important trade-off between encoded connectivity and performance for quantum annealing correction codes, and the code with the higher energy boost results in improved performance, at the expense of a lower-degree encoded graph.

Adiabatic Quantum Computing

- Physics
- 2011

Adiabatic Quantum Computing (AQC) is a relatively new subject in the world of quantum computing, let alone Physics. Inspiration for this project has come from recent controversy around D-Wave Systems…

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