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Localization of toric code defects.

Cyril Stark¹, Lode Pollet, Ataç Imamoğlu

¹Theoretische Physik, ETH Zurich, CH-8093 Zurich, Switzerland.

Physical Review Letters

|August 16, 2011

Summary

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Passive error correction in the toric code model is explored. Anderson localization of defects can remedy logical errors caused by coherent dynamics, potentially enabling self-correcting quantum memory.

Area of Science:

Quantum Information Science
Condensed Matter Physics
Quantum Error Correction

Background:

The toric code model is a leading candidate for fault-tolerant quantum computation.
Coherent dynamics in quantum systems can introduce logical errors, challenging error correction.
Understanding error mechanisms is crucial for developing robust quantum memory.

Purpose of the Study:

To investigate passive error correction mechanisms within the toric code model.
To identify sources of logical errors and propose a method for their mitigation.
To explore the potential for achieving self-correcting quantum memory.

Main Methods:

Analysis of logical error generation from coherent dynamics (spin interactions, magnetic fields).

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Theoretical framework using Anderson localization to explain defect behavior.

Numerical simulations to validate analytical arguments and demonstrate protection.

Main Results:

Coherent dynamics, including spin interactions and magnetic field coupling, induce logical errors in the toric code.
Anderson localization of defects, caused by coupling constant fluctuations, acts as a protective mechanism.
Numerical evidence supports the analytical findings, showing error suppression.

Conclusions:

Passive error correction is feasible in the toric code model.
Anderson localization offers a pathway to mitigate errors arising from coherent dynamics.
Self-correcting quantum memory is achievable in principle with a non-zero density of identical defects.