Abstract
We prove that quantum information encoded in some topological excitations, including certain Majorana zero modes, is protected in closed systems for a time scale exponentially long in system parameters. This protection holds even at infinite temperature. At lower temperatures, the decay time becomes even longer, with a temperature dependence controlled by an effective gap that is parametrically larger than the actual energy gap of the system. This nonequilibrium dynamical phenomenon is a form of prethermalization and occurs because of obstructions to the equilibration of edge or defect degrees of freedom with the bulk. We analyze the ramifications for ordered and topological phases in one, two, and three dimensions, with examples including Majorana and parafermionic zero modes in interacting spin chains. Our results are based on a nonperturbative analysis valid in any dimension, and they are illustrated by numerical simulations in one dimension. We discuss the implications for experiments on quantum-dot chains tuned into a regime supporting end Majorana zero modes and on trapped ion chains.
- Received 2 May 2017
DOI:https://doi.org/10.1103/PhysRevX.7.041062
Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.
Published by the American Physical Society
Physics Subject Headings (PhySH)
Popular Summary
Quantum computation, which relies on some of the nonintuitive behaviors of subatomic particles, is widely seen as a potentially powerful platform for solving computational problems that are too complex for traditional computers. Researchers are making a considerable effort, both theoretically and experimentally, to develop new methods of preserving quantum coherence—that is, enabling quantum effects to be maintained for times long enough to exploit them for computations. One promising approach is to exploit topological invariants, which guarantee the properties of the system remain robust against many types of errors. However, such topological quantum information is not completely protected. One notable issue is quasiparticle poisoning, where thermal effects create quasiparticles that destroy quantum coherence. We develop a method, which applies to systems in any number of dimensions, for keeping such thermal effects at bay for exponentially long times, thus preserving the quantum coherence.
Using a combination of mathematical analysis and numerical simulations, we show precisely how to provide additional protection for the Majorana zero modes being intensively investigated as a platform for topological quantum computation. We explain how our mathematical and numerical results can be seen by experiments on superconducting-semiconductor heterostructures and on trapped ion chains.
Our results show that, because of nonequilibrium effects, topological quantum information may be more strongly protected than previously realized.