Journal
PHYSICAL REVIEW LETTERS
Volume 111, Issue 20, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevLett.111.200501
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Funding
- DARPA [HR0011-09-C-0047]
- IARPA [D11PC20167]
- Korea Foundation for Advanced Studies
- Institute for Quantum Information and Matter
- NSF Physics Frontiers Center
- Gordon and Betty Moore Foundation
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A big open question in the quantum information theory concerns the feasibility of a self-correcting quantum memory. A quantum state recorded in such memory can be stored reliably for a macroscopic time without need for active error correction, if the memory is in contact with a cold enough thermal bath. Here we report analytic and numerical evidence for self-correcting behavior in the quantum spin lattice model known as the 3D cubic code. We prove that its memory time is at least L-c beta, where L is the lattice size, beta is the inverse temperature of the bath, and c > 0 is a constant coefficient. However, this bound applies only if the lattice size L does not exceed a critical value which grows exponentially with beta. In that sense, the model can be called a partially self-correcting memory. We also report a Monte Carlo simulation indicating that our analytic bounds on the memory time are tight up to constant coefficients. To model the readout step we introduce a new decoding algorithm, which can be implemented efficiently for any topological stabilizer code. A longer version of this work can be found in Bravyi and Haah, arXiv:1112.3252.
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