Layer codes as partially self-correcting quantum memories

Abstract

We investigate layer codes, a family of three-dimensional stabilizer codes that can achieve optimal scaling of code parameters and a polynomial energy barrier, as candidates for self-correcting quantum memories. First, we introduce two decoding algorithms for layer codes with provable guarantees for local stochastic and adversarial noise, respectively. We then prove that layer codes constitute partially self-correcting quantum memories which outperform previously analyzed models such as the cubic code and the welded solid code. Notably, we argue that partial self-correction without the requirement of efficient decoding is more common than expected, as it arises solely from a diverging energy barrier. This draws a sharp distinction between partially self-correcting systems and partially self-correcting memories. Another novel aspect of our work is an analysis of layer codes constructed from random Calderbank-Shor-Steane codes. We show that these random layer codes have optimal scaling (up to logarithmic corrections) of code parameters and a polynomial energy barrier. Finally, we present numerical studies of their memory times and report behavior consistent with partial self-correction.

45 pages, 17 figures, updated to match publication version

References in corpus (26)

• Topological quantum memory
• Quantum Error Correction for Quantum Memories
• Local stabilizer codes in three dimensions without string logical operators
• Surface code quantum computing by lattice surgery
• Analytic and numerical demonstration of quantum self-correction in the 3D Cubic Code
• Quantum LDPC codes with positive rate and minimum distance proportional to n^{1/2}
• A no-go theorem for a two-dimensional self-correcting quantum memory based on stabilizer codes
• Fast Decoders for Topological Quantum Codes
• Quantum memories at finite temperature
• Tradeoffs for reliable quantum information storage in 2D systems
• On thermalization in Kitaev's 2D model
• Balanced Product Quantum Codes
• On the energy landscape of 3D spin Hamiltonians with topological order
• NP-hardness of decoding quantum error-correction codes
• Cellular-automaton decoders with provable thresholds for topological codes
• Logical operator tradeoff for local quantum codes
• 3-d topological quantum memory with a power-law energy barrier
• Cellular automaton decoders for topological quantum codes with noisy measurements and beyond
• Topological Order and Memory Time in Marginally Self-Correcting Quantum Memory
• Efficient color code decoders in $d\ge 2$ dimensions from toric code decoders
• A proposal for self-correcting stabilizer quantum memories in 3 dimensions (or slightly less)
• A degeneracy bound for homogeneous topological order
• Can long-range interactions stabilize quantum memory at nonzero temperature?
• Self correction requires Energy Barrier for Abelian quantum doubles
• Layer Codes
• Almost Linear Decoder for Optimal Geometrically Local Quantum Codes