Strictly local one-dimensional topological quantum error correction with symmetry-constrained cellular automata

Abstract

Active quantum error correction on topological codes is one of the most promising routes to long-term qubit storage. In view of future applications, the scalability of the used decoding algorithms in physical implementations is crucial. In this work, we focus on the one-dimensional Majorana chain and construct a strictly local decoder based on a self-dual cellular automaton. We study numerically and analytically its performance and exploit these results to contrive a scalable decoder with exponentially growing decoherence times in the presence of noise. Our results pave the way for scalable and modular designs of actively corrected one-dimensional topological quantum memories.

Submission to SciPost, v2: minor revisions

References in corpus (38)

• Fault-tolerant quantum computation by anyons
• Anyons in an exactly solved model and beyond
• Unpaired Majorana fermions in quantum wires
• Quantum Computing
• The Physical Implementation of Quantum Computation
• Logic gates at the surface code threshold: Superconducting qubits poised for fault-tolerant quantum computing
• Topological quantum memory
• Quantum Error Correction for Quantum Memories
• Exponential Protection of Zero Modes in Majorana Islands
• State preservation by repetitive error detection in a superconducting quantum circuit
• Fault-tolerant quantum computation with high threshold in two dimensions
• Scalable Designs for Quasiparticle-Poisoning-Protected Topological Quantum Computation with Majorana Zero Modes
• Confinement-Higgs transition in a disordered gauge theory and the accuracy threshold for quantum memory
• Virtual Quantum Subsystems
• Majorana qubit decoherence by quasiparticle poisoning
• Analytic and numerical demonstration of quantum self-correction in the 3D Cubic Code
• Fast Decoders for Topological Quantum Codes
• Quantum memories at finite temperature
• Topological quantum computing with a very noisy network and local error rates approaching one percent
• Experimental demonstration of topological error correction
• Towards practical classical processing for the surface code
• Entanglement and topological entropy of the toric code at finite temperature
• Topological Order at Non-zero Temperature
• Error Threshold for Color Codes and Random 3-Body Ising Models
• Reliable Cellular Automata with Self-Organization
• Majorana Fermion Codes
• Solution of the Density Classification Problem with Two Cellular Automata Rules
• Majorana braiding with thermal noise
• Cellular-automaton decoders for topological quantum memories
• Non-deterministic density classification with diffusive probabilistic cellular automata
• Towards practical classical processing for the surface code: timing analysis
• Topological code Autotune
• Cellular automaton decoders of topological quantum memories in the fault tolerant setting
• Quantum memories and error correction
• 3-d topological quantum memory with a power-law energy barrier
• A proposal for self-correcting stabilizer quantum memories in 3 dimensions (or slightly less)
• One Dimensional $n$ary Density Classification Using Two Cellular Automaton Rules
• Engineering autonomous error correction in stabilizer codes at finite temperature

Cited by in corpus (7)

• Entanglement Transition in the Projective Transverse Field Ising Model
• Simulation of non-Abelian braiding in Majorana time crystals
• Reinforcement learning for optimal error correction of toric codes
• Strategies for practical advantage of fault-tolerant circuit design in noisy trapped-ion quantum computers
• Subradiant edge states in an atom chain with waveguide-mediated hopping
• Quantum cellular automata for quantum error correction and density classification
• Snowflake: A Distributed Streaming Decoder