Foliated Quantum Error-Correcting Codes

2016/07/09 by A. Bolt, Guillaume Duclos-Cianci, G. Duclos-Cianci +4 · 3 citations
Computer Science · Physics and Astronomy · #Computer science #Physics #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum mechanics #Quantum-Dot Cellular Automata #quant-ph

paper · pdf · doi:10.1103/physrevlett.117.070501

published as Phys. Rev. Lett. 117, 070501 (2016) · 5 pages

arxiv created 2016/07/09 · openalex publication_date 2016/08/10 · arxiv updated 2016/08/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We show how to construct a large class of quantum error-correcting codes, known as Calderbank-Steane-Shor codes, from highly entangled cluster states. This becomes a primitive in a protocol that foliates a series of such cluster states into a much larger cluster state, implementing foliated quantum error correction. We exemplify this construction with several familiar quantum error-correction codes and propose a generic method for decoding foliated codes. We numerically evaluate the error-correction performance of a family of finite-rate Calderbank-Steane-Shor codes known as turbo codes, finding that they perform well over moderate depth foliations. Foliated codes have applications for quantum repeaters and fault-tolerant measurement-based quantum computation.

Citations

• Description of a Quantum Convolutional Code
• Measurement-based quantum computation
• Universal Quantum Computation with ideal Clifford gates and noisy ancillas
• Topological quantum memory
• Measurement-based quantum computation with cluster states
• Good Quantum Error-Correcting Codes Exist
• Long-distance quantum communication with atomic ensembles and linear optics
• Fault-tolerant quantum computation by anyons
• Quantum LDPC Codes With Positive Rate and Minimum Distance Proportional to the Square Root of the Blocklength

Cited by

• Graph-state representation of the toric code
• Poking Holes and Cutting Corners to Achieve Clifford Gates with the Surface Code
• Universal fault-tolerant measurement-based quantum computation