Topological approach toward quantum codes with realistic physical constraints

Abstract

The following open problems, which concern a fundamental limit on coding properties of quantum codes with realistic physical constraints, are analyzed and partially answered here: (a) the upper bound on code distances of quantum error-correcting codes with geometrically local generators, (b) the feasibility of a self-correcting quantum memory. To investigate these problems, we study stabilizer codes supported by local interaction terms with translation and scale symmetries on a $D$-dimensional lattice. Our analysis uses the notion of topology emerging in geometric shapes of logical operators, which sheds a surprising new light on theory of quantum codes with physical constraints.

This paper has been withdrawn by the author. It is superseded by (and merged into) arXiv:1103.1885

References in corpus (18)

• Fault-tolerant quantum computation by anyons
• Mixed State Entanglement and Quantum Error Correction
• Good Quantum Error-Correcting Codes Exist
• Encoding a qubit in an oscillator
• String-net condensation: A physical mechanism for topological phases
• A Class of Quantum Error-Correcting Codes Saturating the Quantum Hamming Bound
• A Theory of Quantum Error-Correcting Codes
• Topological Quantum Distillation
• Operator Quantum Error Correcting Subsystems for Self-Correcting Quantum Memories
• Stabilizer Formalism for Operator Quantum Error Correction
• A symmetry principle for Topological Quantum Order
• Concatenating Decoherence Free Subspaces with Quantum Error Correcting Codes
• A no-go theorem for a two-dimensional self-correcting quantum memory based on stabilizer codes
• Subsystem fault tolerance with the Bacon-Shor code
• Error correction for continuous quantum variables
• Analog quantum error correction
• Self-dual random-plaquette gauge model and the quantum toric code
• Framework for classifying logical operators in stabilizer codes