Topological quantum memory
Abstract
We analyze surface codes, the topological quantum error-correcting codes introduced by Kitaev. In these codes, qubits are arranged in a two-dimensional array on a surface of nontrivial topology, and encoded quantum operations are associated with nontrivial homology cycles of the surface. We formulate protocols for error recovery, and study the efficacy of these protocols. An order-disorder phase transition occurs in this system at a nonzero critical value of the error rate; if the error rate is below the critical value (the accuracy threshold), encoded information can be protected arbitrarily well in the limit of a large code block. This phase transition can be accurately modeled by a three-dimensional Z(2) lattice gauge theory with quenched disorder. We estimate the accuracy threshold, assuming that all quantum gates are local, that qubits can be measured rapidly, and that polynomial-size classical computations can be executed instantaneously. We also devise a robust recovery procedure that does not require measurement or fast classical processing; however, for this procedure the quantum gates are local only if the qubits are arranged in four or more spatial dimensions. We discuss procedures for encoding, measurement, and performing fault-tolerant universal quantum computation with surface codes, and argue that these codes provide a promising framework for quantum computing architectures.
Read the paper
Related studies
- Diarylethenes for Memories and Switches
- Long-Term Potentiation and Memory
- Social Memory Studies: From “Collective Memory” to the Historical Sociology of Mnemonic Practices
- The Cognitive Neuroscience of Working Memory
- Memory aging and brain maintenance
- Effector and Memory CTL Differentiation
Go deeper in Evidence Hub
Evidence Hub adds a study data sheet (design, sample size, evidence level, key numbers), an AI summary and a chat grounded in the paper's text.