Error correcting power of small topological codes
arXiv:1609.01753
Abstract
Many quantum technologies are now reaching a high level of maturity and control, and it is likely that the first demonstrations of suppression of naturally occurring quantum noise using small topological error correcting codes will soon be possible. In doing this it will be necessary to define clear achievable metrics to measure and compare the performance of real codes. Here we consider the smallest examples of several families of topological codes: surface codes, color codes, and the gauge color code, and determine the minimum requirements to demonstrate error suppression. We use an exact decoder to compare the performance of the codes under simple models of both physical error and measurement error, and determine regions of correctability in the physical parameters for each code.
12 pages, 10 figures
References in corpus (30)
- Fault-tolerant quantum computation by anyons
- Logic gates at the surface code threshold: Superconducting qubits poised for fault-tolerant quantum computing
- Universal Quantum Computation with ideal Clifford gates and noisy ancillas
- State preservation by repetitive error detection in a superconducting quantum circuit
- Demonstration of a small programmable quantum computer with atomic qubits
- High-fidelity quantum logic gates using trapped-ion hyperfine qubits
- High-fidelity two-qubit quantum logic gates using trapped calcium-43 ions
- Topological Quantum Distillation
- High-fidelity preparation, gates, memory and readout of a trapped-ion quantum bit
- Quantum error correction in a solid-state hybrid spin register
- Realization of Three-Qubit Quantum Error Correction with Superconducting Circuits
- Detecting arbitrary quantum errors via stabilizer measurements on a sublattice of the surface code
- Fast Scalable State Measurement with Superconducting Qubits
- Experimental Quantum Computations on a Topologically Encoded Qubit
- Quantum computing with nearest neighbor interactions and error rates over 1%
- Confinement-Higgs transition in a disordered gauge theory and the accuracy threshold for quantum memory
- High fidelity spin entanglement using optimal control
- Low-distance Surface Codes under Realistic Quantum Noise
- Repeated quantum error correction on a continuously encoded qubit by real-time feedback
- Quantum memories at finite temperature
- Superconducting Nanocircuits for Topologically Protected Qubits
- Optimal Resources for Topological 2D Stabilizer Codes: Comparative Study
- Single-shot fault-tolerant quantum error correction
- Universal transversal gates with color codes - a simplified approach
- High threshold error correction for the surface code
- Efficient Decoders for Qudit Topological Codes
- An efficient Markov chain Monte Carlo algorithm for the surface code
- Stacked codes: universal fault-tolerant quantum computation in a two-dimensional layout
- Quantum computing by color-code lattice surgery
- Optimal complexity correction of correlated errors in the surface code