Noise Thresholds for the [[4, 2, 2]]-concatenated Toric Code

Abstract

We analyze the properties of a 2D topological code derived by concatenating the [[4, 2, 2]] code with the toric/surface code, or alternatively by removing check operators from the 2D square-octagon or 4.8.8 color code. We show that the resulting code has a circuit-based noise threshold of $\sim 0.41\%$ (compared to $\sim 0.6\%$ for the toric code in a similar scenario), which is higher than any known 2D color code. We believe that the construction may be of interest for hardware in which one wants to use both long-range two-qubit gates as well as short-range gates between small clusters of qubits.

19 pages, 22 figures

References in corpus (11)

• Surface codes: Towards practical large-scale quantum computation
• Topological Quantum Distillation
• Building logical qubits in a superconducting quantum computing system
• Detecting arbitrary quantum errors via stabilizer measurements on a sublattice of the surface code
• Quantum computing with nearest neighbor interactions and error rates over 1%
• Detecting bit-flip errors in a logical qubit using stabilizer measurements
• Topological Computation without Braiding
• Universal transversal gates with color codes - a simplified approach
• Tricolored Lattice Gauge Theory with Randomness: Fault-Tolerance in Topological Color Codes
• Quantum computing by color-code lattice surgery
• Hierarchical surface code for network quantum computing with modules of arbitrary size

Cited by in corpus (21)

• Fault-Tolerant Logical Gates in the IBM Quantum Experience
• Robust Dynamic Hamiltonian Engineering of Many-Body Spin Systems
• Robustness of Magic and Symmetries of the Stabiliser Polytope
• Using and reusing coherence to realize quantum processes
• Three-dimensional surface codes: Transversal gates and fault-tolerant architectures
• Superradiant to subradiant phase transition in the open system Dicke model: Dark state cascades
• Real Randomized Benchmarking
• All-photonic architectural roadmap for scalable quantum computing using Greenberger-Horne-Zeilinger states
• Morphing quantum codes
• Entanglement characterization using quantum designs
• Scalable Networking of Neutral-Atom Qubits: Nanofiber-Based Approach for Multiprocessor Fault-Tolerant Quantum Computer
• Collective Dissipative Molecule Formation in a Cavity
• Randomized benchmarking for qudit Clifford gates
• Quantum Error Correction with the GKP Code and Concatenation with Stabilizer Codes
• Creating and destroying coherence with quantum channels
• Weak approximate unitary designs and applications to quantum encryption
• Adaptive Syndrome Extraction
• Union-Find Decoders For Homological Product Codes
• A graph-based formalism for surface codes and twists
• Geometric constructions of generalized dual-unitary circuits from biunitarity
• Machine learning logical gates for quantum error correction