Lift-Connected Surface Codes
arXiv:2401.02911 · doi:10.1088/2058-9565/ad5eb6
Abstract
We use the recently introduced lifted product to construct a family of Quantum Low Density Parity Check Codes (QLDPC codes). The codes we obtain can be viewed as stacks of surface codes that are interconnected, leading to the name lift-connected surface (LCS) codes. LCS codes offer a wide range of parameters - a particularly striking feature is that they show interesting properties that are favorable compared to the standard surface code. For example, already at moderate numbers of physical qubits in the order of tens, LCS codes of equal size have lower logical error rate or similarly, require fewer qubits for a fixed target logical error rate. We present and analyze the construction and provide numerical simulation results for the logical error rate under code capacity and phenomenological noise. These results show that LCS codes attain thresholds that are comparable to corresponding (non-connected) copies of surface codes, while the logical error rate can be orders of magnitude lower, even for representatives with the same parameters. This provides a code family showing the potential of modern product constructions at already small qubit numbers. Their amenability to 3D-local connectivity renders them particularly relevant for near-term implementations.
23 pages, 19 figures; Included circuit-level noise simulations
References in corpus (52)
- Surface codes: Towards practical large-scale quantum computation
- Topological quantum memory
- Trapped-Ion Quantum Computing: Progress and Challenges
- Suppressing quantum errors by scaling a surface code logical qubit
- Logical quantum processor based on reconfigurable atom arrays
- Quantum computing with atomic qubits and Rydberg interactions: Progress and challenges
- Surface code quantum computing by lattice surgery
- Synthetic three-dimensional atomic structures assembled atom by atom
- Restrictions on Transversal Encoded Quantum Gate Sets
- High-threshold and low-overhead fault-tolerant quantum memory
- Stim: a fast stabilizer circuit simulator
- Sparse Graph Codes for Quantum Error-Correction
- Quantum Error Correction: An Introductory Guide
- A Race Track Trapped-Ion Quantum Processor
- Resilient Quantum Computation: Error Models and Thresholds
- Confinement-Higgs transition in a disordered gauge theory and the accuracy threshold for quantum memory
- Quantum Low-Density Parity-Check Codes
- Demonstration of fault-tolerant universal quantum gate operations
- Quantum LDPC codes with positive rate and minimum distance proportional to n^{1/2}
- A no-go theorem for a two-dimensional self-correcting quantum memory based on stabilizer codes
- Towards practical classical processing for the surface code
- Tradeoffs for reliable quantum information storage in 2D systems
- Decoding Across the Quantum LDPC Code Landscape
- Balanced Product Quantum Codes
- Flag fault-tolerant error correction with arbitrary distance codes
- Fault-tolerant thresholds for quantum error correction with the surface code
- Fault-Tolerance of "Bad" Quantum Low-Density Parity Check Codes
- Low-overhead fault-tolerant quantum computing using long-range connectivity
- The cost of universality: A comparative study of the overhead of state distillation and code switching with color codes
- Constant-overhead quantum error correction with thin planar connectivity
- Phase Structure of the Random-Plaquette Z_2 Gauge Model: Accuracy Threshold for a Toric Quantum Memory
- Fault-tolerant quantum computing with color codes
- Universal fault-tolerant gates on concatenated stabilizer codes
- Single-shot error correction of three-dimensional homological product codes
- The disjointness of stabilizer codes and limitations on fault-tolerant logical gates
- Improved single-shot decoding of higher dimensional hypergraph product codes
- Fault-tolerant gates on hypergraph product codes
- Thresholds for correcting errors, erasures, and faulty syndrome measurements in degenerate quantum codes
- Fold-Transversal Clifford Gates for Quantum Codes
- Fault-Tolerant Code Switching Protocols for Near-Term Quantum Processors
- Quantum LDPC Codes for Modular Architectures
- Numerical and analytical bounds on threshold error rates for hypergraph-product codes
- Fault-Tolerant Quantum Computation with Constant Overhead
- A degeneracy bound for homogeneous topological order
- QDistRnd: A GAP package for computing the distance of quantum error-correcting codes
- Fault-tolerant gates via homological product codes
- Quantum routing with fast reversals
- Teleportation-based Fault-tolerant Quantum Computation in Multi-qubit Large Block Codes
- Bounds on stabilizer measurement circuits and obstructions to local implementations of quantum LDPC codes
- Software Tools for Decoding Quantum Low-Density Parity Check Codes
- The Physics of (good) LDPC Codes I. Gauging and dualities
- Geometrically Local Quantum and Classical Codes from Subdivision
Cited by in corpus (5)
- Near-Term Spin-Qubit Architecture Design via Multipartite Maximally-Entangled States
- Fault-Tolerant Stabilizer Measurements in Surface Codes with Three-Qubit Gates
- Efficient fault-tolerant code switching via one-way transversal CNOT gates
- Fundamental thresholds for computational and erasure errors via the coherent information
- Streaming Belief Propagation on Mixed-Alphabet Tanner Graphs for Practical Quantum Memory