Single-shot preparation of hypergraph product codes via dimension jump
arXiv:2410.05171 · doi:10.22331/q-2025-10-07-1879
Abstract
Quantum error correction is a fundamental primitive of fault-tolerant quantum computing. But in order for error correction to proceed, one must first prepare the codespace of the underlying error-correcting code. A popular method for encoding quantum low-density parity-check codes is transversal initialization, where one begins in a product state and measures a set of stabilizer generators. In the presence of measurement errors however, this procedure is generically not fault-tolerant, and so one typically needs to repeat the measurements many times, resulting in a deep initialization circuit. We present a protocol that prepares the codespace of constant-rate hypergraph product codes in constant depth with spatial overhead, and we show that the protocol is robust even in the presence of measurement errors. Our construction is inspired by dimension-jumping in topological codes and leverages two properties that arise from the homological product of codes. We provide some improvements to lower the spatial overhead and discuss applications to fault-tolerant architectures.
17 pages, 8 figures, 1 table v2 changes: updated formatting for Quantum
References in corpus (57)
- Fault-tolerant quantum computation by anyons
- Surface codes: Towards practical large-scale quantum computation
- Good Quantum Error-Correcting Codes Exist
- Topological quantum memory
- Multiple Particle Interference and Quantum Error Correction
- Suppressing quantum errors by scaling a surface code logical qubit
- Logical quantum processor based on reconfigurable atom arrays
- Topological Quantum Distillation
- Quantum error correction below the surface code threshold
- Quantum computing with atomic qubits and Rydberg interactions: Progress and challenges
- Surface code quantum computing by lattice surgery
- High-fidelity parallel entangling gates on a neutral atom quantum computer
- A Race Track Trapped-Ion Quantum Processor
- Quantum Low-Density Parity-Check Codes
- 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
- Topological Computation without Braiding
- Long-range quantum entanglement in noisy cluster states
- Tradeoffs for reliable quantum information storage in 2D systems
- Decoding Across the Quantum LDPC Code Landscape
- Single-shot fault-tolerant quantum error correction
- Ytterbium nuclear-spin qubits in an optical tweezer array
- Classification of topologically protected gates for local stabilizer codes
- Unfolding the color code
- Quantum advantage with noisy shallow circuits in 3D
- Poking holes and cutting corners to achieve Clifford gates with the surface code
- Fault-Tolerance of "Bad" Quantum Low-Density Parity Check Codes
- Foliated Quantum Codes
- Benchmarking a trapped-ion quantum computer with 30 qubits
- A theory of single-shot error correction for adversarial noise
- Homological Error Correction: Classical and Quantum Codes
- Quantum Expander Codes
- Three-dimensional surface codes: Transversal gates and fault-tolerant architectures
- A fault-tolerant non-Clifford gate for the surface code in two dimensions
- Single-shot error correction of three-dimensional homological product codes
- Decoding algorithms for surface codes
- NLTS Hamiltonians from good quantum codes
- Improved single-shot decoding of higher dimensional hypergraph product codes
- Higher-dimensional quantum hypergraph-product codes
- Fault-tolerant gates on hypergraph product codes
- Partitioning qubits in hypergraph product codes to implement logical gates
- Connectivity constrains quantum codes
- Fold-Transversal Clifford Gates for Quantum Codes
- Low-Overhead Transversal Fault Tolerance for Universal Quantum Computation
- Entangling four logical qubits beyond break-even in a nonlocal code
- Localized statistics decoding for quantum low-density parity-check codes
- Single-shot decoding of good quantum LDPC codes
- Numerical Implementation of Just-In-Time Decoding in Novel Lattice Slices Through the Three-Dimensional Surface Code
- Long-range-enhanced surface codes
- Experiments with the 4D Surface Code on a QCCD Quantum Computer
- Quantum memory at nonzero temperature in a thermodynamically trivial system
- Sparse Quantum Codes from Quantum Circuits
- Distance-preserving stabilizer measurements in hypergraph product codes
- Decoding Schemes for Foliated Sparse Quantum Error Correcting Codes
- Weight Reduced Stabilizer Codes with Lower Overhead
- Single-Shot Quantum Error Correction in Intertwined Toric Codes
- LDPC Codes Achieve List Decoding Capacity