Fault-tolerant Post-Selection for Low Overhead Magic State Preparation

Abstract

We introduce a framework for fault-tolerant post-selection (FTPS) of fault-tolerant codes and channels -- such as those based on surface-codes -- using soft-information metrics based on visible syndrome and erasure information. We introduce several metrics for ranking configurations of syndromes and erasures. In particular, we introduce the \emph{logical gap} (and variants thereof) as a powerful soft-information metric for predicting logical error rates of fault-tolerant channels based on topological error-correcting codes. The logical gap is roughly the unsigned weight difference between inequivalent logical corrections and is adaptable to any tailored noise model or decoder. We deploy this framework to prepare high-quality surface code magic states with low overhead under a model of independent and identically distributed (\emph{i.i.d.}) Pauli and erasure errors. Post-selection strategies based on the logical gap can suppress the encoding error rate of a magic state preparation channel to the level of the physical error rate with low overhead. For example, when operating at $60\%$ the bulk threshold of the corresponding surface code, an overall reduction of the encoding error rate by a factor of $15$ is achievable with a relative overhead factor of $<2$ (approximately $23$ times less than that of simple syndrome-counting rules). We analyze a schematic buffer architecture for implementing post-selection rules on magic state factories in the context of magic state distillation. The FTPS framework can be utilized for mitigating errors in more general fault-tolerant logical channels.

arXiv comment10+7 pages, 13 figures, comments welcome

References in corpus (38)

• Fault-tolerant quantum computation by anyons
• Anyons in an exactly solved model and beyond
• Topological quantum memory
• Universal Quantum Computation with ideal Clifford gates and noisy ancillas
• Quantum Error Correction for Quantum Memories
• Fault-tolerant quantum computation with high threshold in two dimensions
• Topological Quantum Distillation
• How to factor 2048 bit RSA integers in 8 hours using 20 million noisy qubits
• Topological fault-tolerance in cluster state quantum computation
• Surface code quantum computing by lattice surgery
• Quantum orders in an exact soluble model
• A Game of Surface Codes: Large-Scale Quantum Computing with Lattice Surgery
• Topological Order with a Twist: Ising Anyons from an Abelian Model
• Magic state distillation with low overhead
• Genons, twist defects, and projective non-Abelian braiding statistics
• Quantum computing enhanced computational catalysis
• Magic State Distillation: Not as Costly as You Think
• High-threshold fault-tolerant quantum computation with analog quantum error correction
• Improved Fault-Tolerant Quantum Simulation of Condensed-Phase Correlated Electrons via Trotterization
• Efficient magic state factories with a catalyzed |CCZ> to 2|T> transformation
• Classification of Topological Defects in Abelian Topological States
• Poking holes and cutting corners to achieve Clifford gates with the surface code
• Quantum Measurements and Gates by Code Deformation
• A Threshold for Quantum Advantage in Derivative Pricing
• Surface code implementation of block code state distillation
• Fault-tolerant resource estimate for quantum chemical simulations: Case study on Li-ion battery electrolyte molecules
• A unified framework for magic state distillation and multi-qubit gate-synthesis with reduced resource cost
• The surface code with a twist
• A magic state's fidelity can be superior to the operations that created it
• Codes and Protocols for Distilling $T$, controlled-$S$, and Toffoli Gates
• Magic State Distillation with Low Space Overhead and Optimal Asymptotic Input Count
• Universal fault-tolerant measurement-based quantum computation
• Fault-Tolerant Quantum Gates with Defects in Topological Stabiliser Codes
• Simple scheme for encoding and decoding a qubit in unknown state for various topological codes
• The Capabilities of a Perturbed Toric Code as a Quantum Memory
• High-Fidelity Magic-State Preparation with a Biased-Noise Architecture
• Low overhead Clifford gates from joint measurements in surface, color, and hyperbolic codes
• Resource Optimized Quantum Architectures for Surface Code Implementations of Magic-State Distillation

Cited by in corpus (9)

• Learning to Decode the Surface Code with a Recurrent, Transformer-Based Neural Network
• Mitigating errors in logical qubits
• Low-overhead magic state distillation with color codes
• Thresholds for post-selected quantum error correction from statistical mechanics
• Magic State Injection with Erasure Qubits
• Logical entanglement distribution between distant 2D array qubits
• Low Overhead Qutrit Magic State Distillation
• Entanglement boosting: Low-volume logical Bell pair preparation for distributed fault-tolerant quantum computation
• Hierarchical Quantum Error Correction with Hypergraph Product Code and Rotated Surface Code