Simulation of rare events in quantum error correction

2013/08/31 by Sergey Bravyi, Alexander Vargo · 6 citations
Computer Science · Engineering · Mathematics · Physics and Astronomy · #Advancements in Semiconductor Devices and Circuit Design #Algorithm #Code (set theory) #Computer science #Error detection and correction #Exponential function #Lattice (music) #Mathematical analysis #Mathematics #Monte Carlo method #Pauli exclusion principle #Physics #Quantum #Quantum Computing Algorithms and Architecture #Quantum and electron transport phenomena #Quantum computer #Quantum error correction #Quantum mechanics #Statistical physics #Statistics #quant-ph

paper · pdf · doi:10.1103/physreva.88.062308

published as Phys. Rev. A 88, 062308 (2013) · 16 pages, 11 figures. Version 3: added a new reference

openalex publication_date 2013/12/05 · arxiv created 2013/12/17 · arxiv updated 2013/12/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We consider the problem of calculating the logical error probability for a stabilizer quantum code subject to random Pauli errors. To access the regime of large code distances where logical errors are extremely unlikely we adopt the splitting method widely used in Monte Carlo simulations of rare events and Bennett's acceptance ratio method for estimating the free energy difference between two canonical ensembles. To illustrate the power of these methods in the context of error correction, we calculate the logical error probability P_L for the two-dimensional surface code on a square lattice with a pair of holes for all code distances d\ensuremath≤20 and all error rates p below the fault-tolerance threshold. Our numerical results confirm the expected exponential decay P_L\ensuremath∼exp[\ensuremath-\ensuremathα(p)d] and provide a simple fitting formula for the decay rate \ensuremathα(p). Both noiseless and noisy syndrome readout circuits are considered.

Citations

• Proof of Finite Surface Code Threshold for Matching
• Topological quantum memory
• Fault-tolerant quantum computation by anyons
• Efficient estimation of free energy differences from Monte Carlo data
• Quantum computations: algorithms and error correction
• Paths, Trees, and Flowers

Cited by

• Quantum error correction at ultra-low overhead
• Fast decoders for qudit topological codes
• Analyzing Decoders for Quantum Error Correction
• SyQMA: A memory-efficient, symbolic and exact universal simulator for quantum error correction
• A Simple Decoder for Topological Codes
• Freely Scalable Quantum Technologies Using Cells of 5-to-50 Qubits with Very Lossy and Noisy Photonic Links

Related

• Rare Event Simulation of Quantum Error-Correcting Circuits
• Randomized compiling in fault-tolerant quantum computation
• Scalable accuracy gains from postselection in quantum error correcting codes
• Fail fast: techniques to probe rare events in quantum error correction
• Experimentally Informed Decoding of Stabilizer Codes Based on Syndrome Correlations