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Paper 1
Ultra Low Overhead Syndrome Extraction for the Steane code
Boldizsár Poór, Benjamin Rodatz, Aleks Kissinger
- Year
- 2025
- Journal
- arXiv preprint
- DOI
- arXiv:2511.13700
- arXiv
- 2511.13700
We establish a new performance benchmark for the fault-tolerant syndrome extraction of [[7, 1, 3]] Steane code with a dynamic protocol. Our method is built on two highly optimized circuits derived using fault-equivalent ZX-rewrites: a primary fault-tolerant circuit with 14 CNOTs and an efficient non-fault-tolerant recovery circuit with 11 CNOTs. The protocol uses an adaptive response to internal faults, discarding flagged measurements and falling back to the recovery circuit to correct potentially detrimental errors. Monte Carlo simulations confirm the efficiency of our protocol, reducing the logical error rate per cycle by an average of ~14.3% relative to the optimized Steane method [arXiv:2506.17181] and ~17.7% compared to the Reichardt's three-qubit method [arXiv:1804.06995], the leading prior techniques.
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Quantum circuit design for accurate simulation of qudit channels
Dong-Sheng Wang, Barry C. Sanders
- Year
- 2014
- Journal
- arXiv preprint
- DOI
- arXiv:1407.7251
- arXiv
- 1407.7251
We construct a classical algorithm that designs quantum circuits for algorithmic quantum simulation of arbitrary qudit channels on fault-tolerant quantum computers within a pre-specified error tolerance with respect to diamond-norm distance. The classical algorithm is constructed by decomposing a quantum channel into a convex combination of generalized extreme channels by optimization of a set of nonlinear coupled algebraic equations. The resultant circuit is a randomly chosen generalized extreme channel circuit whose run-time is logarithmic with respect to the error tolerance and quadratic with respect to Hilbert space dimension, which requires only a single ancillary qudit plus classical dits.
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