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Paper 1
Dynamic local single-shot checks for toric codes
Yingjia Lin, Abhinav Anand, Kenneth R. Brown
- Year
- 2025
- Journal
- arXiv preprint
- DOI
- arXiv:2511.20576
- arXiv
- 2511.20576
Quantum error correction typically requires repeated syndrome extraction due to measurement noise, which results in substantial time overhead in fault-tolerant computation. Single-shot error correction aims to suppress errors using only one round of syndrome extraction. However, for most codes, it requires high-weight checks, which significantly degrade, and often eliminate, single-shot performance at the circuit level. In this work, we introduce local single-shot checks, where we impose constraints on check weights. Using a dynamic measurement scheme, we show that the number of required measurement rounds can be reduced by a factor determined by this constraint. As an example, we show through numerical simulation that our scheme can improve decoding performance compared to conventional checks when using sliding-window decoding with a reduced window size under circuit-level noise models for toric codes. Our work provides a new direction for constructing checks that can reduce time overhead in large-scale fault-tolerant quantum computation.
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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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