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Paper 1
Tsim: Fast Universal Simulator for Quantum Error Correction
Rafael Haenel, Xiuzhe Luo, Chen Zhao
- Year
- 2026
- Journal
- arXiv preprint
- DOI
- arXiv:2604.01059
- arXiv
- 2604.01059
We present Tsim, an open-source high-throughput simulator for universal noisy quantum circuits targeting quantum error correction. Tsim represents quantum circuits as ZX diagrams, where Pauli channels are modeled as parameterized vertices. Diagrams are simplified via parameterized ZX rules, and then compiled for vectorized sampling with GPU acceleration. After the one-time compilation, one can sample detector or measurement shots in linear time in the number of Clifford gates and exponentially only in the number of non-Clifford gates. Tsim implements the Stim API and fully supports the Stim circuit format, extending it with T and arbitrary single-qubit rotation instructions. For low-magic circuits, Tsim throughput can match the sampling performance of Stim.
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Asymptotic Expansions for Neural Network Approximations of Quantum Channels
Rômulo Damasclin Chaves dos Santos
- Year
- 2026
- Journal
- arXiv preprint
- DOI
- arXiv:2603.18033
- arXiv
- 2603.18033
This paper establishes the Quantum Voronovskaya--Damasclin (QVD) Theorem, providing a complete asymptotic characterization of Quantum Neural Network Operators in the approximation of arbitrary quantum channels. The result extends the classical Voronovskaya theorem from scalar approximation to the non-commutative operator framework of quantum information theory. We introduce rigorous quantum analogues of Sobolev and Hölder spaces defined through Fréchet differentiability in the Liouville representation and measured using the completely bounded (diamond) norm. Within this framework, we derive an explicit asymptotic expansion of the approximation error and identify the fundamental mechanisms governing convergence. The expansion separates integer-order differential contributions, fractional corrections associated with limited regularity, and intrinsically non-commutative effects arising from operator algebra structure. We also establish a sharp remainder estimate with explicit dependence on the regularity of the channel and the dimension of the underlying Hilbert space. Several applications demonstrate the scope of the theory. These include a quantum central limit theorem describing the fluctuation regime of quantum neural network operators, an optimal interpolation method based on operator geometric means, and a convergence acceleration procedure inspired by Richardson extrapolation. The results provide a rigorous mathematical foundation for the asymptotic analysis of quantum neural network models and establish a direct connection between classical approximation theory, operator algebras, and quantum information science, with implications for quantum algorithms and quantum machine learning.
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