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arXiv · 2408.15459

Statistical modeling of quantum error propagation

Zhuoyang Ye
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Abstract

In this paper, I design a new statistical abstract model for studying quantum error propagation. For each circuit, I give the algorithm to construct the Error propagation space-time graph(\textbf{EPSTG}) graph as well as the bipartite reverse spanning graph (\textbf{RSG}). Then I prove that the problem of finding an error pattern is $\mathcal{P}$ while calculate the error number distribution is $\textit{NP-complete}$. I invent the new measure for error propagation and show that for widely used transversal $CNOT$ circuit in parallel, the shift of distribution is bounded by $\frac{n}{27}$, where $n$ is the number of physical qubits. The consistency between the result of qiskit simulation and my algorithm justify the correctness of my model. Applying the framework to random circuit, I show that there is severe unbounded error propagation when circuit has global connection. We also apply my framework on parallel transversal logical $CNOT$ gate in surface code, and demonstrate that the error threshold will decrease from $0.231$ to $0.134$ per cycle.

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Zhuoyang Ye. 2024-08-28. Statistical modeling of quantum error propagation. https://arxiv.org/abs/2408.15459

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