2024/08/28 by Zhuoyang Ye, Ye, Zhuoyang
Computer Science · #FOS: Physical sciences #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Physics (quant-ph)
paper · pdf · doi:10.48550/arxiv.2408.15459
openalex publication_date 2024/08/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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(EPSTG) graph as well as the bipartite reverse spanning graph (RSG). Then I prove that the problem of finding an error pattern is P while calculate the error number distribution is 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 (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.