Counting anticommuting Pauli pairs in linear time
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866913113418235904 |
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| author | Cha, Hyunho Lee, Jungwoo |
| author_facet | Cha, Hyunho Lee, Jungwoo |
| contents | Many quantum computing workflows manipulate long lists of Pauli strings. A basic classical subroutine involves taking $m$ Pauli strings on $n$ qubits, each of weight bounded by a constant, to determine if they are pairwise commuting, identify any counterexamples, or calculate the exact number of anticommuting unordered pairs. The standard general-purpose route represents Pauli strings in binary symplectic form and checks pairs in $O(m^2)$ time. Here, we provide an $O(m)$ algorithm for the bounded locality regime. It maintains counts of all labeled subpatterns of previously inserted strings and answers each new string query by a subset zeta identity. Our algorithm is particularly useful for processing large collections of Pauli strings within the bounded locality regime. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_11016 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Counting anticommuting Pauli pairs in linear time Cha, Hyunho Lee, Jungwoo Quantum Physics Many quantum computing workflows manipulate long lists of Pauli strings. A basic classical subroutine involves taking $m$ Pauli strings on $n$ qubits, each of weight bounded by a constant, to determine if they are pairwise commuting, identify any counterexamples, or calculate the exact number of anticommuting unordered pairs. The standard general-purpose route represents Pauli strings in binary symplectic form and checks pairs in $O(m^2)$ time. Here, we provide an $O(m)$ algorithm for the bounded locality regime. It maintains counts of all labeled subpatterns of previously inserted strings and answers each new string query by a subset zeta identity. Our algorithm is particularly useful for processing large collections of Pauli strings within the bounded locality regime. |
| title | Counting anticommuting Pauli pairs in linear time |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2605.11016 |