Coherence Response in Noisy Quantum Measurements
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866918517155037184 |
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| author | Malik, Zachariah Langfitt, Quinn Saleem, Zain |
| author_facet | Malik, Zachariah Langfitt, Quinn Saleem, Zain |
| contents | Readout error models for noisy quantum devices almost universally assume that measurement noise is classical: the measurement statistics are obtained from the ideal computational-basis populations by a column-stochastic assignment matrix $A$. This description is equivalent to assuming that the effective positive-operator-valued measurement (POVM) is diagonal in the measurement basis, and therefore completely insensitive to quantum coherences. We relax this assumption and derive a fully general expression for the observed measurement probabilities under arbitrary completely positive trace-preserving (CPTP) noise preceding a computational-basis measurement. Writing the ideal post-circuit state $\tildeρ$ in terms of its populations $x$ and coherences $y$, we show that the observed probability vector $z$ satisfies $z = A x + C y$, where $A$ is the familiar classical assignment matrix and $C$ is a coherence-response matrix constructed from the off-diagonal matrix elements of the effective POVM in the computational basis. The classical model $z = A x$ arises if and only if all POVM elements are diagonal; in this sense $C$ quantifies accessible information about coherent readout distortions and interference between computational-basis states, all of which are invisible to models that retain only $A$. Our numerical experiments show that incorporating $C$ into readout recovery can improve fidelity over classical inversion and enable selective Pauli twirling with exponentially reduced circuit overhead. This work therefore provides a natural, fully general framework for coherence-sensitive readout modeling on current and future quantum devices. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2512_13949 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Coherence Response in Noisy Quantum Measurements Malik, Zachariah Langfitt, Quinn Saleem, Zain Quantum Physics Mathematical Physics 81P15 Readout error models for noisy quantum devices almost universally assume that measurement noise is classical: the measurement statistics are obtained from the ideal computational-basis populations by a column-stochastic assignment matrix $A$. This description is equivalent to assuming that the effective positive-operator-valued measurement (POVM) is diagonal in the measurement basis, and therefore completely insensitive to quantum coherences. We relax this assumption and derive a fully general expression for the observed measurement probabilities under arbitrary completely positive trace-preserving (CPTP) noise preceding a computational-basis measurement. Writing the ideal post-circuit state $\tildeρ$ in terms of its populations $x$ and coherences $y$, we show that the observed probability vector $z$ satisfies $z = A x + C y$, where $A$ is the familiar classical assignment matrix and $C$ is a coherence-response matrix constructed from the off-diagonal matrix elements of the effective POVM in the computational basis. The classical model $z = A x$ arises if and only if all POVM elements are diagonal; in this sense $C$ quantifies accessible information about coherent readout distortions and interference between computational-basis states, all of which are invisible to models that retain only $A$. Our numerical experiments show that incorporating $C$ into readout recovery can improve fidelity over classical inversion and enable selective Pauli twirling with exponentially reduced circuit overhead. This work therefore provides a natural, fully general framework for coherence-sensitive readout modeling on current and future quantum devices. |
| title | Coherence Response in Noisy Quantum Measurements |
| topic | Quantum Physics Mathematical Physics 81P15 |
| url | https://arxiv.org/abs/2512.13949 |