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| Format: | Preprint |
| Veröffentlicht: |
2026
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| Online-Zugang: | https://arxiv.org/abs/2601.16081 |
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| _version_ | 1866909048084889600 |
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| author | Majumdar, Aishwarya Liu, Yuan |
| author_facet | Majumdar, Aishwarya Liu, Yuan |
| contents | A relevant signal in the quantum domain may manifest as a displacement or a squeezing operator in the bosonic phase space. For a real parameter $β$ embedded in such a Gaussian operator, the task of determining if $β\in [β_{-th}, β_{+th}]$ for real asymmetric thresholds $(β_{-th} \ne -β_{+th})$ is a binary decision problem. We propose a framework, the \emph{generalized quantum signal processing interferometry} (GQSPI), to solve this parameter detection problem by recasting the practical task of active binary hypothesis testing on quantum systems to a polynomial approximation problem. We achieve a small decision error probability $p_{\text{err}}$ on the order of $\mathcal{O}(\frac{1}{d}\log{(d)})$, with $d$ as the circuit depth. We analyze the protocol when (i) $β$ is a deterministic parameter, and (ii) when $β$ is drawn randomly from a known prior distribution. The GQSPI protocol is also shown to be robust under oscillator dephasing noise. We further extend our protocol from two thresholds to more general multi-threshold cases. Overall, the proposed framework enables decision-making over arbitrary thresholds for any general Gaussian signal in a single or a few shots. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_16081 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Robust Quantum Algorithmic Binary Decision-Making on Gaussian Signals Majumdar, Aishwarya Liu, Yuan Quantum Physics A relevant signal in the quantum domain may manifest as a displacement or a squeezing operator in the bosonic phase space. For a real parameter $β$ embedded in such a Gaussian operator, the task of determining if $β\in [β_{-th}, β_{+th}]$ for real asymmetric thresholds $(β_{-th} \ne -β_{+th})$ is a binary decision problem. We propose a framework, the \emph{generalized quantum signal processing interferometry} (GQSPI), to solve this parameter detection problem by recasting the practical task of active binary hypothesis testing on quantum systems to a polynomial approximation problem. We achieve a small decision error probability $p_{\text{err}}$ on the order of $\mathcal{O}(\frac{1}{d}\log{(d)})$, with $d$ as the circuit depth. We analyze the protocol when (i) $β$ is a deterministic parameter, and (ii) when $β$ is drawn randomly from a known prior distribution. The GQSPI protocol is also shown to be robust under oscillator dephasing noise. We further extend our protocol from two thresholds to more general multi-threshold cases. Overall, the proposed framework enables decision-making over arbitrary thresholds for any general Gaussian signal in a single or a few shots. |
| title | Robust Quantum Algorithmic Binary Decision-Making on Gaussian Signals |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2601.16081 |