Near-Optimal Simultaneous Estimation of Quantum State Moments
Fuente:
arXiv
Saved in:
| Main Authors: | , , , , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866912615110803456 |
|---|---|
| author | Shi, Xiao Jiang, Jiyu Wu, Xian Xie, Jingu Yao, Hongshun Wang, Xin |
| author_facet | Shi, Xiao Jiang, Jiyu Wu, Xian Xie, Jingu Yao, Hongshun Wang, Xin |
| contents | Estimating nonlinear properties such as Rényi entropies and observable-weighted moments serves as a central strategy for spectrum spectroscopy, which is fundamental to property prediction and analysis in quantum information science, statistical mechanics, and many-body physics. However, existing approaches are susceptible to noise and require significant resources, making them challenging for near-term quantum hardware. In this work, we introduce a framework for resource-efficient simultaneous estimation of quantum state moments via qubit reuse. For an $m$-qubit quantum state $ρ$, our method achieves the simultaneous estimation of the full hierarchy of moments $\text{Tr}(ρ^2), \dots, \text{Tr}(ρ^k)$, as well as arbitrary polynomial functionals and their observable-weighted counterparts. By leveraging qubit reset operations, our core circuit for simultaneous moment estimation requires only $2m+1$ physical qubits and $\mathcal{O}(k)$ CSWAP gates, achieving a near-optimal sample complexity of $\mathcal{O}(k \log k / \varepsilon^2)$. We demonstrate this protocol's utility by showing that the estimated moments yield tight bounds on a state's maximum eigenvalue and present applications in quantum virtual cooling to access low-energy states of the Heisenberg model. Furthermore, we show the protocol's viability on near-term quantum hardware by experimentally measuring higher-order Rényi entropy on a superconducting quantum processor. Our method provides a scalable and resource-efficient route to quantum system characterization and spectroscopy on near-term quantum hardware. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_24842 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Near-Optimal Simultaneous Estimation of Quantum State Moments Shi, Xiao Jiang, Jiyu Wu, Xian Xie, Jingu Yao, Hongshun Wang, Xin Quantum Physics Estimating nonlinear properties such as Rényi entropies and observable-weighted moments serves as a central strategy for spectrum spectroscopy, which is fundamental to property prediction and analysis in quantum information science, statistical mechanics, and many-body physics. However, existing approaches are susceptible to noise and require significant resources, making them challenging for near-term quantum hardware. In this work, we introduce a framework for resource-efficient simultaneous estimation of quantum state moments via qubit reuse. For an $m$-qubit quantum state $ρ$, our method achieves the simultaneous estimation of the full hierarchy of moments $\text{Tr}(ρ^2), \dots, \text{Tr}(ρ^k)$, as well as arbitrary polynomial functionals and their observable-weighted counterparts. By leveraging qubit reset operations, our core circuit for simultaneous moment estimation requires only $2m+1$ physical qubits and $\mathcal{O}(k)$ CSWAP gates, achieving a near-optimal sample complexity of $\mathcal{O}(k \log k / \varepsilon^2)$. We demonstrate this protocol's utility by showing that the estimated moments yield tight bounds on a state's maximum eigenvalue and present applications in quantum virtual cooling to access low-energy states of the Heisenberg model. Furthermore, we show the protocol's viability on near-term quantum hardware by experimentally measuring higher-order Rényi entropy on a superconducting quantum processor. Our method provides a scalable and resource-efficient route to quantum system characterization and spectroscopy on near-term quantum hardware. |
| title | Near-Optimal Simultaneous Estimation of Quantum State Moments |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2509.24842 |