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<p>Estimating expectation values of quantum Hamiltonians is a fundamental task in quantum information processing, especially for near-term quantum devices. CS and their variants provide powerful randomized measurement strategies, but they typically assume either complete knowledge of the observables or no prior information at all. In many realistic scenarios, however, only partial information about the Hamiltonian is available—for instance, a known Hamiltonian followed by an unknown one, or only the probability distribution of Pauli operators on each qubit. Here, we address this gap by introducing a unified framework based on random unsharp Pauli measurements. The randomness enables the estimation of unknown observables while we provide a multi-qubit global optimization cost function for the known part of the Hamiltonian. We further consider the scenario where only the probability distribution of Pauli matrices on each qubit is known as prior information, and we analyze two random Hamiltonian models: the Bernoulli appearance model and fixed-term sampling model. For both, we derive an optimal measurement probability distribution. Furthermore, our framework derives unbiased estimators for both the Hamiltonian and the quantum state under local unsharp measurement noise. We experimentally demonstrate the feasibility and superiority of our approach on an optical platform. This work fills an important gap in observable estimation in the regime of partial prior knowledge and provides a practical, noise-robust tool for noisy quantum devices.</p>

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Robust Hamiltonian estimation with partial prior information via random unsharp Pauli measurements

  • 期刊论文

  • 发表日期：

    2026年7月28日

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  • Xiaolin Zhang,
  • Chaobo Xi,
  • Yuyang Tang,
  • Yunlong Wang,
  • Chenhui Wang,
  • Hong Gao,
  • Fuli Li,
  • Yu Xiang,
  • Feiran Wang,
  • Pei Zhang

摘要

Estimating expectation values of quantum Hamiltonians is a fundamental task in quantum information processing, especially for near-term quantum devices. CS and their variants provide powerful randomized measurement strategies, but they typically assume either complete knowledge of the observables or no prior information at all. In many realistic scenarios, however, only partial information about the Hamiltonian is available—for instance, a known Hamiltonian followed by an unknown one, or only the probability distribution of Pauli operators on each qubit. Here, we address this gap by introducing a unified framework based on random unsharp Pauli measurements. The randomness enables the estimation of unknown observables while we provide a multi-qubit global optimization cost function for the known part of the Hamiltonian. We further consider the scenario where only the probability distribution of Pauli matrices on each qubit is known as prior information, and we analyze two random Hamiltonian models: the Bernoulli appearance model and fixed-term sampling model. For both, we derive an optimal measurement probability distribution. Furthermore, our framework derives unbiased estimators for both the Hamiltonian and the quantum state under local unsharp measurement noise. We experimentally demonstrate the feasibility and superiority of our approach on an optical platform. This work fills an important gap in observable estimation in the regime of partial prior knowledge and provides a practical, noise-robust tool for noisy quantum devices.