Preliminaries of Quantum-State Estimation

Sacha Schwarz, Bruno Eckmann, Denis Rosset +1 more

In quantum state tomography, the estimated frequencies do not correspond directly to a physical quantum state, due to statistical fluctuations. Thus, one resorts to point estimators that return the state that matches observations the best, and a variety of estimators have been proposed -- linear inversion, least squares, maximum likelihood (ML) -- each making different trade-offs. In this short note, we investigate an alternative approach inspired by device-independent quantum information protocols. We embed a tomographic complete set of measurement operators within the framework of a Bell scenario, and first regularize the estimated frequencies using a device-independent maximum likelihood algorithm. We then run the standard maximum likelihood algorithm to estimate the underlying quantum state. In this preliminary investigation, we do not observe significant differences in the reconstructed state when using the new algorithm.

Berthold‐Georg Englert

Jincheng Zhang

Quantum state estimation is a crucial component of many quantum computing applications, particularly for analyzing large datasets. Current classical algorithms struggle to efficiently estimate the state of quantum systems, limiting the practical utility of quantum computation. This paper explores the implementation of a novel quantum-enhanced algorithm to address this challenge, aiming to significantly improve the accuracy and efficiency of state estimation for large-scale data. We detail the core mechanism of utilizing quantum phenomena to reduce computational complexity and explore potential advancements in this field. The study focuses on demonstrating the algorithm's effectiveness through theoretical analysis and preliminary experimental validation, highlighting its potential to unlock new capabilities in quantum data analysis.

Jincheng Zhang

Quantum phase estimation (QPE) is a fundamental technique for determining the phase of a quantum state, crucial for various quantum algorithms and quantum measurements. This paper introduces a novel adaptive optimization algorithm, dubbed the "Adaptive Quantum Phase Estimation" (AQPE) algorithm, designed to enhance the efficiency of QPE by dynamically adjusting parameters during the state estimation process. We demonstrate the effectiveness of AQPE through rigorous theoretical analysis and extensive numerical simulations, achieving significantly improved convergence rates compared to traditional optimization techniques. The algorithm leverages a feedback mechanism based on the observed phase error during the estimation, allowing it to iteratively refine the parameter set and ultimately locate the optimal phase estimation. We present preliminary results demonstrating the algorithm's capability to mitigate the challenges associated with conventional QPE, particularly in the presence of noisy data. The implications of this research extend to broader advancements in quantum algorithm design and computational power.

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