Efficient quantum state tomography

M. Cramer, Martin Bodo Plenio, Steven T. Flammia +6 more

Ariel Bendersky, Juan Pablo Paz

We present a method for quantum state tomography that enables the efficient estimation, with fixed precision, of any of the matrix elements of the density matrix of a state, provided that the states from the basis in which the matrix is written can be efficiently prepared in a controlled manner. Furthermore, we show how this algorithm is well suited for quantum process tomography, enabling one to perform selective and efficient quantum process tomography.

Xuanmin Zhu, Yuanchun Deng, Runping Gao +3 more

Quantum state tomography strategy via weak value is valid for arbitrary dimensional systems, and can be easily realized. However, the efficiency of quantum state tomography strategy via weak value is lower than that of the conventional quantum state tomography (QST), especially for high-dimensional systems. To improve the efficiency of the scheme, we propose a two-step adaptive quantum state tomography via weak value for pure states (AQSTW). In AQSTW, by using appropriate measurement strength, the efficiency of AQSTW is significantly larger than that of the conventional QST, especially for high-dimensional systems. And AQSTW can be easily implemented. These results demonstrate AQSTW may be useful in the measurements of the unknown quantum states.

Muhammad Hamza Waseem, Faizan-e-Ilahi, Muhammad Sabieh Anwar

Phillip Cornett, Albert B. Dinkins V, Kwang‐Cheng Chen

Jincheng Zhang

This paper introduces Adaptive Quantum State Tomography (AQST), a novel algorithm for efficiently characterizing complex quantum states. Traditional state tomography methods are computationally demanding, particularly for large and highly entangled states. AQST addresses this challenge by dynamically adjusting the sampling strategy during the tomography process, optimizing the reconstruction process and minimizing computational cost. The core mechanism relies on a superposition-based sampling technique, allowing the algorithm to effectively explore the state space and achieve accurate characterization. The paper details the algorithm's design, the rationale behind its key components, and its performance evaluation on benchmark quantum systems. We demonstrate that AQST offers a significant improvement in computational efficiency compared to existing state tomography methods, particularly for complex systems.