巴西物理研究中心Diego Noguera团队研究了线性偏振光的量子电路复杂性。相关论文于2025年3月11日发表于《物理评论A》杂志上。

研究组探索了一种扩展到开放系统的量子电路复杂性。为了说明该方法，他们关注一个基本模型，其中状态的投影希尔伯特空间由欧几里德平面中的一组方向来描述。具体来说，研究了混合量子态在与一系列门相互作用时的动力学。后者的目标是精确地调整从参照物到目标的路径，使其尽可能与研究组选择的路径对齐。

该方法涉及对实数2×2密度矩阵序列的分析。这个数学模型在物理上由斯托克斯密度矩阵和门来举例说明，斯托克斯密度矩阵描述了准单色光束的线性偏振，门被视为量子偏振器，其状态也是实的2×2密度矩阵。偏振器线性偏振光之间的相互作用是在这种量子形式的背景下解释的。

在连续门之间的时间间隔内，光的每个密度矩阵都以类似于Gorini-Kosakowski-Lindblad-Sudarshan（GKLS）过程的方式演变。值得注意的是，当考虑容差或准确性的上限时，研究组发现门的数量遵循幂律关系，这给出了复杂性的上限。

附：英文原文

Title: Quantum circuit complexity for linearly polarized light

Author: Evaldo M. F. Curado, Sofiane Faci, Jean-Pierre Gazeau, Tomoi Koide, Alan C. Maioli, Diego Noguera

Issue&Volume: 2025/03/11

Abstract: In this study, we explore a form of quantum circuit complexity that extends to open systems. To illustrate our methodology, we focus on a basic model where the projective Hilbert space of states is depicted by the set of orientations in the Euclidean plane. Specifically, we investigate the dynamics of mixed quantum states as they undergo interactions with a sequence of gates. The latter aim to accurately adjust the path from referent to target, aligning it as closely as possible with the path we have chosen. Our approach involves the analysis of sequences of real 2×2 density matrices. This mathematical model is physically exemplified by the Stokes density matrices, which delineate the linear polarization of a quasimonochromatic light beam, and the gates, which are viewed as quantum polarizers, whose states are also real 2×2 density matrices. The interaction between polarizer-linearly polarized light is construed within the context of this quantum formalism. Each density matrix for the light evolves in an approach analogous to a Gorini-Kossakowski-Lindblad-Sudarshan (GKLS) process during the time interval between consecutive gates. Notably, when considering an upper limit for the tolerance or accuracy, we unearth that the number of gates follows a power-law relationship which gives an upper bound of the complexity.

DOI: 10.1103/PhysRevA.111.032208

Source: https://journals.aps.org/pra/abstract/10.1103/PhysRevA.111.032208