Efficient algorithm for optimizing data pattern tomography

黎曼优化的正则化：应用于过程层析成像与量子机器学习

Regularization of Riemannian optimization: Application to process tomography and quantum machine learning

本文提出在黎曼优化中加入秩惩罚正则化项，用于量子信道优化，在过程层析成像中加速收敛并提高保真度，在分类任务中降低信道秩且保持精度，揭示数据所需最小秩。

Radon transform and pattern functions in quantum tomography

The two-dimensional Radon transform of the Wigner quasiprobability is introduced in canonical form and the functions playing a role in its inversion are discussed. The transformation properties of this Radon transform with respect to displacement and squeezing of states are studied and it is shown that the last is equivalent to a symplectic transformation of the variables of the Radon transform with the contragredient matrix to the transformation of the variables in the Wigner quasiprobability. The reconstruction of the density operator from the Radon transform and the direct reconstruction of…

使用Transformer模型统一量子态层析与哈密顿量学习：一种面向量子系统的类语言翻译方法

Unified Quantum State Tomography and Hamiltonian Learning Using Transformer Models: A Language-Translation-Like Approach for Quantum Systems

本文提出利用Transformer注意力机制将量子态层析与哈密顿量学习统一到一个模型中，通过精心设计训练数据实现多量子系统上的有效学习，并展示其可扩展性与少样本学习潜力。

Reconstruction of spatial qutrit states based on realistic measurement operators

Spatial qudit states can be realized by using multi-slits to discretize the transverse momentum of a photon. The merit of this kind of spatial qudit states is that the implementation of higher dimensional qudits is relatively easy. As we have recently shown, the quantum states of these spatial qudits can be analyzed by scanning a single interference pattern. This method of single scan tomography can also be applied at higher dimensions, but the reconstruction becomes more sensitive to smaller details of the scanned patterns as the dimensions increase. In this paper, we investigate the effect o…

Graphix: optimizing and simulating measurement-based quantum computation on local-Clifford decorated graph

We introduce an open-source software library Graphix, which optimizes and simulates measurement-based quantum computation (MBQC). By combining the measurement calculus with an efficient graph state simulator, Graphix allows the classical preprocessing of Pauli measurements in the measurement patterns, significantly reducing the number of operations required to perform the quantum computation while maintaining determinism. For a measurement pattern translated from a quantum circuit, this corresponds to the preprocessing of all Clifford gates, and this improvement in the one-way model is importa…

Optimizing Timing of High-Success-Probability Quantum Repeaters

Optimizing a connection through a quantum repeater network requires careful attention to the photon propagation direction of the individual links, the arrangement of those links into a path, the error management mechanism chosen, and the application's pattern of consuming the Bell pairs generated. We analyze combinations of these parameters, concentrating on one-way error correction schemes (1-EPP) and high success probability links (those averaging enough entanglement successes per round trip time interval to satisfy the error correction system). We divide the buffering time (defined as minim…

Optimizing a Polynomial Function on a Quantum Simulator

Gradient descent method, as one of the major methods in numerical optimization, is the key ingredient in many machine learning algorithms. As one of the most fundamental way to solve the optimization problems, it promises the function value to move along the direction of steepest descent. For the vast resource consumption when dealing with high-dimensional problems, a quantum version of this iterative optimization algorithm has been proposed recently[arXiv:1612.01789]. Here, we develop this protocol and implement it on a quantum simulator with limited resource. Moreover, a prototypical experim…

Reliable optimization of arbitrary functions over quantum measurements

As the connection between classical and quantum worlds, quantum measurements play a unique role in the era of quantum information processing. Given an arbitrary function of quantum measurements, how to obtain its optimal value is often considered as a basic yet important problem in various applications. Typical examples include but not limited to optimizing the likelihood functions in quantum measurement tomography, searching the Bell parameters in Bell-test experiments, and calculating the capacities of quantum channels. In this work, we propose reliable algorithms for optimizing arbitrary fu…

Direct parameter estimations from machine-learning enhanced quantum state tomography

With the capability to find the best fit to arbitrarily complicated data patterns, machine-learning (ML) enhanced quantum state tomography (QST) has demonstrated its advantages in extracting complete information about the quantum states. Instead of using the reconstruction model in training a truncated density matrix, we develop a high-performance, lightweight, and easy-to-install supervised characteristic model by generating the target parameters directly. Such a characteristic model-based ML-QST can avoid the problem of dealing with large Hilbert space, but keep feature extractions with high…

一种用于利用经典影子成像识别多样化量子相变的无监督框架

A Unsupervised Framework for Identifying Diverse Quantum Phase Transitions Using Classical Shadow Tomography

本文提出一种结合经典影子表示与无监督主成分分析的机器学习方法，用于识别不同量子相变。通过随机Pauli测量采样自旋配置，分析数据中的隐藏统计模式，捕捉量子临界性的特征。

利用量子计算机优化二维等距张量网络

Optimizing two-dimensional isometric tensor networks with quantum computers

本文提出混合量子-经典等距张量网络优化算法，无需近似收缩即可求解二维量子系统基态，在25量子比特二维横场伊辛模型上验证其开销远低于传统变分量子本征求解器，为可扩展变分量子算法提供新路径。