Extracting quantum dynamics from feedback learning algorithms through principal component analysis

Mehjabin Khatoon, K. Niha

J. L. White, Brett J. Pearson, P. H. Bucksbaum

Genetic learning algorithms are widely used to control ultrafast optical pulse shapes for photo-induced quantum control of atoms and molecules. An outstanding issue is how to use the solutions found by these algorithms to learn about the system's quantum dynamics. We propose a simple method based on principal component analysis of the control space, which can reveal the degrees of freedom responsible for control, and aid in the construction of an effective Hamiltonian for the dynamics.

Renzo Mosetti

Emanuele Dri, Antonello Aita, Tommaso Fioravanti +5 more

Quantum Machine Learning has gained significant attention in recent years as a way to leverage the relationship between quantum information and machine learning. Principal Component Analysis (PCA) is a fundamental technique in machine learning, and the potential for its quantum acceleration has been extensively studied. However, an algorithmic end-to-end implementation remains challenging. This paper covers quantum PCA implementation up to extracting the principal components. We extend existing processes for quantum state tomography to extract the eigenvectors from the output state, addressing the challenges of dealing with complex amplitudes in the case of non-integer eigenvalues. Finally, we apply our implementation to a practical quantum finance use case related to interest rate risk, and present the results of our experiments.

Matthew Choi, Daniel Flam-Shepherd, Thi Ha Kyaw +1 more

Zhaokai Li, Zihua Chai, Yuhang Guo +6 more

Principal component analysis (PCA) has been widely adopted to reduce the dimension of data while preserving the information. The quantum version of PCA (qPCA) can be used to analyze an unknown low-rank density matrix by rapidly revealing the principal components of it, i.e., the eigenvectors of the density matrix with the largest eigenvalues. However, because of the substantial resource requirement, its experimental implementation remains challenging. Here, we develop a resonant analysis algorithm with minimal resource for ancillary qubits, in which only one frequency-scanning probe qubit is required to extract the principal components. In the experiment, we demonstrate the distillation of the first principal component of a 4 × 4 density matrix, with an efficiency of 86.0% and a fidelity of 0.90. This work shows the speedup ability of quantum algorithm in dimension reduction of data and thus could be used as part of quantum artificial intelligence algorithms in the future.