Retrieving Quantum Information with Active Learning

Active learning is a machine learning method aiming at optimal design for model training. At variance with supervised learning, which labels all samples, active learning provides an improved model by labeling samples with maximal uncertainty according to the estimation model. Here, we propose the use of active learning for efficient quantum information retrieval, which is a crucial task in the design of quantum experiments. Meanwhile, when dealing with large data output, we employ active learning for the sake of classification with minimal cost in fidelity loss. Indeed, labeling only 5% samples, we achieve almost 90% rate estimation. The introduction of active learning methods in the data analysis of quantum experiments will enhance applications of quantum technologies.

Figure 1

(a) The quantum state in a lattice of $21\times 21=441$ qubits, prepared by Alice for binary classification. The value of $⟨\widehat{{\sigma }_z}⟩=\cos \alpha \in [-1,1]$ is plotted in the color map from blue ($-1$) to red (1). (b) USAMP protocol. Thick black dashed line represents the initial SVM that divides the lattice into two parts, using standardized support vectors of two oracles provided by Alice (circled by red and blue). Thin dash-dotted lines with colors from black to green illustrate the update of the model, where candidates which are selected according to USAMP strategy are circled in the same color. Qubits with the minimal fidelities among their $n$ copies are identified by Gaussian weak measurements with $\sigma =10$ and $n=500$. We have covered their initial states by smaller circles in different color, depending on the outcome. Thick green dotted line represents the SVM after labeling 20 samples via weak measurements. (c) QBC protocol. We present the evolution of the SVM as one model in our committee, where other parameters are unchanged. (d) Weak values of all qubits after performing weak measurements only once on the quantum state. These weak values contain little information which is hardly useful for classification, which requires $n$ copies of the quantum state for obtaining statistically meaningful information.

Figure 2

Mean correct rates of classification model (SVM) with random sampling (red dots), USAMP (blue triangles) and QBC (green diamonds) as different sampling strategies. Error bars denote confidence intervals of 0.95. Each qubit is sampled over an ensemble of (a) 5, (b) 50, (c) 100, and (d) 500 qubits. Other parameters agree with those in Fig. 1.

Figure 3

Mean correct rates of classification model (SVM) with USAMP. Each qubit is labeled by strong measurement (red dots) and weak measurement (blue triangles). Parameters remain the same as in previous figures.