Experimental Realization of a Quantum Support Vector Machine

The fundamental principle of artificial intelligence is the ability of machines to learn from previous experience and do future work accordingly. In the age of big data, classical learning machines often require huge computational resources in many practical cases. Quantum machine learning algorithms, on the other hand, could be exponentially faster than their classical counterparts by utilizing quantum parallelism. Here, we demonstrate a quantum machine learning algorithm to implement handwriting recognition on a four-qubit NMR test bench. The quantum machine learns standard character fonts and then recognizes handwritten characters from a set with two candidates. Because of the wide spread importance of artificial intelligence and its tremendous consumption of computational resources, quantum speedup would be extremely attractive against the challenges of big data.

Figure 1

Samples of optical character recognition for SVM. (a) The standard font (Times New Roman) images of characters “6” and “9” for training SVM. ${\overrightarrow{x}}_1$ and ${\overrightarrow{x}}_2$ are the feature vectors extracted from the sample images, which are labeled as the “positive” and “negative” class, respectively $(y=\pm 1)$. (b) The arbitrarily chosen handwritten samples for testing the SVM and their corresponding feature vectors. (See Ref. [13] for detailed derivation).

Figure 2

The schematic diagram of the quantum SVM. $H$ is the Hadamard gate. The matrix inversion is employed to acquire the hyperplane parameters. Then, the training-data oracle is applied to prepare the training-data state $|\tilde{u}⟩$. The information of vector ${\overrightarrow{x}}_0$ is introduced by $U_{x_0}$ and then used for classification. The auxiliary phase estimation register for matrix inversion is not shown.

Figure 3

(a) Properties of the ${}^{13}\mathrm{C}$-iodotrifluroethylene. The chemical shifts ${\nu }_i$ and scalar coupling constants ($J_{jk}$) are on and below the diagonal of the table, respectively. The chemical shifts are given with respect to the reference frequencies of 100.62 MHz (Carbon) and 376.48 MHz (Fluorines). (b) The quantum circuit for building the kernel matrix $K$. The rotation angles ${\theta }_i=\mathrm{arccot}[{(x_i)}_1/{(x_i)}_2],i=0,1,2$. After discarding the training-data register (the second qubit), the desired kernel matrix $K$ is obtained as the quantum density matrix of the first qubit. (c) The quantum circuit for classification. $H$ and $S$ are the Hadamard and phase gates, respectively.

Figure 4

(a) The recognition results given by the quantum OCR. The results are indicated by the orientation of the labeled peak in the ${}^{13}\mathrm{C}$ spectrum. The upward peak in this spectrum represents a positive result, which classifies the incoming handwritten character as 6. (b) The recognition results corresponding to the handwritten characters in Fig. 1. Rows 1–4 represent the handwritten characters, experimental indicators, amplitude of the coherent term, and recognition results, respectively.