Simulating quantum walkers: Quantum walks are the quantum mechanical analogs of classical random walks, describing the propagation of a quantum walker across a lattice, and find application in developing algorithms for simulating quantum many-body systems. Gong et al. used an 8-by-8 two-dimensional (2D) superconducting qubit square lattice containing 62 functional qubits to show how multiple (two) walkers traverse a 2D qubit array, interfering as they go. The authors were also able to program the paths that the walkers follow, demonstrating a Mach-Zehnder interferometer in which a single or multiple quantum walkers coherently traverse two paths before interfering and exiting at a single port. The results illustrate the potential for superconducting-based quantum processors in simulating large-scale quantum systems. Science , abg7812, this issue p. 948

Support vector machine (SVM) is a particularly powerful and flexible supervised learning model that analyzes data for both classification and regression, whose usual algorithm complexity scales polynomially with the dimension of data space and the number of data points. To tackle the big data challenge, a quantum SVM algorithm was proposed, which is claimed to achieve exponential speedup for least squares SVM (LS-SVM). Here, inspired by the quantum SVM algorithm, we present a quantum-inspired classical algorithm for LS-SVM. In our approach, an improved fast sampling technique, namely indirect sampling, is proposed for sampling the kernel matrix and classifying. We first consider the LS-SVM with a linear kernel, and then discuss the generalization of our method to nonlinear kernels. Theoretical analysis shows our algorithm can make classification with arbitrary success probability in logarithmic runtime of both the dimension of data space and the number of data points for low rank, low condition number, and high dimensional data matrix, matching the runtime of the quantum SVM.