Displaying items by tag: Machine learning

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Many quantum machine learning algorithms use a quantum linear system solver (QLS) as a subroutine. HHL type QLS algorithms achieve exponential speedup over classical algorithms for sparse matrices, however for dense matrices the speed-up is less profound, In this paper, Wossnig et al. describe a new QLS algorithm using the quantum singular value estimation. When applied to a dense matrix with spectral norm bounded by a constant, the runtime of this proposed algorithm is bounded by O(κ^2 √n.polylog(n)/e), which is a quadratic improvement over HHL based QLS algorithms. In comparison, classical (non-quantum) linear system solvers typically require time O(n^3) for dense matrices.

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Superpositions of bit strings (many-body spin configurations) have been recently proposed as a key to quantum machine learning applications. Adiabatic protocols may serve as an effective method to prepare such states. If the ground state of the final Hamiltonian in an adiabatic protocol is energetically degenerate, the final state of the protocol is a superposition of the configurations in the degenerate manifold. The challenge is to be able to control the dynamics of the protocol such that the amplitudes of the final state can be deterministically programmed. In this paper, Sieberer et al. present a framework to do precisely that. They apply an adiabatic protocol with controlled diabatic transitions to dynamically prepare programmable superpositions, where the control parameters can, even for large systems, be determined efficiently.

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Topological data analysis (TDA) offers a robust way to extract useful information from noisy, unstructured data by identifying its underlying structure. In this paper, Huang et al. show an experimental proof-of-principle of a recently developed TDA quantum algorithm for calculating Betti numbers of data points (which count the number of topological holes of various dimensions in a scatterplot), using a six-photon quantum processor on a network of three data-points.

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