Quantum circuits with hierarchical structure have been used to perform binary classification of classical data encoded in a quantum state. We demonstrate that more expressive circuits in the same family achieve better accuracy and can be used to classify highly entangled quantum states, for which there is no known efficient classical method. We compare performance for several different parameterizations on two classical machine learning datasets, Iris and MNIST, and on a synthetic dataset of quantum states. Finally, we demonstrate that performance is robust to noise and deploy an Iris dataset classifier on the ibmqx4 quantum computer. * edward.grant.16@ucl.ac.uk arXiv:1804.03680v2 [quant-ph]
Thermalisation in closed quantum systems occurs through a process of dephasing due to parts of the system outside of the window of observation, gradually revealing the underlying thermal nature of eigenstates. In contrast, closed classical systems thermalize due to dynamical chaos. We demonstrate a deep link between these processes. Projecting quantum dynamics onto variational states using the time-dependent variational principle, results in classical chaotic Hamiltonian dynamics. We study an infinite spin chain in two ways—using the matrix product state ansatz for the wavefunction and for the thermofield purification of the density matrix—and extract the full Lyapunov spectrum of the resulting dynamics. We show that the entanglement growth rate is related to the Kolmogorov–Sinai entropy of dynamics projected onto states with appropriate entanglement, extending previous results about initial entanglement growth to all times. The Lyapunov spectra for thermofield descriptions of thermalizing systems show a remarkable semi-circular distribution.
Five new carbazole-containing polymers have been synthesized. With poly(N-vinylcarbazole) these form two series in which (a) the nitrogen atom of the chromophore is attached to the polymer backbone with an increasingly flexible linking moiety, PNVK, I, -II, -III, and (b) a series in which the backbone is attached to the 9-, 2-and 3-ring positions, I, IV, V. The molecular weights of the polymers have been characterized by membrane osmometry and gel permeation chromatography. These polymers are susceptible to photochemical degradation which causes both scission of the chain backbone and diminution of carbazole chromophore fluorescence. Sensitive viscosity measurements made on samples undergoing this main-chain scission have been used to obtain the intrinsic viscosity-molecular weight K, a values of the resulting fragments. Comparison of the absorption and emission spectra shows that appreciable excimer emission occurs only in the case of poly(lV-vinylcarbazole) (PNVK) and poly [2-(9-ethyl)carbazolylmethyl methacrylate] (IV). Excimer emission from the latter is weakest in polar fluid solvents and strongest in a rigid glassy matrix. Luminescence decay measurements in the presence and absence of anthracene quencher suggest that down-chain energy migration is virtually absent in the sterically unhindered polymers I, II, III, and V, and this is confirmed by steady state analysis of collisional quenching. Collisional quenching of monomer excitation from IV indicates that the excitation is effectively immobilized in the region of not more than three neighboring chromophores. These
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