arXiv subjects

Andrew Hallam

Publications and source records attributed to Andrew Hallam.

23 records · Page 2Linked to original sources

arXiv2021

Emergence of Gaussianity in the thermodynamic limit of interacting fermions

Systems of interacting fermions can give rise to ground states whose correlations become effectively free-fermion-like in the thermodynamic limit, as shown by Baxter for a class of integrable models that include the one-dimensional XYZ spin-$\frac{1}{2}$ chain. Here, we quantitatively analyse this behaviour by establishing the relation between system size and correlation length required for the fermionic Gaussianity to emerge. Importantly, we demonstrate that this behaviour can be observed through the applicability of Wick's theorem and thus it is experimentally accessible. To establish the relevance of our results to possible experimental realisations of XYZ-related models, we demonstrate that the emergent Gaussianity is insensitive to weak variations in the range of interactions, coupling inhomogeneities and local random potentials.

cond-mat.str-el↗

arXiv2019

Entanglement compression in scale space: from the multiscale entanglement renormalization ansatz to matrix product operators

The multiscale entanglement renormalization ansatz (MERA) provides a constructive algorithm for realizing wavefunctions that are inherently scale invariant. Unlike conformally invariant partition functions however, the finite bond dimension $χ$ of the MERA provides a cut-off in the fields that can be realized. In this letter, we demonstrate that this cut-off is equivalent to the one obtained when approximating a thermal state of a critical Hamiltonian with a matrix product operator (MPO) of finite bond dimension $χ$. This is achieved by constructing an explicit mapping between the isometries of a MERA and the local tensors of the MPO.

cond-mat.str-el↗

arXiv2018

Hierarchical quantum classifiers

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.

quant-ph↗

arXiv2018

Compact Neural Networks based on the Multiscale Entanglement Renormalization Ansatz

This paper demonstrates a method for tensorizing neural networks based upon an efficient way of approximating scale invariant quantum states, the Multi-scale Entanglement Renormalization Ansatz (MERA). We employ MERA as a replacement for the fully connected layers in a convolutional neural network and test this implementation on the CIFAR-10 and CIFAR-100 datasets. The proposed method outperforms factorization using tensor trains, providing greater compression for the same level of accuracy and greater accuracy for the same level of compression. We demonstrate MERA layers with 14000 times fewer parameters and a reduction in accuracy of less than 1% compared to the equivalent fully connected layers, scaling like O(N).

cs.NE↗

arXiv2018

The Lyapunov Spectrum of Quantum Thermalisation

The eigenstate thermalisation hypothesis resolves the paradox of emergent thermal or classical behaviour in a closed quantum system by focussing upon local observations. This permits the remainder of the system to act as a bath, thermalisation arising due to a process of de-phasing that gradually reveals the thermal nature of local observables measured in an eigenstate. This is very different from thermalisation in closed classical systems, which is driven by dynamical chaos. We show how quantum thermalisation in closed systems can be recast in a way that is directly related to classical thermalisation. Local observables can be accurately captured by projecting states onto a suitable variational manifold. Evolving on this manifold using the time-dependent variational principle projects the quantum dynamics onto a (semi-)classical Hamiltonian dynamics. Thermalisation in this setting is driven by dynamical chaos. We carry out this procedure for an infinite spin chain in two ways --- using the matrix product state ansatz for the wavefunction and for the thermofield double purification of the density matrix --- and extract the full Lyapunov spectrum of the resulting chaotic dynamics. This provides an alternative perspective upon eigenstate thermalisation, pre-thermalisation and integrability.

cond-mat.str-el↗