arXiv subjects

Jake Southall

Publications and source records attributed to Jake Southall.

5 recordsLinked to original sources

arXiv2024

Using Quantum Solved Deep Boltzmann Machines to Increase the Data Efficiency of RL Agents

Deep Learning algorithms, such as those used in Reinforcement Learning, often require large quantities of data to train effectively. In most cases, the availability of data is not a significant issue. However, for some contexts, such as in autonomous cyber defence, we require data efficient methods. Recently, Quantum Machine Learning and Boltzmann Machines have been proposed as solutions to this challenge. In this work we build upon the pre-existing work to extend the use of Deep Boltzmann Machines to the cutting edge algorithm Proximal Policy Optimisation in a Reinforcement Learning cyber defence environment. We show that this approach, when solved using a D-WAVE quantum annealer, can lead to a two-fold increase in data efficiency. We therefore expect it to be used by the machine learning and quantum communities who are hoping to capitalise on data-efficient Reinforcement Learning methods.

quant-ph↗

arXiv2022

Comparing Hermitian and Non-Hermitian Quantum Electrodynamics

In recent years, non-Hermitian quantum physics has gained a lot in popularity in the quantum optics and condensed matter communities in order to model quantum systems with varying symmetries. In this paper, we identify a non-standard inner product that implies bosonic commutator relations for local electric and magnetic field observables and leads to a natural local biorthogonal description of the quantised electromagnetic field. When comparing this description with an alternative local Hermitian description, in which the states of local photonic particles - i.e. of so-called bosons localised in position (blips) - are orthogonal under the conventional Hermitian inner product, we find that there is an equivalence between the two approaches. Careful consideration needs to be given to the physical interpretation of the different descriptions. Whether a Hermitian or a non-Hermitian approach is more suitable depends on the circumstances that we want to model.

quant-ph↗

arXiv2021

Local photons

The classical free-space solutions of Maxwell's equations for light propagation in one dimension include wave packets of any shape that travel at the speed of light. This includes highly-localised wave packets that remain localised at all times. Motivated by this observation, this paper builds on recent work by Southall et al. [J. Mod. Opt. 68, 647 (2021)] and shows that a local description of the quantised electromagnetic field, which supports such solutions and which must overcome several no-go theorems, is indeed possible. Starting from the assumption that the basic building blocks of photonic wave packets are so-called bosons localised in position (blips), we identify the relevant Schr\"odinger equation and construct Lorentz-covariant electric and magnetic field observables. In addition we show that our approach simplifies to the standard description of quantum electrodynamics when restricted to a subspace of states.

quant-ph↗

arXiv2019

Efficiency of free auxiliary models in describing interacting fermions: from the Kohn-Sham model to the optimal entanglement model

Density functional theory maps an interacting Hamiltonian onto the Kohn-Sham Hamiltonian, an explicitly free model with identical local fermion densities. Using the interaction distance, the minimum distance between the ground state of the interacting system and a generic free fermion state, we quantify the applicability and limitations of the exact Kohn-Sham model in capturing the various properties of the interacting system. As a byproduct, this distance determines the optimal free state that reproduces the entanglement properties of the interacting system as faithfully as possible. The parent Hamiltonian of the optimal free state identifies a system that can determine the expectation value of any observable with controlled accuracy. This optimal entanglement model opens up the possibility of extending the systematic applicability of auxiliary free models into the non-perturbative, strongly-correlated regimes.

quant-ph↗

arXiv2019

Locally-acting mirror Hamiltonians

Photons, i.e. the basic energy quanta of monochromatic waves, are highly non-localised and occupy all available space in one dimension. This non-local property can complicate the modelling of the quantised electromagnetic field in the presence of optical elements that are local objects. Therefore, in this paper, we take an alternative approach and quantise the electromagnetic field in position space. Taking into account the negative- {\em and} the positive-frequency solutions of Maxwell's equations, we construct annihilation operators for highly-localised field excitations with bosonic commutator relations. These provide natural building blocks of wave packets of light and enable us to construct locally-acting interaction Hamiltonians for two-sided semi-transparent mirrors.

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