Discovery Early Career Researcher Award - Grant ID: DE230100829
Funder
Australian Research Council
Funding Amount
$425,100.00
Summary
Geometric approaches to quantum many body problems. The project aims to utilise results from differential geometry and related areas to investigate the physics of interacting many-body quantum systems. This project expects to generate new knowledge in the area of mathematical physics with broad applications in quantum information, condensed matter physics and statistical mechanics. The key focus will lie on the development of variational methods for the efficient simulation of quantum evolution ....Geometric approaches to quantum many body problems. The project aims to utilise results from differential geometry and related areas to investigate the physics of interacting many-body quantum systems. This project expects to generate new knowledge in the area of mathematical physics with broad applications in quantum information, condensed matter physics and statistical mechanics. The key focus will lie on the development of variational methods for the efficient simulation of quantum evolution and the characterisation of suitable quantum state families by their correlation structures.Read moreRead less
Unifying discrete and continuous methods in quantum information theory. This project aims to address a critical gap in quantum information theory by unifying the way that both discrete and continuous quantum systems are represented in mathematical models. This project expects to generate new knowledge in quantum information science by using cutting-edge mathematical tools and insights from signal processing theory. Expected outcomes of this project include a new mathematical framework for use in ....Unifying discrete and continuous methods in quantum information theory. This project aims to address a critical gap in quantum information theory by unifying the way that both discrete and continuous quantum systems are represented in mathematical models. This project expects to generate new knowledge in quantum information science by using cutting-edge mathematical tools and insights from signal processing theory. Expected outcomes of this project include a new mathematical framework for use in quantum science and technology development. This should provide significant benefits, such as new ways to efficiently simulate certain quantum processes on ordinary computers and novel approaches to handling noise in quantum computers.Read moreRead less
Shuffle algebras and vertex models. Shuffle algebras are important new mathematical structures that offer a new approaches and techniques to solve outstanding open problems in a variety of branches of mathematics, including mathematical physics, algebraic geometry and combinatorics. This project proposes to find solutions to key open problems using connections between shuffle algebras and integrable lattice models. The expected outcomes include (i) a new framework of shuffle algebra techniques t ....Shuffle algebras and vertex models. Shuffle algebras are important new mathematical structures that offer a new approaches and techniques to solve outstanding open problems in a variety of branches of mathematics, including mathematical physics, algebraic geometry and combinatorics. This project proposes to find solutions to key open problems using connections between shuffle algebras and integrable lattice models. The expected outcomes include (i) a new framework of shuffle algebra techniques to solve challenging research problems in mathematical physics and statistical mechanics, (ii) practical and computationally feasible constructions of shuffle algebras using vertex models, (iii) solutions to unresolved spectral problems of open quantum systems.Read moreRead less
Transformative simulation techniques for complex polymer networks. The study of long chain polymers like DNA using computer simulations has uncovered exciting insights over many years. Generally these have been limited to simple topologies, interactions, and environments. This project aims to develop the next generation of simulation techniques to tackle a new frontier of polymer models, including those with complex topologies like stars, knots, and links, which have hitherto been inaccessible. ....Transformative simulation techniques for complex polymer networks. The study of long chain polymers like DNA using computer simulations has uncovered exciting insights over many years. Generally these have been limited to simple topologies, interactions, and environments. This project aims to develop the next generation of simulation techniques to tackle a new frontier of polymer models, including those with complex topologies like stars, knots, and links, which have hitherto been inaccessible. Expected outcomes include new simulation methods which harness modern computational clusters, leading to greater understanding of polymers with complex topologies and in complicated environments. Important elements of biological processes may be discovered, such as how polymer structure affects DNA transcription.Read moreRead less