Algebraic methods, Quantum Gravity and Quantum Computing

Quantum algebra covers the interface between algebra, representation theory and category theory on the one hand, and mathematical physics and integrable systems on the other. It emerged with the discovery of the Jones knot invariant and quantum groups as a new notion of symmetry applicable to certain quantum systems. Quantum groups, a.k.a. Hopf algebras, can also be viewed as key examples of noncommutative geometry, which is our second theme.

In a quantum or noncommutative geometry coordinates can be noncommutative operators, much as in quantum mechanics. Even spacetime itself could be better modelled in this way due to quantum gravity corrections visible at the Planck scale of 10^-35 metres. By now, there is a systematic framework of quantum Riemannian geometry extending the tools of Einstein's General Relativity, such as curvature and geodesics, to this quantum setting. This has then been used to solve baby quantum gravity models in which the Universe is modelled as a small graph. 

Modern physics problems require advanced computation to extract information from big data, often exceeding the capabilities of traditional methods. Quantum computing, a rapidly emerging technology rooted in quantum physics, has shown great promise in addressing these challenges beyond the scope of classical computing. At our Centre, we explore potential applications of quantum computing and quantum simulation on gravitational wave astronomy, quantum gravity, and superstring theory.

In the near term, the Queen Mary's LIGO Scientific Collaboration team led by Dr Hong Qi is completing the development of the world's first quantum algorithm for extracting the source properties of gravitational waves from colliding black holes and neutron stars. In the meanwhile, Dr Masanori’s team is working on simulating simple quantum systems that are dual to black holes via holography. 

Looking forward, Dr Masanori’s team anticipates achieving a microscopic description of the high-density environment in neutron stars based on quantum chromodynamics. They also aim to simulate supersymmetric gauge theories, crucial to superstring theory, and enhance algorithms for nonlinear partial differential equations.  Dr. Hong Qi’s team will be developing quantum algorithms for gravitational wave detection and inference for the next generation of detectors like Cosmic Explorer, Einstein Telescope, and LISA.