Quantum gravity simulation on a quantum computer

A unified theory encompassing general relativity and quantum mechanics has remained elusive since research began in the 1930s. Current approaches addressing this challenge have progressed slowly and have made limited predictions for this theory.

However, the recent application of tensor networks to the Anti-de Sitter/Conformal field theory (AdS/CFT) duality offers a fresh and promising route to gain insights into quantum gravity. This duality conjectures that quantum gravity theories defined in asymptotically anti-de Sitter spaces of d + 1 dimensions are dual to conformal field theories defined on their d-dimensional boundaries. By leveraging tensor networks, the entanglement structure and the emergence of spacetime geometry can be effectively captured. The mathematical tractability of discrete tensor networks also circumvents the complexities inherent in other approaches to quantum gravity. A discrete spacetime realisation of the AdS/CFT correspondence would useful for the development of quantum error correcting codes and for providing a numerical framework to study strong interactions.

The objective of this PhD research is to investigate whether conformal dual-unitary circuits constitute a discrete spacetime realisation of the AdS/CFT correspondence and serve as a viable toy model of quantum gravity. This investigation will involve characterising the underlying physics of this model and developing methods for its efficient simulation on a quantum computer.