Quantum Computing
Using large-N theory to study VQE ansatzes
One of the most promising applications of near-term quantum computers is to use a variational quantum eigensolver (VQE) to approximate the ground states of Hamiltonians found in quantum chemistry. However, this method requires ansatz wavefunctions which can consistently provide good approximations to the ground states of strongly correlated Hamiltonians, which is in general very hard to prove. Interestingly, as we show in [1], the approximation ratio achieved by certain anzatzes when approximating the ground state of strongly correlated Hamiltonians can be calculated exactly thanks to large-N techniques developed in the context of the Sachdev-Ye-Kitaev model. More generally, we propose large-N techniques as a novel tool to assess and find new variational states for near-term implementations of VQE.
[1] Arijit Haldar, Omid Tavakol, Thomas Scaffidi, "Variational wavefunctions for Sachdev-Ye-Kitaev models", Phys. Rev. Research 3, 023020 (2021)
Protecting quantum information with gapless SPT edge states
The interplay between topology and criticality is also a question of direct relevance to practical quantum information processing, since real-life systems often have unavoidable gapless degrees of freedom like phonons. We showed in [1] how to utilize the concept of gapless SPTs to dramatically enhance the coherence of edge modes in gapless and symmetry-broken systems.
[1] Daniel E. Parker, Romain Vasseur, Thomas Scaffidi, "Topologically-Protected Long Edge Coherence Times in Symmetry-Broken Phases", Phys. Rev. Lett. 122, 240605