Quantum Information at High and Low Energies

Citation

Tang, Yu Qing (Eugene) (2021) Quantum Information at High and Low Energies. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/xc66-tc77. https://resolver.caltech.edu/CaltechTHESIS:05182021-042001387

Abstract

In this thesis, we take a look at how quantum information theory can be used to study physical systems at both high and low energies.

In the first part of this thesis, we examine the structure of the low-energy subspaces of quantum many-body systems. We show that the existence of error-correcting properties in low-energy subspaces is a generic feature of quantum systems. Using the formalism of matrix product states, we construct explicit quantum error-detecting codes formed from the momentum eigenstates of a quantum many-body system.

We also examine how topological order can persist past the ground state space into the low-energy subspace of excited states by studying the No Low-Energy Trivial States (NLTS) conjecture. We prove a version of the NLTS conjecture under the assumption of symmetry protection. Moreover, we show that our symmetric NLTS result has implications for the performance of quantum variational optimization algorithms by using it to prove a bound on the Quantum Approximate Optimization Algorithm (QAOA).

In the second part of this thesis, we examine problems related to bulk reconstruction in holography and the black hole firewall paradox. Using the formalism of the tensor Radon transform, we devise and implement a numerical algorithm for reconstructing (perturbatively in AdS₃/CFT₂) the bulk metric tensor from a given boundary entropy profile.

We finally examine the black hole firewall problem from the perspective of quantum error-correction and quantum computational complexity. We argue that the state of the Hawking radiation has the special property of being computationally pseudorandom, meaning that it cannot be distinguished from the maximally mixed state by any efficient quantum computation. We show that this implies that each black hole has a natural structure as a quantum error-correcting code.

Thesis Files