CAREER: Complexity of quantum many-body systems: learnability, approximations, and entanglement

Harvard University, Cambridge MA

Investigators

Abstract

Interaction between particles gives rise to the matter seen in the physical world and facilitates the study as well as the manipulation of matter. However in the quantum realm, interaction between quantum particles can lead to daunting challenges - it enforces complex collective behaviour of the particles that appear very hard to study using current computational means. This project aims to pin down the nature of this complexity by investigating a series of fundamental questions. First, are the interactions themselves simple enough that their precise knowledge can be gained by a practical algorithm? Such an algorithm is also expected to benefit quantum technologies, facilitating learning and testing of quantum devices. Second, how computationally difficult is it to estimate physical properties of the quantum particles, even if the knowledge of interactions is available? This question will help understand the limits of near term quantum devices in probing quantum particles. Third, could the collective behaviour of particles be simple rather than complex, under some common assumptions on the interactions? This would allow efficient means to computationally simulate systems that respect the assumptions. The educational plan centers around computation and physics, encompassing a seminar series at Harvard University with a diverse list of speakers, development of a quantum computing curriculum at Harvard University for graduate and undergraduate students, and teaching quantum theory to students from Boston high-schools with limited access to Science, Technology, Engineering and Math education. This project will study local Hamiltonians - the quantum analogues of constraint satisfaction problems in theoretical computer science - that model interactions in quantum many-body systems. In particular, it will aim to make progress on three long-standing questions: Can a local Hamiltonian be learned efficiently from the Gibbs quantum states? What are the fundamental limits on the approximations to the ground energies of a local Hamiltonian (the quantum Probabilistically-Checkable-Proofs conjecture)? Does limited entanglement hold for the ground states of two-dimensional gapped local Hamiltonians (the area law conjecture)? These questions address the complexity of quantum many-body systems from the view of three well-studied measures: learnability, approximability and entanglement. This is inspired by three successful ways to measure complexity of a computation in theoretical computer science - time complexity, space complexity and randomness. In fact, ideas from theoretical computer science are expected to be crucial in making progress on the above questions. Furthermore, research will add to the knowledge in quantum technologies: Hamiltonian learning techniques will find use in the testing of programmable quantum devices and progress on the quantum Probabilistically-Checkable-Proofs conjecture will limit the efficiency of various near-term quantum algorithms for quantum many-body problems. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.