Why can’t we classically describe quantum systems?
Chinmay Nirkhe (UC Berkeley (IBM Quantum))
Colloquium
Thursday, March 2, 2023, 3:30 pm
Abstract
A central goal of physics is to understand the low-energy solutions of quantum interactions between particles. This talk will focus on the complexity of describing low-energy solutions; I will show that we can construct quantum systems for which the low-energy solutions are highly complex and unlikely to exhibit succinct classical descriptions. I will discuss the implications these results have for robust entanglement at constant temperature and the quantum PCP conjecture. En route, I will discuss our positive resolution of the No Low-energy Trivial States (NLTS) conjecture on the existence of robust complex entanglement.
Mathematically, for an n-particle system, the low-energy states are the eigenvectors corresponding to small eigenvalues of an exp(n)-sized matrix called the Hamiltonian, which describes the interactions between the particles. Low-energy states are the quantum generalizations of approximate solutions to satisfiability problems such as 3-SAT. In this talk, I will discuss the theoretical computer science techniques used to prove circuit lower bounds for all low-energy states. This morally demonstrates the existence of Hamiltonian systems whose entire low-energy subspace is robustly entangled.
Bio
Chinmay Nirkhe is a research staff scientist with IBM Quantum at the MIT-IBM Watson AI Lab, primarily focusing on the intersection of computational complexity theory and quantum computation. Some of his research interests include error correction, hardness of approximation, and demonstrations of quantum/classical separations. His favorite open questions are the quantum PCP conjecture and whether QCMA equals QMA. He received his Ph.D. in Computer Science from UC Berkeley and his B.S. in Mathematics and Computer Science from Caltech.