Chinmay Nirkhe (IBM)
Why can’t we classically describe quantum systems?
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 [Anshu, Breuckmann, and Nirkhe] 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. I will also discuss stronger separations between ground-states of local Hamiltonians and the set of classically describable quantum states; these separations are provable [Natarajan and Nirkhe] in the distribution-testing oracle model.
Research Interests: Chinmay Nirkhe’s research interests are in theoretical computer science centered around quantum information and hardness of approximation. He is currently interesting in studying the quantum PCP conjecture and the complexity of quantum states.