Itai Arad, The Hebrew University of Jerusalem
Abstract:
A striking aspect of the quantum world is the exponentiallity of its
underlying Hilbert space. To describe a general state of n quantum
particles, exp(O(n)) numbers are needed, whereas only O(n) numbers
are needed in the classical case.
However, quantum states in nature are not arbitrary; they are governed
by local interactions, and additionally, at non-zero temperatures
quantum effects may weaken due to decoherence. What is then the actual
number of parameters that are needed to describe such states? This
question is crucial for our understanding of many important questions
in condensed matter physics and quantum information, including: the
nature of many-particles entanglement, the power of quantum computers,
and our ability (or inability) to simulate many-body quantum systems.
In my talk I will discuss this question and its relation to two major
open problems in the field of quantum Hamiltonian complexity: area
laws and the quantum PCP conjecture. I will present some recent
results in these areas, as well as some of the remaining open
questions.