Monday, Dec. 1st, 2014
at 4:00 p.m. in Time Room (294)
Perimeter Institute Quantum Discussions – Ground state connectivity of local Hamiltonians - with Jamie Sikora, Universite Paris Diderot
The study of ground spaces of local Hamiltonians is a fundamental task in condensed matter physics. In terms of computational complexity theory, a common focus in this area has been to estimate a given Hamiltonian’s ground state energy. However, from a physics perspective, it is sometimes more relevant to understand the structure of the ground space itself. In this talk, we pursue the latter direction by introducing the notion of “ground state connectivity” of local Hamiltonians. In particular, we show that determining how “connected” the ground space of a local Hamiltonian is can range from QCMA-complete to NEXP-complete. (Here, QCMA is the same as QMA, but with a classical witness.) As a result, we obtain a natural QCMA-complete problem, a task which has generally proven difficult since the conception of QCMA over a decade ago.
Wednesday, Dec. 3rd, 2014
at 4:00 p.m. in Time Room (294)
Perimeter Institute Quantum Discussions – Different Strategies for Quantum Adiabatic Optimization, and the Computational Power of Simulated Quantum Annealing - with Elizabeth Crosson, MIT
Quantum Adiabatic Optimization proposes to solve discrete optimization problems by mapping them onto quantum spin systems in such a way that the optimal solution corresponds to the ground state of the quantum system. The standard method of preparing these ground states is using the adiabatic theorem, which tells us that quantum systems tend to remain in the ground state of a time-dependent Hamiltonian which transforms sufficiently slowly. In this talk I'll show that alternative strategies using non-adiabatic effects can in some cases be dramatically faster for instances which are hard for the traditional adiabatic method. I will also discuss Simulated Quantum Annealing (SQA), which is a classical simulation of adiabatic optimization at non-zero temperature based on Path-Integral Quantum Monte Carlo. SQA is widely used in practice to study adiabatic optimization, but relatively little is known about the rate of convergence of the markov chain that underlies the algorithm. By focusing on a family of instances which adiabatic optimization solves in polynomial time, but require exponential time to solve using classical (thermal) simulated annealing, I will present numerical evidence as well as a work-in-progress proof that SQA can be exponentially faster than classical simulated annealing.