Southwest Quantum Information and Technology

Fourteenth Annual Meeting, February 16-19, 2012
Albuquerque, New Mexico

Full Program | Thursday | Friday | Saturday | Sunday | All Sessions

SESSION 6: Quantum Many-Body Physics and QIP - Alvarado "D"
Session Chair:
4:00pm-4:45pm	Norbert Schuch, California Institute of Technology (invited)
	Matrix Product States, Projected Entangled Pair States, and the entanglement spectrum of two-dimensional quantum systems
	Abstract. Matrix Product States (MPS) and Projected Entangled Pair States (PEPS) provide a description of correlated quantum many-body states from a local perspective. They faithfully approximate ground states of local Hamitonians which makes them powerful numerical tools, while at the same time their ability to explain the global behavior of quantum many-body systems from local properties makes them useful for analytical studies. In my talk, I will give an introduction to Matrix Product States and PEPS as analytical and numerical tools, and illustrate their usefulness by showing how PEPS can be used to establish a full bulk-boundary duality for two-dimensional quantum systems. In particular, PEPS provide an explicit construction relating the entanglement spectrum of a two-dimensional region to the spectrum of a one-dimensional model associated to its boundary, and thereby provide new tools for the analytical and numerical study of boundary models.
4:45pm-5:15pm	Rolando Somma, Los Alamos National Laboratory
	Spectral Gap Amplification
	Abstract. Several problems in science can be solved by preparing a specific eigenstate of some Hamiltonian H. The generic cost of quantum algorithms for these problems is determined by the inverse spectral gap of H for that eigenstate and the cost of evolving with H for some fixed time. The goal of spectral gap amplification is to construct a Hamiltonian H' with the same eigenstate as H but a bigger spectral gap, requiring that constant-time evolutions with H' and H are implemented with nearly the same cost. I will show that a quadratic spectral gap amplification is possible when H satisfies a frustration-free property and construct H' for these cases. This results in quantum speedups for optimization problems. It also yields improved constructions for adiabatic simulations of quantum circuits and for the preparation of projected entangled pair states (PEPS), which play an important role in quantum many-body physics. Defining a suitable black-box model, I will establish that the quadratic amplification is optimal for frustration-free Hamiltonians and that no spectral gap amplification is possible, in general, if the frustration-free property is removed. Interestingly, this results in some limits on the power of some classical methods that simulate quantum adiabatic evolutions.