This series covers all areas of research at Perimeter Institute, as well as those outside of PI's scope.
Tensor networks offer an efficient representation of many-body wave-functions in an exponentially large Hilbert space by exploiting the area law of ground state quantum entanglement. I will start with a gentle introduction to the tensor network formalism. Then I will describe its application to realizing Wilson's renormalization group directly on quantum lattice models (e.g. quantum spin chains), with emphasis on the RG fixed points corresponding to conformal field theories.
Scale invariant transfer matrices and Hamiltonians Abstract We investigate the possibility of strictly scale invariant transfer matrices in quantum spin chains based on a certain planar algebra, both as operators and as quadratic forms.
Recent explorations of the space of quantum field theories have provided novel topological and geometric information about this space. This voyage has resulted in the solution of some long-standing questions: the computation of sought-after topological invariants (Gromov-Witten invariants) by a new physics-based approach, the first instance of exact correlation functions in a four-dimensional QFT and the unearthing of the action of dualities on the basic observables of three dimensional gauge theories.
Experimentalists are getting better and better at building qubits, but no matter how hard they try, their qubits will never be perfect. In order to build a large quantum computer, we will almost certainly need to encode the qubits using quantum error-correcting codes and encode the quantum circuits using fault-tolerant protocols. This will eventually allow reliable quantum computation even when the individual components are imperfect.
I will review recent progress in understanding the dynamics of confining strings in pure Yang-Mills theory.
Should we revisit the concept of space solely based on quantum mechanics?
Do we need a radically new physical principle to address the problem of quantum gravity?
In this talk I will adress these questions. I will review what are the central challenges one faces when trying to understand the theory of quantum gravity from first principles and focus on the main one which is non-locality.
I will present a collection of results and ideas that have been developed in the recent years that provides a radical new perspective on these issues.
Dark energy, the driver of the accelerated expansion of the universe, remains a conundrum. New physics may well be needed to explain it; from Lorentz invariance, this new physics should contain scalar fields, which should be straightforward to detect — so where are they? Physicists have now realized that scalar fields can hide from detection by three distinct screening mechanisms, which respectively rely on nonlinear features in the scalar’s kinetic energy, potential energy, or coupling to normal matter.
Fault-tolerant quantum computers will compute by applying
a sequence of elementary unitary operations, or gates, to an
error-protected subspace. While algorithms are typically expressed
over arbitrary local gates, there is unfortunately no known theory
that can correct errors for a continuous set of quantum gates.
However, theory does support the fault-tolerant construction of
various finite gate sets, which in some cases generate circuits that
100 years after the existence of gravitational waves was first postulated by Albert Einstein, the LIGO and Virgo Collaborations detected gravitational waves for the first time on September 14, 2015. The gravitational waves originated from a pair of black holes that merged over one billion years ago. The merger was so powerful that it shook the very fabric of space and sent a ripple across the Universe that we observed here on Earth at present day.
Recent developments in our understanding of black hole evaporation and the information paradox suggest that effects from quantum gravity are not necessarily hidden at the Planck scale. They might even one day be testable by gravitational wave measurements. To prepare ourselves, we must first understand what quantum gravity really means. Thankfully, we are pre-armed with a deep principle about gravity—that spacetime is really a hologram—and a powerful model for making this idea precise: gauge/gravity duality.