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In unidirectional communication theory, two of the most prominent problems are those of compressing a source of information and of transmitting data noiselessly over a noisy channel. In 1948, Shannon introduced information theory as a tool to address both of these problems. Since then, information theory has flourished into an important field of its own. It has also been successfully extended to the quantum setting, where it has also served to address questions about quantum source compression and transmission of classical and quantum data over noisy quantum channels.

However, in interactive communication theory, more specifically communication complexity, it is much more recently that tools from information theory have been successfully applied. Indeed, the interactive nature of communication protocols in this setting imposes new constraints and tools specific to this setting need to be developed, both for the interactive analogue of source compression and that of coding for noisy channels. The exciting field of classical interactive information theory has been very active in recent years.

We discuss recent works for its quantum counterpart. In particular, we discuss joint work showing that a constant factor overhead is sufficient for robustly implementing interactive quantum communication over noisy channels [1]. We also discuss work introducing a new notion of quantum information complexity that exactly captures the amortized cost per copy for implementing many copies of a communication task in parallel, such that compressing to this information complexity leads to a bounded-round direct sum theorem [2].

For both of these, we further discuss many interesting potential research directions that follow.

[1] joint work with Gilles Brassard, Ashwin Nayak, Alain Tapp, Falk Unger, QIP’14, FOCS’14 [2] Merge of arXiv:1404.3733 and arXiv:1409.4391, to appear at QIP’15

Quantum many-body systems ranging from a many-electron atom to a solid material are described by effective Hamiltonians which are obtained from more accurate Hamiltonians by neglecting or treating weak interactions perturbatively. Quantum complexity theory asks about the quantum computational power of such quantum many-body models for both practical as well as fundamental purposes. Three distinct computational classes have emerged within this framework: namely (1) classical Hamiltonians such as the Ising model, (2) sign-free or stoquastic Hamiltonians such as the transverse field Ising model, and (3) fully quantum Hamiltonians such as the Heisenberg model. Each class can be characterized by certain prototype universal Hamiltonians which can encode the physics of any other Hamiltonian in that class. We will show how this encoding is established through the use of perturbation theory via perturbative gadgets. We will discuss the technical expression of this classification in terms of the complexity classes NP, Stoquastic MA and QMA and the power of these Hamiltonians for performing quantum adiabatic computation.

We present a first principles approach to a probabilistic description of nature based on two guiding principles: spacetime locality and operationalism. No notion of time or metric is assumed, neither any specific physical model. Remarkably, the emerging framework converges with the recently proposed positive formalism of quantum theory, obtained constructively from known quantum physics. However, it also seems to embrace classical physics.

We present an analytic, gauge invariant tensor network ansatz for the ground state of lattice Yang-Mills theory for nonabelian gauge groups. It naturally takes the form of a MERA, where the top level is the strong coupling limit of the lattice theory. Each layer performs a fine-graining operation defined in a fixed way followed by an optional step of adiabatic evolution, resulting in the ground state at an intermediate coupling. The ansatz is very much in the spirit of Kogut and Susskind's Hamiltonian approach to understanding confinement by starting from the strong coupling limit and perturbing, but exploiting a tensor network structure to go beyond perturbative approaches.

A new experiment called PTOLEMY (Princeton Tritium Observatory for Light, Early-Universe, Massive-Neutrino Yield) is under development at the Princeton Plasma Physics Laboratory with the goal of challenging one of the most fundamental predictions of the Big Bang – the present-day existence of relic neutrinos produced less than one second after the Big Bang.  Using a gigantic graphene surface to hold 100 grams of a single-atomic layer of tritium, low noise antennas that sense the radio waves of individual electrons undergoing cyclotron motion, and a massive array of cryogenic sensors that sit at the transition between normal and superconducting states, the PTOLEMY project has the potential to challenge one of the most fundamental predictions of the Big Bang, to potentially uncover new interactions and properties of the neutrinos, and to search for the existence of a species of light dark matter known as sterile neutrinos.

Velocity fields are a powerful probe of structure formation and the energy content of our Universe. Additionally, the motion of ionized gas on intermediate scales can be used to measure the clustering of baryons and shed light on galaxy formation and feedback mechanisms.  I will discuss techniques that can be used to both constrain cosmology and measure baryon properties. I will also present some preliminary results.

We exactly evaluate the partition function (index) of N=4 supersymmetric quiver quantum mechanics in the Higgs phase by using the localization techniques. We show that the path integral is localized at the fixed points, which are obtained by solving the BRST equations, and D-term and F-term conditions. We turn on background gauge fields of R-symmetries for the chiral multiplets corresponding to the arrows between quiver nodes, but the partition function does not depend on these R-charges. We give explicit examples of the quiver theory including a non-coprime dimension vector. The partition functions completely agree with the mathematical formulae of the Poincare polynomials and the wall crossing for the quiver moduli spaces. We also discuss exact computation of the expectation values of supersymmetric (Q-closed) Wilson loops in the quiver theory.