Scientific Series

We prove that constant-depth quantum circuits are more powerful than their classical counterparts. We describe an explicit (i.e., non-oracular) computational problem which can be solved with certainty by a constant-depth quantum circuit composed of one- and two-qubit gates. In contrast, we prove that any classical probabilistic circuit composed of bounded fan-in gates that solves the problem with high probability must have depth logarithmic in the input size. This is joint work with Sergey Bravyi and Robert Koenig (arXiv:1704.00690).

What can we say about the spectra of a collection of microscopic variables when only their coarse-grained sums are experimentally accessible? In this paper, using the tools and methodology from the study of quantum nonlocality, we develop a mathematical theory of the macroscopic fluctuations generated by ensembles of independent microscopic discrete systems. We provide algorithms to decide which multivariate gaussian distributions can be approximated by sums of finitely-valued random vectors. We study non-trivial cases where the microscopic variables have an unbounded range, as well as asymptotic scenarios with infinitely many macroscopic variables. From a foundational point of view, our results imply that bipartite gaussian states of light cannot be understood as beams of independent d-dimensional particle pairs. It is also shown that the classical description of certain macroscopic optical experiments, as opposed to the quantum one, requires variables with infinite cardinality spectra.

Recent studies of highly frustrated antiferromagnets (AFMs) have demonstrated the qualitative impact of virtual, longer-range singlet excitations on the effective RVB tunneling parameters of the low energy sector of the problem [1,2]. Here, I will discuss the current state of affairs on the RVB description of the spin-1/2 kagome AFM, and present new results that settle a number of issues in this problem [3].

[1] I. Rousochatzakis, Y. Wan, O. Tchernyshyov, and F. Mila, PRB 90,

100406(R) (2014)

[2] A. Ralko and I. Rousochatzakis, PRL 115, 167202 (2015) [3] in preparation.

Since the Higgs, the LHC has offered no discoveries despite a sweeping hunt for new resonances. However, many well-motivated new physics models would not turn up in resonance searches, but could instead be uncovered in existing and forthcoming LHC data, by searching for novel angular distributions of Standard Model particles. I will show that in the upcoming years at the LHC, (1) through radiative corrections, dark matter can turn up in dilepton scattering angles in the parametric regions where it would elude conventional missing energy-based searches; the scattering patterns can reveal dark matter's mass, self-conjugation property, spin, and chirality of interactions, (2) through tree level interference, leptoquarks may emerge in dilepton scattering angles long before they would in dedicated direct searches; these angular measurements would also overtake the excellent sensitivities of low-energy precision measurements of atomic parity violation, and (3) Higgs Yukawa couplings to light quarks of the size of the bottom Yukawa could be measured using the Higgstrahlung scattering angle.

We apply the recently suggested strategy to lift state spaces and operators for (2+1)-dimensional topological quantum field theories to state spaces and operators for a (3+1)-dimensional TQFT with defects. We start from the (2+1)-dimensional Turaev-Viro theory and obtain a state space, consistent with the state space expected from the Crane-Yetter model with line defects. This work has important applications for quantum gravity as well as the theory of topological phases in (3+1) dimensions.

I present three possible non-standard additions to cosmology.  First I show that a very long early period of inflation could exist in which parameters evolve, or 'relax', to seemingly fine-tuned values.  Next, I show that even if cosmic inflation existed, a period after inflation with anisotropic stress can dramatically affect super-horizon modes and thus the imprint on the cosmic microwave background.  Finally, I show that cosmological singularities can be avoided by a bounce without using exotic matter that violates the Null Energy Condition, but by the addition of vorticity in compact extra dimensions.

We consider the problem of certifying entanglement and nonlocality in one-dimensional translation-invariant (TI) infinite systems when just averaged near-neighbor correlators are available. Exploiting the triviality of the marginal problem for 1D TI distributions, we arrive at a practical characterization of the near-neighbor density matrices of multi-separable TI quantum states. This allows us, e.g., to identify a family of separable two-qubit states which only admit entangled TI extensions. For nonlocality detection, we show that, when viewed as a vector in R^n, the set of boxes admitting an infinite TI classical extension forms a polytope, i.e., a convex set defined by a finite number of linear inequalities. Using DMRG, we prove that some of these inequalities can be violated by distant parties conducting identical measurements on an infinite TI quantum state. Both our entanglement witnesses and our Bell inequalities can be used to certify entanglement and nonlocality in large spin chains (namely, finite, and not TI chains) via neutron scattering.

Our attempts at generalizing our results to TI systems in 2D and 3D lead us to the virtually unexplored problem of characterizing the marginal distributions of infinite TI systems in higher dimensions. In this regard, we show that, for random variables which can only take a small number of possible values (namely, bits and trits), the set of nearest (and next-to-nearest) neighbor distributions admitting a 2D TI infinite extension forms a polytope. This allows us to compute exactly the ground state energy per site of any classical nearest-neighbor Ising-type TI Hamiltonian in the infinite square or triangular lattice. Remarkably, some of these results also hold in 3D.

In contrast, when the cardinality of the set of possible values grows (but remaining finite), we show that the marginal nearest-neighbor distributions of 2D TI systems are not described by a polytope or even a semi-algebraic set. Moreover, the problem of computing the exact ground state energy per site of arbitrary 2D TI Hamiltonians is undecidable.

The talk will review the computation of the three point function of gauge-invariant operators in the planar N=4 SYM theory using integrability-based methods. The structure constant can be decomposed, as proposed by Basso, Komatsu and Vieira, in terms of two form-factor-like objects (hexagons). The multiple sums and integrals implied by the hexagon decomposition can be performed in the large-charge limit, and be compared to the results obtained by semiclassics. I will discuss a method to perform these sums and the contributions currently accessible by this approach.

A number of ground based CMB surveys that will survey large fractions of the sky to high sensitivity are currently in the planning stages.  I will give an overview of what can be learned from these surveys about the Universe since recombination, focussing on gravitational lensing science.  I will also discuss some new CMB observables that would be accessible with even more futuristic surveys.

The physics proof of the Atiyah-Singer index theorem relates the Hamiltonian and Lagrangian approaches to quantization of N=1 supersymmetric mechanics. Similar ideas applied to the N=(0,1) supersymmetric sigma model construct two versions of elliptic cohomology: elliptic cohomology at the Tate curve over the integers and the universal elliptic cohomology theory over the complex numbers. Quantization procedures give analytic constructions of wrong-way maps in these cohomology theories. Relating these to the Ando-Hopkins-Strickland-Rezk string orientation of topological modular points to intricate torsion invariants associated with these sigma models. 

Quantum annealing with superconducting qubits: status and prospects
Adrian Lupascu, Institute for Quantum Computing

Quantum-enhanced Gibbs sampling in statistical relational learning
Peter Wittek, Institute of Photonic Sciences, University of Boras

In 1983, Nielsen and Ninomiya predicted that the Adler-Bell-Jakiw (or chiral) anomaly should be observable in a crystal that has protected Dirac states in the bulk (3+1 D). Following recent progress in the field of Topological Quantum Matter, the anomaly has now been observed, most clearly in the two semimetals Na3Bi and GdPtBi. I will discuss the general problem of realizing Weyl Fermions in semimetals, and explain what the chiral anomaly is in condensed matter. I will remark on its historical context, starting with pion decay. Several tests that support our conclusion will be described.

*Supported by the Moore Foundation, ARO and NSF.