Scientific Series

Motivated by puzzles in quantum gravity AdS/CFT, Lenny Susskind posed the following question: supposing one had the technological ability to distinguish a macroscopic superposition of two given states |v> and |w> from incoherent mixture of those states, would one also have the technological ability to map |v> to |w> and vice versa?  More precisely, how does the quantum circuit complexity of the one task relate to the quantum circuit complexity of the other?  Here we resolve Susskind's question -- showing that the two complexities are essentially identical, even for approximate versions of these tasks, with the one caveat that a unitary transformation that maps |v> to |w> and |w> to -|v> need not imply any distinguishing ability.  Informally, "if you had the ability to prove Schrödinger's cat was in superposition, you'd necessarily also have the ability to bring a dead cat back to life."  I'll also discuss the optimality of this little result and some of its implications.

Paper (with Yosi Atia) in preparation

Last fall, a team at Google announced the first-ever demonstration of "quantum computational supremacy"---that is, a clear quantum speedup over a classical computer for some task---using a 53-qubit programmable superconducting chip called Sycamore.  In addition to engineering, Google's accomplishment built on a decade of research in quantum computing theory.  This talk will discuss questions like: what exactly was the contrived computational problem that Google solved?  How does one verify the outputs using a classical computer?  And how confident are we that the problem really is classically hard---especially in light of subsequent counterclaims by IBM?  I'll end with a proposed application for Google's experiment---namely, the generation of certified random bits, for use (for example) in proof-of-stake cryptocurrencies---that I've been developing and that Google is now working to demonstrate.

Meta-learning involves learning mathematical devices using problem instances as training data. In this talk, we first describe recent meta-learning approaches involving the learning of objects such as: initial weights, parameterized losses, hyper-parameter search strategies, and samplers. We then discuss learned optimizers in further detail and their applications towards optimizing variational circuits. This talk also covers some lessons learned starting a spin-off from academia.

We propose a unified manner of understanding two important phenomena: color confinement in large-N gauge theory, and Bose-Einstein condensation (BEC). We do this by clarifying the relation between the standard criteria, based on the off-diagonal long range order (ODLRO) for the BEC and the Polyakov loop for gauge theory: the constant offset of the distribution of Polyakov line phase is ODLRO. Indistinguishability associated with the symmetry group --- SU(N) or O(N) in gauge theory, and S_N permutation in the system of identical bosons --- plays the key role in both cases. This viewpoint may have implications to confinement at finite N, and to quantum gravity via gauge/gravity duality. 

We propose a model for combining the Standard Model (SM) with gravity. It relies on a non-minimal coupling of the Higgs field to the Ricci scalar and on the Palatini formulation of gravity. Without introducing any new degrees of freedom in addition to those of the SM and the graviton, this scenario achieves two goals. First, it generates the electroweak symmetry breaking by a non-perturbative gravitational effect. In this way, it does not only address the hierarchy problem but opens up the possibility to calculate the Higgs mass. Second, the model incorporates inflation at energies below the onset of strong-coupling of the theory. Provided that corrections due to new physics above the scale of inflation are not unnaturally large, we can relate inflationary parameters to data from collider experiments.
 

Cosmologists wish to explain how our universe, in all its complexity, could ever have come about. This is the problem of initial conditions and the first step towards its solution is the assessment of the universe’s entropy today. It is widely agreed upon that the entropy of vacuum energy, given by the Bekenstein bound, makes up the bulk of the current entropy budget, dominating over that of gravity and over thermal motions of the cosmic radiation background.

Have we counted all significant contributions to the entropy inventory? There is one number which we have not considered: the number of degrees of freedom in our vibrant, complex biosphere. What is the entropy of life? Is it sizeable enough to need to be accounted for at the Big Bang, or negligible compared to vacuum entropy?

Fundamental physics (including physics beyond the Standard Model) can be tested using table-top precision measurements. The talk will describe measurements of the size of the proton, the fine-structure constant and the electric dipole moment of the electron. Two recently completed measurements will be described. For the first measurement, the n=2 Lamb shift of atomic hydrogen is measured, allowing for a new determination of the charge radius of the proton. This determination is crucial to resolving the decade-old proton radius puzzle, in which it appeared that the proton radius took on a different value when measured with muons compared to measurements using electrons. The second measurement is of the n=2 triplet P fine structure of atomic helium, and this work is part of a program to obtain a new determination of the fine-structure constant. Both of these measurements use a new measurements technique: Frequency offset separated oscillatory fields. Finally, a new major effort (EDM^3) is starting at York University to measure the electron electric dipole moment using polar molecules embedded into inert-gas solids. This measurement will test for T violation and will probe physics up to the PeV energy scale.    

I will consider simple scalar gauge theories with one scalar field in a low-dimensional representation of a gauge group. The renormalizable action often has accidental symmetries that lead to one or more stable states, providing Dark Matter candidates. The gauge group can confine, or be spontaneously broken by the scalar field: I will discuss the spectrum and symmetries in both cases, focusing in particular on possible dualities between the Higgs and confined phases. I will then discuss the Dark Matter phenomenology in a few illustrative cases, showing that the thermal relic abundance can reproduce the cosmological value for masses around 100 TeV.

In this talk, I will outline the forward model approach to reconstruct cosmological fields in a Bayesian framework. I will focus on two examples - galaxy clustering and neutral hydrogen intensity mapping.

In galaxy clustering example, I will use the observations of galaxy surveys to reconstruct the initial Lagrangian field. Here, we develop a novel framework with neural networks to forward model halo masses and positions and demonstrate that our method outperforms standard reconstruction in both real and redshift space. This reconstructed initial field has enhanced signal for baryon acoustic oscillations and can enhance science returns for surveys like DESI.

For neutral hydrogen surveys, we lose over 50% of the modes at high redshifts due to foregrounds and it severely hampers their feasibility for cosmological analysis. With a novel bias framework for the forward model, I will show that we are able to reconstruct over 90% of these modes and this recovers cross-correlations with photo-z surveys like LSST and tracers like CMB lensing.

Lastly, I will briefly touch upon assumptions made in this reconstruction framework regarding noise models and likelihood. I will discuss preliminary ways to improve upon them using deep learning.