Talks

Given the large push by academia and industry (e.g., IBM and Google), quantum computers with hundred(s) of qubits are at the brink of existence with the promise of outperforming any classical computer. Demonstration of computational advantages of noisy near-term quantum computers over classical computers is an imperative near-term goal. The foremost candidate task for showing this is Random Circuit Sampling (RCS), which is the task of sampling from the output distribution of a random circuit. This is exactly the task that recently Google experimentally performed on 53-qubits.

Stockmeyer's theorem implies that efficient sampling allows for estimation of probability amplitudes. Therefore, hardness of probability estimation implies hardness of sampling. We prove that estimating probabilities to within small errors is #P-hard on average (i.e. for random circuits), and put the results in the context of previous works.

Some ingredients that are developed to make this proof possible are construction of the Cayley path as a rational function valued unitary path that interpolate between two arbitrary unitaries, an extension of Berlekamp-Welch algorithm that efficiently and exactly interpolates rational functions, and construction of probability distributions over unitaries that are arbitrarily close to the Haar measure.

I will give an overview of holographic cosmology and discuss recent results and work in progress.

In holographic cosmology time evolution is mapped to inverse RG flow of the dual QFT. As such this framework naturally explains the arrow of time via the

monotonicity of RG flows. Properties of the RG flow are also responsible for the holographic resolution of the classic puzzles of hot big bang cosmology, such as the horizon problem, the flatness problem and the relic problem.

The holographic framework includes qualitatively new models describing a non-geometric  very early Universe, and such models provide an excellent fit to CMB data.  In the last part of the talk I will present on-going work with lattice gauge theorists aiming to compute on the lattice the QFT observables(the 2-point function of stress energy tensor) needed to compute holographically the cosmological  power spectrum in the regime where the dual QFT is non-perturbative.

The discovery of the Higgs boson has revealed that the quartic Higgs self-coupling becomes small at very high energy scales. Guided by this observation, I introduce Higgs Parity, which is a spontaneously broken symmetry exchanging the standard model Higgs with its parity partner. In addition to explaining the small Higgs quartic coupling, Higgs Parity can provide a dark matter candidate, solve the strong CP problem, and arise from an SO(10) grand unified gauge symmetry. I will show that the Higgs Parity symmetry breaking scale is determined by standard model parameters and predicts experimental signals such as the proton decay rate and the warmness of dark matter. As a result, Higgs Parity provides a tight correlation between future precision measurements of standard model parameters and these experimental signals.

Hawking famously observed that the formation and evaporation of black holes appears to violate the unitary evolution of quantum mechanics. Nonetheless, it has been recently discovered that a signature of unitarity, namely the "Page curve" describing the evolution of entropy, can be recovered from semiclassical gravity. This result relies on "replica wormholes" appearing in the gravitational path integral, which are examples of spacetime wormholes studied more than 30 years ago and related to interactions with closed "baby" universes. I will discuss the connection between these new and old ideas and the consequences for the black hole information problem. A central lesson is that a Hilbert space in quantum gravity can be dramatically modified by nonperturbative topology-changing processes.

We introduce a new technique to study the critical point equations of the eprl model. We show that it correctly reproduces the 4-simplex asymptotics, and how to apply it to an arbitrary vertex. We find that for general vertices, the asymptotics can be linked to a Regge action for polytopes, but contain also more general geometries, called conformal twisted geometries. We present explicit examples including the hypercube, and discuss implications.

To predict the gravitational waves emitted by a black hole binary, one needs to understand the dynamics of the binary in general relativity. No closed form solutions of this problem exist. Instead one must introduce some form of approximation. One such approximation, can be made if one of the components is much heavier than the other, suggesting a perturbative expansion in the mass-ratio. I will review this small mass-ratio (SMR) expansion of the dynamics, and the progress that has been made over the last two decades. In particular, I will discuss some recent results on the convergence of this series, suggesting that at relatively low orders this SMR expansion can be used to model even equal mass binaries.

The full theory of LQG presents enormous challenge to create physical computable models. In this talk we will present the new modern version of Quantum Reduced Loop Gravity. We will show that this framework provide an arena to study the full LQG in a certain limit, where the quantum computations are possible. We will analyze all the major step necessary to build this framework, how is connected with the full theory, its mathematical consistency and the physical intuition behind It.

Basic statistical properties of quantum many-body systems in thermal equilibrium can be obtained from their partition function. In this talk, I will present a quasi-polynomial time classical algorithm that estimates the partition function of quantum many-body systems at temperatures above the thermal phase transition point. It is known that in the worst case, the same problem is NP-hard below this temperature. This shows that the transition in the phase of a quantum system is also accompanied by a transition in the computational hardness of estimating its statistical properties. The key to this result is a characterization of the phase transition and the critical behavior of the system in terms of the complex zeros of the partition function. I will also discuss the relation between these complex zeros and another signature of the thermal phase transition, namely, the exponential decay of correlations. I will show that in a system of n particles above the phase transition point, where the complex zeros are far from the real axis, the correlation between two observables whose distance is at least log(n) decays exponentially. This is based on joint work with Aram Harrow and Saeed Mehraban.

MIP* denotes the class of problems that admit interactive proofs with quantum entangled provers. It has been an outstanding question to characterize the complexity of this class. Most notably, there was no known computable upper bound on MIP*.

We show that MIP* is equal to the class RE, the set of recursively enumerable languages. In particular, this shows that MIP* contains uncomputable problems. Through a series of known connections, this also yields a negative answer to Connes’ Embedding Problem from the theory of operator algebras. In this talk, I will explain the connection between Connes' Embedding Problem, quantum information theory, and complexity theory. I will then give an overview of our approach, which involves reducing the Halting Problem to the problem of approximating the entangled value of nonlocal games.

Joint work with Zhengfeng Ji, Anand Natarajan, Thomas Vidick, and John Wright.

In a special live webcast with Perimeter Institute on May 6, 2020, theoretical cosmologist and science communicator Katie Mack — known to her many Twitter followers as @AstroKatie — answered questions about her favourite subject: the end of the universe. Mack is currently a Simons Emmy Noether Fellow at Perimeter and an Assistant Professor at North Carolina State University.

Schur-Weyl duality is a ubiquitous tool in quantum information. At its heart is the statement that the space of operators that commute with the tensor powers of all unitaries is spanned by the permutations of the tensor factors. In this work, we describe a similar duality theory for tensor powers of Clifford unitaries. The Clifford group is a central object in many subfields of quantum information, most prominently in the theory of fault-tolerance. The duality theory has a simple and clean description in terms of finite geometries. We demonstrate its effectiveness in several applications: (1) We resolve an open problem in quantum property testing by showing that "stabilizerness" is efficiently testable: There is a protocol that, given access to six copies of an unknown state, can determine whether it is a stabilizer state, or whether it is far away from the set of stabilizer states. We give a related membership test for the Clifford group. (2) We find that tensor powers of stabilizer states have an increased symmetry group. We provide corresponding de Finetti theorems, showing that the reductions of arbitrary states with this symmetry are well-approximated by mixtures of stabilizer tensor powers (in some cases, exponentially well). (3) We show that the distance of a pure state to the set of stabilizers can be lower-bounded in terms of the sum-negativity of its Wigner function. This gives a new quantitative meaning to the sum-negativity (and the related mana) -- a measure relevant to fault-tolerant quantum computation. The result constitutes a robust generalization of the discrete Hudson theorem. (4) We show that complex projective designs of arbitrary order can be obtained from a finite number (independent of the number of qudits) of Clifford orbits. To prove this result, we give explicit formulas for arbitrary moments of random stabilizer states. (5) Lastly, we comment on the structure of the irreducible representations of the Clifford group.

Cooling atomic gases to ultracold temperatures revolutionized the field of atomic physics, connecting with and impacting many other areas in physics. Advances in producing ultracold molecules suggest similarly dramatic discoveries are on the horizon. First, I will review the physics of ultracold molecules, including our work bringing a new class of molecules to nanokelvin temperatures. Chemistry at these temperatures has a very different character than at room temperature. One striking effect is our recent result using spin states of reactants to control chemical reaction pathways. I will also describe how the strong electric dipole moments of ultracold molecules present an exciting new tool for quantum information and quantum computing.