Spring 2021

Recent technological developments have focused the interest of the quantum computing community on investigating how near-term devices could outperform classical computers for practical applications. A central question that remains open is whether their noise can be overcome or it fundamentally restricts any potential quantum advantage. We present a transparent way of comparing classical algorithms to quantum ones running on near-term quantum devices for a large family of problems that include optimization problems and approximations to the ground state energy of Hamiltonians.

Covering areas as large as entire continents, high-voltage power grids have a priori little to do with quantum mechanics. Yet, upon closer inspection, interesting analogies emerge with quantum / wave-coherent phenomena such as the Josephson effect, vortices in superfluids or multiple coherent scattering. This is so, because the operational state of AC power grids is determined by complex voltages at buses on a two-dimensional network.

Twisted bilayer graphene (TBG) realizes an exquisitely tunable, strongly interacting system featuring superconductivity and various correlated insulating states.  In this talk I will introduce gate-defined wires in TBG as an enticing platform for Majorana-based fault-tolerant qubits.  Our proposal notably relies on “internally” generated superconductivity in TBG – as opposed to “external” superconducting proximity effects commonly employed in Majorana devices – and may operate even at zero magnetic field.

We finally made it to what seemed like sci-fi wishful thinking. Quantum computers are real and available on the cloud, and their power is growing at a greater-than-Moore’s-Law pace. What does this mean for those entering the job market soon? What will we be using these qubit-loaded behemoths for? Join us for some informal Q&A about this post-quantum era we find ourselves within.

Commuting projector models (CPMs) have provided microscopic theories for a host of gauge theories and are the venue for Kitaev’s toric code. An immediate question that arises is whether there exist CPMs for the Hall effect, the discovery of which ignited a revolution in modern condensed matter physics. In fact, a no-go theorem has recently appeared suggesting that no CPM can host a nonzero Hall conductance. In this talk, we present a CPM for just that: U(1) states with nonzero Hall conductance.

Dissertation Committee Chair: Prof. Christopher Monroe
Committee: 
Professor Norbert M. Linke
Professor James Williams
Professor Alexey Gorshkov
Professor Christopher Jarzynski
Abstract:

Quantum phase transitions are ubiquitous in nature and come in a variety of flavors, including symmetry-breaking transitions and symmetry-protected topological transitions. While these paradigms are by now well understood for closed systems, their generalization to dissipative open systems remains largely unexplored. In this talk, I describe recent progress in this direction. This task has practical relevance: A non-trivial phase can be characterized by an emergent steady state degeneracy in the thermodynamic limit, which is the key ingredient for "autonomous" error correction.

Recently, works such as the landmark MIP*=RE paper by Ji et. al. have established deep connections between computability theory and the power of nonlocal games with entangled provers. Many of these works start by establishing compression procedures for nonlocal games, which exponentially reduce the verifier's computational task during a game. These compression procedures are then used to construct reductions from uncomputable languages to nonlocal games, by a technique known as iterated compression.

The accurate computation of ground and excited states of many-fermion quantum systems is one of the most important challenges in the physical and computational sciences whose solution stands to benefit significantly from the advent of quantum computing devices. Existing methodologies using phase estimation or variational algorithms have potential drawbacks such as deep circuits requiring substantial error correction or non-trivial high-dimensional classical optimization.

For non-interacting fermions at zero temperature, it is well established that charge transport is quantized whenever the chemical potential lies in a gap of the single-body Hamiltonian. Proving the same result with interactions was an open problem for nearly 30 years until it was solved a few years ago by Hastings and Michalakis. The solution uses new tools originally developed in the context of the classification of exotic phases of matter, and was used before in the proof of the many-dimensional Lieb-Schultz-Mattis theorem.