Summer 2020

We investigate 2-dimensional periodic superstructures consisting of 1-dimensional conducting segments. Such structures naturally appear in twisted transition metal dichalcogenides, some charge-density-wave materials, and a marginally twisted bilayer graphene, in which intriguing non-Fermi liquid transports have been experimentally observed. We model such a system as a network of Tomonaga-Luttinger Liquids, and theoretically derive a variety of non-Fermi liquid behaviors, based on a Renormalization-Group analysis of the junctions of Tomonaga-Luttinger Liquids.

We propose an integrated superconducting circuit design in combination with a general symmetry principle – combinatorial gauge symmetry – to build artificial quantum spin liquids that serve as foundation for the construction of topological qubits. The superconducting wire arrays exhibit rich features. In the classical limit of large capacitances its ground state consists of two superimposed spin liquids; one is a crystal of small loops containing disordered U(1) degrees of freedom, and the other is a soup of loops of all sizes associated to Z_2 topological order.

Exactly solvable models are essential in physics. For many-body spin-1/2 systems, an important class of such models consists of those that can be mapped to free fermions hopping on a graph. We provide a complete characterization of models which can be solved this way. Specifically, we reduce the problem of recognizing such spin models to the graph-theoretic problem of recognizing line graphs, which has been solved optimally. A corollary of our result is a complete set of constant-sized commutation structures that constitute the obstructions to a free-fermion solution.

Given the unprecedented effort 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.

Given a nonlocal game, we'd like to be able to find the optimal quantum winning probability, and the set of optimal strategies. However, the recent MIP*=RE result implies that we cannot determine the quantum winning probability to within constant error.

Interference is an essential part of quantum mechanics.  However, an important class of Hamiltonians considered are those with "no sign problem", where all off-diagonal matrix elements of the Hamiltonian are non-negative.  This means that the ground state wave function can be chosen to have all amplitudes real and positive.  In a sense, no destructive interference is possible for these Hamiltonians so that they are "almost classical", and there are several simulation algorithms which work well in practice on classical computers today.  In this talk, I'll discuss what happens when one consid