QuICS Special Seminar

Hyperbolic lattices are tessellations of the hyperbolic plane using, for instance, heptagons or octagons. They are relevant for quantum error correcting codes and experimental simulations of curved space quantum physics in circuit quantum electrodynamics. Underneath their perplexing beauty lies a hidden and, perhaps, unexpected periodicity that allows us to identify the unit cell and Bravais lattice for a given hyperbolic lattice.

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.

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.

We develop approximations to a perturbed quantum dynamics beyond the standard approximation based on quantum Zeno dynamics and adiabatic elimination. The effective generators describing the approximate evolutions are endowed with the same block structure as the unperturbed part of the generator, and their adiabatic error is “eternal” - it does not accumulate over time. We show how this gives rise to Schrieffer-Wolff generators in open systems.

Matrix syntax is a formal model of syntactic relations, based on a conservative and a radical assumption. The conservative assumption dates back to antiquity: that the fundamental divide in human language is between nouns and verbs, which are “conceptually at right angles” (as different as substantive words can be). The radical assumption is that such a conceptual orthogonality could be treated as a formal orthogonality in a vector space, with all its consequences.

Entanglement is a critical resource for a useful quantum computer. There is a not a consensus on whether large-scale entanglement is physically possible, and entanglement on mixed states at non-zero temperature is poorly understood.  We discuss theoretical and computable bounds on how much entropy a quantum system can tolerate and still be useful for computation, and some directions for further exploration.  This is not a research talk, but rather a review of interesting results.

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.

The position states of the harmonic oscillator describe the location of a particle moving on the real line. Similarly, the phase difference between two superconductors on either side of a Josephson junction takes values in the configuration space of a particle on a circle. More generally, many physical systems can be described by a basis of "position states," describing a particle moving on a more general configuration or state space. Most of this space is usually ignored due to the energy cost required to pin a particle to a precise "position".

Demonstrating a superpolynomial quantum speedup using feasible schemes has become a key near-term goal in the field of quantum simulation and computation. The most prominent schemes for "quantum supremacy" such as boson sampling or random circuit sampling are based on the task of sampling from the output distribution of a certain randomly chosen unitary. But to convince a skeptic of a successful demonstration of quantum supremacy, one must verify that the sampling device produces the correct outcomes.

Quantum dots formed in silicon heterostructures have emerged as a promising candidate for creating qubits, the building blocks of quantum computing. Their small size, ease of control, and compatibility with modern semiconductor processes make them especially enticing. However, the intrinsic near-degeneracy (valley splitting) of the conduction band electrons that form these quantum dots poses a serious concern for the viability of these qubits, but may also hold the solution.