Fall 2022

Dissertation Committee Chair: Victor Galitski
Committee: 
Alexey Gorshkov (co-advisor)
Brian Swingle (co-advisor)
Andrew Childs
Xiaodi Wu

Abstract: A fundamental distinction between many-body quantum states are those with short- and long-range entanglement (SRE and LRE). The latter, such as cat states, topological order, or critical states cannot be created by finite-depth circuits. Remarkably, examples are known where LRE is obtained by performing single-site measurements on SRE states such as preparing the toric code from measuring a sublattice of a 2D cluster state.

Abstract: Recent optical probes have used excitons, electron-hole bound states, to probe correlated insulating phases of two-dimensional semiconducting materials. Motivated by these experiments, we investigate these composite particles involving Mott physics. In this talk, we will discuss the formalism of two types of Mott excitons: Intraband exciton with both charges from a single band Hubbard model, and interband exciton with only one charge in the Mott. We discuss the role of magnetism on these bound states and compare their properties with those from band insulators.

Dissertation Committee Chair: Norbert Linke
Committee: 
Trey Porto
Ian B. Spielman
Wendell T. Hill
Yanne K. Chembo

Abstract: Non-Abelian defects that bind Majorana or parafermion zero modes are prominent in several topological quantum computation schemes. Underpinning their established understanding is the quantum Ising spin chain, which can be recast as a fermionic model or viewed as a standalone effective theory for the surface-code edge -- both of which harbor non-Abelian defects. We generalize these notions by deriving an effective Ising-like spin chain describing the edge of quantum-double topological order.

Abstract: Quantum state and unitary $t$-designs play an important role in several applications, including tomography, randomized benchmarking, state discrimination, cryptography, sensing, and fundamental physics. In this work, we generalize the notion of state designs to infinite-dimensional, separable Hilbert spaces. We first prove that under the definition of continuous-variable (CV) state $t$-designs from [Comm. Math. Phys 326, 755-771 (2014)], no state designs exist for $t\geq2$. Similarly, we prove that no CV unitary $t$-designs exist for $t\geq 2$.

Abstract: Hybridizing light and matter by means of cavities can be used as a tool to influence material properties.

Abstract: While it can be useful in some cases to abstract away all but 2 levels of the atoms used for quantum computing, it should not be forgotten that these qubit hosts often have many levels capable of participating in processing tasks.  These include long-lived states within hyperfine, Zeeman, and electronic-state structure in atoms, but extend to rotational, vibrational, and more exotic level landscapes if one considers molecules instead of just atoms.  Given the effectively atom-limited regime in which many (possibly all) atomic processors currently operate,

Abstract: In this talk I will discuss some exotic phases of excitons beyond the conventional exciton condensation phase.    (1) In the first part, I will consider a coulomb coupled quantum Hall bilayer at filling (1/3,-1/3). (Equivalently (1/3,2/3)) and then tune d/l_b.

The central philosophy of statistical mechanics and random-matrix theory of complex systems is that while individual instances are essentially intractable to simulate, the statistical properties of random ensembles obey simple universal “laws”. This same philosophy promises powerful methods for studying the dynamics of quantum information in ideal and noisy quantum circuits – for which classical description of individual circuits is expected to be generically intractable.