Universal Sharpness Dynamics in Neural Network Training: Fixed Point Analysis, Edge of Stability, and Route to Chaos
Abstract: In gradient descent dynamics of neural networks, the top eigenvalue of the Hessian of the loss (sharpness) displays a variety of robust phenomena throughout training. This includes early time regimes where the sharpness may decrease during early periods of training (sharpness reduction), and later time behavior such as progressive sharpening and edge of stability. We demonstrate that a simple $2$-layer linear network (UV model) trained on a single training example exhibits all of the essential sharpness phenomenology observed in real-world scenarios.
How non-Hermitian superfluids are special
Committee: Steven Rolston (chair)
Ian Spielman (advisor)
Mohammad Hafezi (dean's rep)
William Phillips
Trey Porto
Generalized framework for fermion-to-qubit mappings through Clifford transformations
Abstract: In order to simulate interacting fermionic systems on quantum computers, the first step is to encode the physical Hamiltonian into qubit operators. Existing encoding procedures such as the Jordan-Wigner transformation and Bravyi-Kitaev transformation are not resource efficient because they encode each second-quantized fermionic operator into a Pauli string without incorporating the structure of the Hamiltonian in question.
Collective exciton properties in charge-ordered moire' transition metal dichalcogenide bilayers
Abstract: Light emitters within two-dimensional arrays have been demonstrated to exhibit various cooperative effects, including super- and sub-radiance, collective line-shift and linewidth, and topological features such as Chern bands and edge states. Motivated by these intriguing properties, the realization of emitter arrays has been attempted in cold atom experiments, which nevertheless cannot access the deep subwavelength regime.
Turbulence and superfluidity in atomic Bose-Einstein condensates
Dissertation Committee Chair: Daniel Lathrop
Committee:
Ian Spielman
Nathan Schine
Thomas Antonsen
Johan Larsson (Dean’s Rep)
Total functions exhibit exponential quantum advantage — albeit in a parallel universe
Abstract: We construct a total function which exhibits an exponential quantum parallel query advantage despite having no sequential query advantage. This is interesting for two reasons: (1) For total functions an exponential sequential query advantage is impossible, and was conjectured to not be possible in the parallel setting by Jeffery et al (2017)— our result refutes this conjecture. (2) The exponential speedup emerges entirely from quantum algorithms being able to utilize parallelism more effectively than classical algorithms, making this a genuinely parallel phenomenon.
Macroscopic quantum motion of a nanogram-scale object
Abstract: I will describe measurements of individual phonons in a 1 ng body of superfluid helium. When this body is in equilibrium, its phonon correlations are consistent (up to 4th order) with a thermal state of mean occupancy ~ 1. This purity is preserved even when the mode is driven to a coherent state with an amplitude corresponding to ~100,000 phonons. I will describe how these results can be used to constrain nonlinear extensions of quantum mechanics, and to distribute entanglement over kilometer-scale optical fiber networks.
Harnessing Temporal Entanglement for Quantum Many-Body Dynamics
Abstract: The dynamics of quantum many-body systems out-of-equilibrium are pivotal in various fields, ranging from quantum information and the theory of thermalization to impurity physics. Fundamentally, the numerical study of larger quantum systems is challenging due to the exponential number of parameters necessary to describe the wavefunction. If their entanglement is low, wavefunctions can be approximated with relatively few parameters using tensor networks. Since equilibrium wavefunctions have low entanglement, this makes computations viable.