JQI

Committee: Steven Rolston (chair)

Ian Spielman (advisor)

Mohammad Hafezi (dean's rep)

William Phillips

Trey Porto

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.

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.

Dissertation Committee Chair: Daniel Lathrop

Committee: 

Ian Spielman

Nathan Schine

Thomas Antonsen

Johan Larsson (Dean’s Rep)

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.

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.

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.

In the wake of recent progress on quantum computing hardware, the National Institute of Standards and Technology (NIST) is standardizing cryptographic protocols that are resistant to attacks by quantum adversaries. The primary digital signature scheme that NIST has chosen is CRYSTALS-Dilithium. The hardness of this scheme is based on the hardness of three computational problems: Module Learning with Errors (MLWE), Module Short Integer Solution (MSIS), and SelfTargetMSIS. MLWE and MSIS have been well-studied and are widely believed to be secure.