Fall 2024

Dissertation Committee Chair: Alicia Kollár

Committee:

Ben Palmer

Steven Rolston

Nathan Schine

Ron Walsworth (Dean’s Rep)

Characterizing higher-order interactions in quantum processes with unknown Hamiltonians presents a significant challenge. This challenge arises, in part, because two-body interactions can lead to an arbitrary evolution, and two-local gates are considered universal in quantum computing. However, recent research has demonstrated that when the unknown Hamiltonian follows a U(1) symmetry, like charge or number conservation, N-body interactions display a distinct and symmetry-protected feature called the N-body phase.

Quantum sensing extends the vast benefits of a quantum advantage to traditional metrology.  A common method of quantum sensing utilizes coherent, crystal defects in semi-conductors (such as nitrogen vacancy centers in diamond) to perform high-precision measurements on a variety of length scales.  Such measurements might span from vectorized magnetometry of macroscopic computer chips to nanoscale strain or temperature mapping in a target matrial.  In exploring new regimes for quantum sensing, we need to model and assess their viability through theoretical or simula

We analyse the entanglement structure of states generated by random constant-depth two-dimensional quantum circuits, followed by projective measurements of a subset of sites. By deriving a rigorous lower bound on the average entanglement entropy of such post-measurement states, we prove that macroscopic long-ranged entanglement is generated above some constant critical depth in several natural classes of circuit architectures, which include brickwork circuits and random holographic tensor networks.

Arrays of gate-defined semiconductor quantum dots are among the leading candidates for building scalable quantum processors.  High-fidelity initialization, control, and readout of spin qubit registers require exquisite and targeted control over key Hamiltonian parameters that define the electrostatic environment.  However, due to the tight gate pitch, capacitive crosstalk between gates hinders independent tuning of chemical potentials and interdot couplings.  While virtual gates offer a practical solution, determining all the required cross-capacitance matrices accurate

Between NISQ (noisy intermediate scale quantum) approaches without any proof of robust quantum advantage and fully fault-tolerant quantum computation, we propose a scheme to achieve a provable superpolynomial quantum advantage (under some widely accepted complexity conjectures) that is robust to noise with minimal error correction requirements. We choose a class of sampling problems with commuting gates known as sparse IQP (Instantaneous Quantum Polynomial-time) circuits and we ensure its fault-tolerant implementation by introducing the tetrahelix code.