JQI

Abstract: Optical spectroscopy is used to study a material by measuring the intensity of light modes that scatter off it. In this work, we develop a theory for G2 spectroscopy of correlated materials, where instead of measuring the intensity of scattered photons, one measures the second order coherence between pairs of photons scattered off a material. We map this correlation function of the photons to the correlation functions of the material being probed.

Randomized benchmarking (RB) is a widely used strategy to assess the quality of available quantum gates in a computational context. The quality is usually expressed as an effective depolarizing error per step. RB involves applying random sequences of gates to an initial state and making a final measurement to determine the probability of an error. Current implementations of RB estimate this probability by repeating each randomly chosen sequence many times.

Simulating Fermionic Hamiltonians requires a mapping from fermionic to qubit operators. This mapping must obey the underlying algebra of fermionic operators; in particular, their specific anticommutation relations. The traditional mapping is the Jordan-Wigner encoding, which is simple and qubit minimal, but can incur significant overheads during simulation. This is because the qubit weight of fermionic operators is high, i.e. operators typically must involve many qubits. New mappings address this trade-off and hold other intriguing features.

Decoding algorithms based on approximate tensor network contraction have proven tremendously successful in decoding 2D local quantum codes such as surface/toric codes and color codes, effectively achieving optimal decoding accuracy. We introduce several techniques to generalize tensor network decoding to higher dimensions so that it can be applied to 3D codes as well as 2D codes with noisy syndrome measurements (phenomenological noise or circuit-level noise).

We use time-dependent density functional theory to investigate the possibility of hosting organic color centers in (6, 6) armchair single-walled carbon nanotubes, which are known to be metallic. Our calculations show that in short segments of (6, 6) nanotubes ∼5 nm in length there is a dipole-allowed singlet transition related to the quantum confinement of charge carriers in the smaller segments. The introduction of sp3 defects to the surface of (6, 6) nanotubes results in new dipole-allowed excited states.

Dissertation Committee Chair: Chris Monroe

Committee: 

Zohreh Davoudi

Alexey Gorshkov

Chris Jarzynski

Qudsia Quraishi

Abstract: We consider the logical gate of (3+1)D Z2 gauge theory with an emergent fermionic particle, and point out that pumping the p+ip topological state through the 3d space defines the emergent Z8 global symmetry. We then show that in the context of stabilizer quantum codes, one can obtain logical CCZ and CS gates by placing the code on a discretization of T^3 (3-torus) and mapping torus of T^2 respectively, and pumping p+ip states. Our considerations also imply the possibility of a logical T gate by placing the code on RP3 and pumping a p+ip topological state.

Learning properties of quantum processes is a fundamental task in physics. It is well known that full process tomography scales exponentially in the number of qubits. In this work, we consider online learning quantum processes in a mistake bounded model and prove exponentially improved bounds compared to the stronger notion of diamond norm learning. The problem can be modelled as an interactive game over any given number of rounds, T, between a learner and an adversary.