Fall 2023

We analyze a model of qubits which we argue has an emergent quantum gravitational description similar to the fermionic Sachdev-Ye-Kitaev (SYK) model. The model we consider is known as the quantum q-spin model because it features q-local interactions between qubits. It was previously studied as a model of a quantum spin glass, and while we find that the model is glassy for q=2, q=3, and likely q=4, we also find evidence for previously unexpected SYK-like behavior for the quenched free energy down to the lowest temperatures for q >= 5.

Abstract: Thermodynamics plays an important role both in the foundations of physics and in technological applications. An operational perspective adopted in recent years is to formulate it as a quantum resource theory. I will begin with a quick introduction to the general framework of quantum resource theories, in particular motivating it and explaining why the convertibility of resourceful states is at its core.

Abstract: Composite fermion wavefunctions describe a one to one correspondence between the low energy properties of the FQH and the IQH phases which has been tested extensively in experiments and through numerical studies [1]. Here we consider the FQH state in the presence of a weak disorder potential. The full many-body problem is numerically difficult [2,3] but the effective Hamiltonian of a single quasiparticle can numerically be calculated in a weak disorder regime; and here we find a one to one correspondence between the FQH and the IQH systems [4].

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.