Dissertation Committee Chair: Maissam Barkeshli
Committee:
Michael Gullans (co-chair, co-advisor)
Alexey Gorshkov (co-chair, co-advisor)
Christopher Monroe
Christopher Jarzynski (Dean’s Representative)
Abstract: Random Circuits has emerged as an invaluable tool in the quantum computing toolkit. On one hand, the task of sampling outputs from a random circuit has established itself as a leading contender to experimentally demonstrate the intrinsic superiority of quantum computers using near-term, noisy platforms. On the other hand, random circuits have also been used to deduce far-reaching conclusions about the theoretical foundations of quantum information and communication.
One intriguing aspect of random circuits is exemplified by the measurement-induced entanglement phase transition that occurs in monitored quantum circuits, where unitary gates compete with projective measurements to determine the entanglement structure of the resulting quantum state. When the measurements are sparse, the circuit is unaffected and entanglement grows ballistically; when the measurements are too frequent, the unitary dynamics is arrested or frozen. The two phases are separated by a sharp-phase transition. In this work, we discuss an experiment probing such phases using a trapped-ion quantum computer.
While entanglement is an important resource in quantum communication, it does not capture the non-classicality needed to achieve universal quantum computation. A new family of measures, termed magic, is used to quantify the extent to which a quantum state is non-classical or can enable universal quantum computation. In this dissertation, we also discuss a newly uncovered phase transition in magic, using quantum circuits that implement a random stabilizer code. This `magic' phase transition is intimately related to the error-correction threshold. In this work, we present numerical and analytic characterizations of the magic transition.
Finally, we use a statistical mechanical map from random circuits acting on qubits to Ising models to suggest thresholds in error mitigation whenever the underlying noise of a quantum device is imperfectly characterized. We show the existence of an error-mitigation threshold for random circuits in dimensions larger than one.