Dissertation Defense

Statistical learning is emerging as a new paradigm in science.

This has ignited interest within our inherently quantum world in exploring quantum machines for their advantages in learning, generating, and predicting various aspects of our universe by processing both quantum and classical data. In parallel, the pursuit of scalable science through physical simulations using both digital and analog quantum computers is rising on the horizon.

Quantum simulation stands as an important application of quantum computing, offering insights into quantum many-body systems that are beyond the reach of classical computational methods. For many quantum simulation applications, accurate initial state preparation is typically the first step for subsequent computational processes. This dissertation specifically focuses on state preparation procedures for quantum states with chiral topological order, states that are notable for their robust edge modes and topological properties.

Since the discovery of Shor’s factoring algorithm, there has been a sustained interest in finding more such examples of quantum advantage, that is, tasks where a quantum device can outperform its classical counterpart. While the universal, programmable quantum computers that can run Shor’s algorithm represent one direction in which to search for quantum advantage, they are certainly not the only one. In this dissertation, we study the theory of quantum advantage along two alternative avenues: sensing and simulation.

Quantum information science offers a remarkable promise: by thinking practically about how quantum systems can be put to work to solve computational and information processing tasks, we gain novel insights into the foundations of quantum theory and computer science. Or, conversely, by (re)considering the fundamental physical building blocks of computers and sensors, we enable new technologies, with major impacts for computational and experimental physics.

Quantum computers are likely to have a significant impact on cryptography. Many commonly used cryptosystems will be completely broken once large quantum computers are available. Since quantum computers can solve the factoring problem in polynomial time, the security of RSA would not hold against quantum computers. For symmetric-key cryptosystems, the primary quantum attack is key recovery via Grover search, which provides a quadratic speedup. One way to address this is to double the key length.

Quantum computing promises to transform our approach to solving significant computational challenges, such as factorization and quantum system simulation. Harnessing this quantum power in real life necessitates software stack support. This talk focuses on the critical challenges encountered in the software for quantum computing, aiming to shape high-assurance software stacks for controlling quantum computing devices in the immediate future and beyond.

Continuous optimization problems arise in virtually all disciplines of quantitative research, including applied mathematics, computer science, and operations research. While convex optimization has been well studied in the past decades, nonconvex optimization generally remains intractable in theory and practice. Quantum computers, an emerging technology that exploits quantum physics for information processing, could pave an unprecedented path toward nonconvex optimization.

Optomechanical systems have enabled a variety of novel sensors that transduce an external force on a mechanical sensor to an optical signal which can be read out through different measurement techniques. Based on recent advances in these sensing technologies, we suggest that heavy dark matter candidates around the Planck mass range could be detected solely through their gravitational interaction.

Random Circuits have emerged as an invaluable tool in the quantum mechanics’ 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.