Phase Transitions in Random Quantum Circuits
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.
Quantum Simulation and Dynamics with Synthetic Quantum Matter
Significant advancements in controlling and manipulating individual quantum degrees of freedom have paved the way for the development of programmable strongly-interacting quantum many-body systems. Quantum simulation emerges as one of the most promising applications of these systems, offering insights into complex natural phenomena that would otherwise be difficult to explore.
Optical quantum memory with processing capabilities
Abstract: Optical quantum memories can be used for storage or generation and subsequent retrieval of quantum light for the purpose of long-distance quantum communication. However, it is beneficial to consider more functions of quantum memories, which may then become parts of more complex hybrid quantum networks. In my works I have demonstrated protocols for spin-wave processing based on interference in multiplexed optical quantum memories [1,2].
On Quantum Speedups for Nonconvex Optimization via Quantum Tunneling Walks
Classical algorithms are often not effective for solving nonconvex optimization problems where local minima are separated by high barriers. In this paper, we explore possible quantum speedups for nonconvex optimization by leveraging the global effect of quantum tunneling. Specifically, we introduce a quantum algorithm termed the quantum tunneling walk (QTW) and apply it to nonconvex problems where local minima are approximately global minima.
Probing quasiparticle interactions and statistics through nonlinear response
Abstract: In this talk, I will summarise recent theoretical work on understanding nonlinear response functions in systems with interacting quasiparticles.
Tunneling properties in Fe-based superconductor, FeTe.55Se.45 (FTS)
Dissertation Committee Chair: Prof. Jay D Sau
Committee:
Leveraging Hamiltonian Simulation Techniques to Compile Operations on Bosonic Devices
Circuit QED enables the combined use of qubits and oscillator modes. Despite a variety of available gate sets, many hybrid qubit-boson (i.e., oscillator) operations are realizable only through optimal control theory (OCT) which is oftentimes intractable and uninterpretable. We introduce an analytic approach with rigorously proven error bounds for realizing specific classes of operations via two matrix product formulas commonly used in Hamiltonian simulation, the Lie–Trotter and Baker–Campbell–Hausdorff product formulas.
Classification and characterization of crystalline topological invariants in quantum many-body states
Dissertation Committee Chair: Professor Maissam Barkeshli (advisor)
Committee:
New Avenues in Quantum Computing: Beyond Quantum Circuits with Trapped-Ion Qubits
Abstract: Trapped ions are a leading quantum technology for quantum computation and simulation, with the capability to solve computationally hard problems and deepen our understanding of complex quantum systems.
Hidden time-reversal symmetry, quantum detailed balance, and exactly-solvable driven-dissipative quantum systems
Abstract: "In this talk, we discuss a new kind of symmetry that underlies a wide class of driven-dissipative quantum systems, a *hidden time-reversal symmetry*. This symmetry represents a generalization of the notion of “detailed balance” that is fully applicable to truly quantum systems. The introduction of this symmetry resolves the problem of how to usefully define “detailed balance” in a quantum setting (a problem that has been studied since the early 70’s by AMO physicists).