Tunable Topology and Correlated States in Twisted Homobilayer Transition Metal Dichalcogenides
Abstract: We create honeycomb superlattice structures in TMD moiré materials as model systems to
study magnetism, electronic correlations and topology. In twisted MoTe 2 , we realize topological flat
bands that closely resemble the lowest Landau level but in the absence of an external magnetic field.
We present evidence for integer and fractional Chern states [1], which are the lattice analogues of
integer and fractional quantum Hall states at zero magnetic field. We further explore correlated states in
Achieving low circuit depth with few qubits, for arithmetic and the QFT
In this work we present fast constructions for the quantum Fourier transform and quantum integer multiplication, using few ancilla qubits compared to the size of the input. For the approximate QFT we achieve depth O(log n) using only n + O(n / log n) total qubits, by applying a new technique we call "optimistic quantum circuits." To our knowledge this is the first circuit for the AQFT with space-time product O(n log n), matching a known lower bound.
Topological Photonics: Nested Frequency Combs and Edge Mode Tapering
Dissertation Committee Chair: Prof. Mohammad Hafezi
Committee:
Professor Kartik Srinivasan
Professor Yanne Chembo
Professor Carlos A. Rios Ocampo
Professor Miao Yu (Dean’s Representative)
Bright Soliton Pulse Pairs in High-Q Thin-Film Si3N4 Microresonators
Abstract: Optical microresonators can trap light within compact volumes at discrete resonant frequencies, and soliton microcombs have advanced the miniaturization of various comb systems. Thin-film silicon nitride (Si3N4) microresonators, fabricated using CMOS foundry techniques, possess high-Q factors and have demonstrated many applications towards photonic integration. However, this platform has traditionally struggled to support bright solitons due to its normal dispersion nature.
One Hundred Years After Heisenberg: Discovering the World of Simultaneous Measurements of Noncommuting Observables - CANCELED
Abstract: One hundred years after Heisenberg’s Uncertainty Principle, the question of how to make simultaneous measurements of noncommuting observables lingers. I will survey one hundred years of measurement
theory, which brings us to the point where we can formulate how to measure any set observables weakly and simultaneously and then concatenate such measurements continuously to determine what is
No switch, no limit – Diffraction-unlimited imaging of multiple point scatterers
Abstract: From bio-physics to quantum simulators, many fields depend on sub-diffraction imaging of multiple point sources.
Stabilization of cat-state manifolds using nonlinear reservoir engineering
Reservoir engineering has become valuable for preparing and stabilizing quantum systems. Notably, it has enabled the demonstration of dissipatively stabilized Schrödinger’s cat qubits through engineered two-photon loss which are interesting candidates for bosonic error-corrected quantum computation. Reservoir engineering is however limited to simple operators often derived from weak low-order expansions of some native system Hamiltonians. In this talk, I will introduce a novel reservoir engineering approach for stabilizing multi-component Schrödinger’s cat states.
Exponential Quantum Space Advantage for Approximating Maximum Directed Cut in the Streaming Model
While the search for quantum advantage typically focuses on speedups in execution time, quantum algorithms also offer the potential for advantage in space complexity. Previous work has shown such advantages for data stream problems, in which elements arrive and must be processed sequentially without random access, but these have been restricted to specially-constructed problems [Le Gall, SPAA `06] or polynomial advantage [Kallaugher, FOCS `21]. We show an exponential quantum space advantage for the maximum directed cut problem.
Quadratic lower bounds on the stabilizer rank: A probabilistic approach
The approximate stabilizer rank of a quantum state is the minimum number of terms in any approximate decomposition of that state into stabilizer states. We expect that the approximate stabilizer rank of n-th tensor power of the “magic” T state scale exponentially in n, otherwise there is a polynomial time classical algorithm to simulate arbitrary polynomial time quantum computations. Despite this intuition, several attempts using various techniques could not lead to a better than a linear lower bound on the “exact” rank.
Catalysis of quantum entanglement and entangled batteries
We discuss recent progress on entanglement catalysis, including the equivalence between catalytic and asymptotic transformations of quantum states and the impossibility to distill entanglement from states having positive partial transpose, even in the presence of a catalyst. A more general notion of catalysis is the concept of entanglement battery. In this framework, we show that a reversible manipulation of entangled states is possible. This establishes a second law of entanglement manipulation without relying on the generalized quantum Stein's lemma.