JQI

Many applications of quantum simulation require qubit representations of a fixed number of fermions (F) in a larger number of possible modes (M). Representing such states is possible with I := ⌈log(M choose F)⌉ qubits, but existing constructions achieving this level of compactness result in fermion operators with gate complexity exponential in I.

Learning properties of unknown quantum systems or processes is of fundamental importance to the development of quantum technologies. While many learning algorithms require access to external ancillary qubits (referred to as quantum memory), the statistical complexity and experimental costs for these algorithms vary considerably due to different sizes of quantum memory. Here, we investigate the transitions for statistical complexity required for learning quantum data with bounded quantum memory.

Demonstrations of quantum advantage for random circuit and boson sampling over the past few years have generated considerable excitement for the future of quantum computing and has further spurred the development of a wide range of gate-based digital quantum computers, which represent quantum programs as a sequence of quantum gates acting on one and two qubits.

There is a rich connection between classical and quantum codes and holographic correspondence connecting 2d CFTs and abelian 3d Chern-Simons theories. In the 3d language the codes emerge as a way to parametrize condensable anyons. Upon condensation 3d topological field theory gives rise to 2d CFT at the boundary. This provides a way to construct 2d CFTs from codes - the so called "code CFTs." This construction of code CFT has a natural interpretation in terms of a CSS quantum code (defined in terms of the original classical code, defining the CFT).

I will discuss recent advances in improving and costing quantum algorithms for linear differential equations. I will introduce a stability-based analysis of Berry et al.’s 2017 algorithm that greatly extends its scope and leads to complexities sublinear in time in a broad range of settings – Hamiltonian simulation being a boundary case that prevents this kind of broad fast-forwarding. I illustrate these gains via toy examples such as the linearized Vlasov-Possion equation, networks of coupled, damped, forced harmonic oscillators and quadratic nonlinear systems of ODEs.

I will review the concept of Floquet quantum error-correcting codes, and, more generally, dynamic codes. These codes are defined through sequences of low-weight measurements that change the instantaneous code in time and enable error correction.  I will explain a few viewpoints on these codes, including state teleportation and anyon condensation, and will explain how to implement gates purely by adjusting the sequences of low-weight measurement.

Dissertation Committee Chair: Jay Sau

Committee: 

Steven Anlage

Christopher Jarzynski

Johnpierre Paglione

Victor Yakovenko

Abstract: In many-body systems of cold atoms and their applications to quantum metrology and quantum computing, there are important questions around how large an entangled many-body state we can usefully and reliably prepare in the presence of decoherence. Information spreading and entanglement growth are typically limited by Lieb-Robinson bounds, so that the useful system size with short-range interactions will grow only linearly with the coherence time.

Abstract: In this talk, we present a demonstration of “giant artificial atoms” realized with superconducting qubits in a waveguide QED architecture. The superconducting qubits couple to the waveguide at multiple, well-separated locations. In this configuration, the dipole approximation no longer holds, and the giant atom may quantum mechanically self-interfere. Multiple, interleaved qubits in this architecture can be switched between protected and emissive configurations, while retaining waveguide-mediated qubit-qubit interactions.

Abstract: Polyatomic molecules uniquely enable the simultaneous combination of multiple features advantageous for precision measurement and quantum science. Searches for fundamental symmetry violations benefit from large internal molecular fields, high polarizability, internal co-magnetometry, and the ability to cycle photons - all of which can be found in certain engineered polyatomic species. We discuss experimental and theoretical developments in several linear metal hydroxide (MOH) species, including spectroscopy, photon cycling, andquantum control.