Developing a strong driving toolkit for Floquet systems with superconducting qubits
Dissertation Committee Chair: Alicia Kollár
Committee:
Ben Palmer
Steven Rolston
Nathan Schine
Ron Walsworth (Dean’s Rep)
Experimental observation of symmetry-protected signatures of N-body interactions
Abstract: Characterizing higher-order interactions in quantum processes with unknown Hamiltonians presents a significant challenge. This challenge arises, in part, because two-body interactions can lead to an arbitrary evolution, and two-local gates are considered universal in quantum computing. However, recent research has demonstrated that when the unknown Hamiltonian follows a U(1) symmetry, like charge or number conservation, N-body interactions display a distinct and symmetry-protected feature called the N-body phase.
Measurement-induced entanglement and complexity in random constant-depth 2D quantum circuits
Abstract: We analyse the entanglement structure of states generated by random constant-depth two-dimensional quantum circuits, followed by projective measurements of a subset of sites. By deriving a rigorous lower bound on the average entanglement entropy of such post-measurement states, we prove that macroscopic long-ranged entanglement is generated above some constant critical depth in several natural classes of circuit architectures, which include brickwork circuits and random holographic tensor networks.
Robust sparse IQP sampling in constant depth
Abstract: Between NISQ (noisy intermediate scale quantum) approaches without any proof of robust quantum advantage and fully fault-tolerant quantum computation, we propose a scheme to achieve a provable superpolynomial quantum advantage (under some widely accepted complexity conjectures) that is robust to noise with minimal error correction requirements. We choose a class of sampling problems with commuting gates known as sparse IQP (Instantaneous Quantum Polynomial-time) circuits and we ensure its fault-tolerant implementation by introducing the tetrahelix code.
When less is more; modelling and simulating new approaches in quantum sensing
Abstract: Quantum sensing extends the vast benefits of a quantum advantage to traditional metrology. A common method of quantum sensing utilizes coherent, crystal defects in semi-conductors (such as nitrogen vacancy centers in diamond) to perform high-precision measurements on a variety of length scales. Such measurements might span from vectorized magnetometry of macroscopic computer chips to nanoscale strain or temperature mapping in a target matrial. In exploring new regimes for quantum sensing, we need to model and assess their viability through theoretical or si
MAViS: Modular Autonomous Virtualization System for Two-Dimensional Semiconductor Quantum Dot Arrays
Abstract: Arrays of gate-defined semiconductor quantum dots are among the leading candidates for building scalable quantum processors.
High-fidelity initialization, control, and readout of spin qubit registers require exquisite and targeted control over key Hamiltonian parameters that define the electrostatic environment.
However, due to the tight gate pitch, capacitive crosstalk between gates hinders independent tuning of chemical potentials and interdot couplings.
Catalysis of quantum entanglement and entangled batteries
Abstract: 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.
A General Quantum Duality for Representations of Groups with Applications to Quantum Money, Lightning, and Fire
Aaronson, Atia, and Susskind established that swapping quantum states |ψ〉 and |ϕ〉 is computationally equivalent to distinguishing their superpositions |ψ〉 ± |ϕ〉. We extend this to a general duality principle: manipulating quantum states in one basis is equivalent to extracting values in a complementary basis. Formally, for any group, implementing a unitary representation is computationally equivalent to Fourier subspace extraction from its irreducible representations.
A Landau Level at Zero Flux, Magic, and Abelianization
Abstract: A Landau level (which is a flat band) forms only when a magnetic flux with non-zero total flux threads a system. In fact the degeneracy at the flat band is proportional to the flux. So no flat band can form when the magnetic flux averages to zero. We will discuss this and then show otherwise. This is relevant to time reversal symmetric systems that form flat bands such as magic-angle twisted bilayer graphene. In this talk the magic behind those systems will be revealed through the simplest model that gives rise to magical behaviour.