Friday Quantum Seminar

Topological mixed quantum states in or out of equilibrium can arise in open quantum systems. Their linear responses are generally non-quantized, even though quantized topological invariants can be defined. In this talk, I will present a real-time U(1) topological gauge field action capable of reconciling this paradoxical phenomenology. In addition to non-quantized linear responses, this action encodes quantized non-linear responses associated with mixed state topology.

Arrays of neutral atoms promise to enable a variety of goals across quantum science, including quantum information processing, metrology, and many-body physics. While there have been recent significant improvements in quantum control, coherence times, and entanglement generation, one outstanding limitation is the efficient implementation of dissipation or measurement.

Concepts from topology provide insight into wide ranging areas from fluid mechanics to quantum condensed matter physics. We studied the topology of ultracold 87Rb atoms in a highly tunable bipartite optical lattice, using a form of quantum state tomography, to measure the full pseudospin state throughout the Brillouin zone. We used this capability to follow the evolution of two topological quantities: the Zak phase and chiral winding number, after changing the lattice configuration.

Abstract: Semidefinite Programming (SDP) is a class of convex optimization programs with vast applications in control theory, quantum information, combinatorial optimization, machine learning and operational research. In this talk, I will discuss how SDP can be used to address two major challenges in quantum computing research: near-term quantum advantage and device certification.

Semidefinite Programming (SDP) is a class of convex optimization programs with vast applications in control theory, quantum information, combinatorial optimization, machine learning and operational research. In this talk, I will discuss how SDP can be used to address two major challenges in quantum computing research: near-term quantum advantage and device certification.

Motivated by recent experimental demonstrations of Floquet topological insulators, there have been several theoretical proposals for using structured light, either spatial or spectral, to create other properties such as flat band and vortex states. In particular, the generation of vortex states in a massive Dirac fermion insulator irradiated by light carrying nonzero orbital angular momentum (OAM) has been proposed recently. Here, we evaluate the orbital magnetization and  optical conductivity as physical observables for such a system.

Quantum memory will play an important role in quantum networks, notably as components in quantum repeaters. One promising technique for realizing broadband quantum memory, the atomic frequency comb (AFC) protocol, calls for a material with large inhomogeneous broadening and small homogeneous broadening: spectral-hole burning techniques can be used to prepare the absorption spectrum in a periodic pattern of narrow peaks (an AFC). A single photon, absorbed as a collective excitation, will be re-emitted after a time interval fixed by the AFC tooth spacing.

Recent work has predicted that quenched near-integrable systems can exhibit dynamics associated with thermal, quantum, or purely non-equilibrium phase transitions, depending on the initial state [1]. Using a trapped-ion quantum simulator with intrinsic long-range interactions, we investigate collective non-equilibrium properties of critical fluctuations after quantum quenches.

We argue that all locality-preserving mappings between fermionic observables and Pauli matrices on a two-dimensional lattice can be generated from the exact bosonization (arXiv:1711.00515), whose gauge constraints project onto the subspace of the toric code with emergent fermions. Starting from the exact bosonization and applying Clifford finite-depth generalized local unitary (gLU) transformation, we can achieve all possible fermion-to-qubit mappings (up to the re-pairing of Majorana fermions).

Dirac Spin Liquids (DSLs) are gapless symmetric states in 2+1 dimensions with no magnetic order. They are featureless, yet interesting because their low energy physics is believed to be described by QED-3, an effective field theory in terms of gapless Dirac fermions coupled to an emergent U(1) gauge field. They also serve as a parent state for seemingly unrelated magnetically ordered states, where the ordered states arise from condensation of ``monopole excitations” of the DSL. Can such a description have experimentally observable consequences?