Seminar

Motivated by the recent progress of quantum chaos and quantum information scrambling, the growth of an operator under the Heisenberg evolution has attracted a lot of attentions. I will first introduce a recently proposed perspective on the operator growth problem from the Lanczos algorithm point of view and the associated “Krylov complexity”.

With the long-term goal of studying quantum gravity on a quantum computer, I will discuss several results that make promising progress in this direction. Firstly, I will discuss a proposal for a holographic teleportation protocol that can be readily executed in table-top experiments. This protocol exhibits similar behavior to that seen in recent traversable wormhole constructions.

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.

A fundamental distinction between many-body quantum states are those with short- and long-range entanglement (SRE and LRE). The latter, such as cat states, topological order, or critical states cannot be created by finite-depth circuits. Remarkably, examples are known where LRE is obtained by performing single-site measurements on SRE states such as preparing the toric code from measuring a sublattice of a 2D cluster state.

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.

In this talk I will give an introduction to proofs of quantumness. Such protocols can be executed using local quantum computations and only classical communication. I will begin by defining and motivating proofs of quantumness. I will then describe the specific construction by Brakerski et al. [1] and how it uses the Learning with Errors problem. Finally, I will briefly describe proofs of quantumness protocols based on other cryptographically hard problems.

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.

In this talk I will be giving a brief introduction to some post-quantum cryptography concepts that appear frequently when discussing quantum cryptographic protocols with classical communication. The objective of this talk is to give intuition on how some of the protocols that will be described in this seminar series derive their security. To that end, I will be explaining the Learning with Errors problem (LWE) and how it relates to the conjectured hardness of lattice problems.

Near-term quantum information processors will not be capable of quantum error correction, but instead will implement algorithms using the physical native interactions of the device. These interactions can be used to implement quantum gates that are often continuously-parameterized (e.g., by rotation angles), as well as to implement analog quantum simulations that seek to explore the dynamics of a particular Hamiltonian of interest.

Monitored random quantum circuits (MRCs) exhibit a measurement-induced phase transition between area-law and volume-law entanglement scaling. In this talk, I will argue that MRCs with a conserved charge additionally exhibit two distinct volume-law entangled phases that cannot be characterized by equilibrium notions of symmetry-breaking or topological order, but rather by the non-equilibrium dynamics and steady-state distribution of charge fluctuations.