Talks

Quantum neural networks have been widely studied in recent years, given their potential practical utility and recent results regarding their ability to efficiently express certain classical data. However, analytic results to date rely on assumptions and arguments from complexity theory. Due to this, there is little intuition as to the source of the expressive power of quantum neural networks or for which classes of classical data any advantage can be reasonably expected to hold. In this talk, I will discuss my recent results (arXiv:2209.14353) studying the relative expressive power between a broad class of neural network sequence models and a class of recurrent models based on Gaussian operations with non-Gaussian measurements. We explicitly show that quantum contextuality is the source of an unconditional memory separation in the expressivity of the two model classes. Additionally, we use this intuition to study the relative performance of our introduced model on a standard translation data set exhibiting linguistic contextuality and show that the quantum model outperforms state-of-the-art classical models even in practice. I will also briefly discuss connections to my previous work studying the trainability of variational quantum algorithms (arXiv:2109.06957, arXiv:2205.05786).

Constraint satisfaction problems are known to always be "easy" or "hard", in the sense of being either solvable in P or being NP-complete, with no intermediate difficulty levels. The quantum analog of constraint problems, frustration-free Hamiltonians, are known to exhibit at least two more levels of complexity: QMA (for arbitrary local Hamiltonians) and MA (for stoquastic Hamiltonians). Wondering if other complexity classes can occur, we answer in the affirmative: there are interactions which can be freely arranged on qubits in any arrangement, such that the resulting frustration problem is BQP-complete, and captures exactly the difficulty of quantum computation. Simple modifications of this construction show that quantum constraint problems can be complete for QCMA and BPP as well. Based on https://arxiv.org/abs/2101.08381

The multipartite entanglement structure for the ground states of two dimensional topological phases is an interesting albeit not well understood question. Utilizing the bulk-boundary correspondence, the tripartite entanglement calculation of 2d topological phases can be reduced to that on the vertex state, defined by the boundary conditions at the interfaces between spatial regions. In this work, we use the conformal interface technique to calculate the entanglement measures of the vertex state, which include the area-law, geometrical and topological pieces, and the possible extra order one contribution. This explains our previous observation of Markov gap h=\frac{c}{3}\ln 2 in the 3-vertex state, and generalizes it to the p-vertex state as well as rational conformal field theory, and more general choices of subsystem. Finally, we support our prediction by numerical evidence. 

Zoom link:  https://pitp.zoom.us/j/93914854044?pwd=eWl3eGVLU25XUGhKbnFRSm5ab0JuUT09

A fundamental aspect of a random walk is determining when it reaches a specified threshold position for the first time.  This first-passage time, and more generally, the distribution of first passage times underlies many non-equilibrium phenomena, such as the triggering of integrate and fire neurons, the statistics of cell division, and the execution of stock options.  The computation of the first-passage time and its distribution is both simple and beautiful, with profound connections to electrostatic potential theory.  I will present some aspects of these fundamentals and then discuss applications of first-passage ideas to diverse phenomena, including stochastic search processes and a toy model of wealth sharing.

Zoom link:  https://pitp.zoom.us/j/98293478936?pwd=NTR3dWZoNElWRmd2NVJ1bzk5aC9ZQT09

Optical astronomical imaging looks for better imaging quality in extreme cases of weak and subdiffraction limits. I focus on the quantum enhancement of astronomical interferometric imaging, including its fundamental limit and practical issues. For the fundamental aspects, I ignore any resource limit and noise and consider the ideal imaging problems. I show that the resolution limit can be enhanced with more carefully chosen measurement strategies and the general imaging quality can be enhanced by postprocessing the stellar photons with a quantum computer. For the practical aspects, I try to overcome the transmission loss suffered by interferometric imaging using quantum network, consider the possibility to implement a local scheme with better performance, and discuss the feasibility of decomposing thermal states into temporally localized pulses.

Scrambling of quantum information is an important feature at the root of randomization and benchmarking protocols, the onset of quantum chaos, and black-hole physics.

Unscrambling this information is possible given perfect knowledge of the scrambler [ArXiv: 1710.03363].

We show that one can retrieve the scrambled information without any previous knowledge of the scrambler, by a learning algorithm that allows the building of an efficient decoder. Surprisingly, complex quantum scramblers admit Clifford decoders: the salient properties of a scrambling unitary can be efficiently described even if exponentially complex, as long as it is not fully chaotic. This is possible because all the redundant complexity can be described as an entropy, and for non-chaotic black holes can be efficiently pushed away, just like in a refrigerator. This entropy is not due to thermal fluctuations but to the non-stabilizer behavior of the scrambler.

In the holographic approach to quantum gravity, quantum information theory plays a fundamental role in understanding how semiclassical gravity emerges from the microscopic description.  The map (sometimes called the dictionary) between these two descriptions has the structure of a quantum error correcting code.  In the context of an evaporating black hole, this code can be arbitrarily far from an isometry.  Such codes are novel from a quantum information standpoint, and their properties are not yet well understood.  I will describe a simple toy model of an evaporating black hole which allows for an explicit construction of the dictionary using the Euclidean gravity path integral.  I will also describe the sense in which this dictionary is a non-isometric code, explain its basic properties, and comment on implications for semiclassical physics in the black hole interior.

Zoom link:  https://pitp.zoom.us/j/94869738394?pwd=dGNBWXpmTTZaRSs3c0NQUDA1UkZCZz09