• Speaker: Ramis Movassagh, IBM
• Title: Proof of average-case #P- hardness of random circuit sampling with some robustness, and a protocol for blind quantum computation
• Date: 09/05/2019
• Time: 11:00 AM - 12:00 PM
• Place: C304 Wells Hall

A one-parameter unitary-valued interpolation between any two unitary matrices (e.g., quantum gates) is constructed based on the Cayley transformation. We prove that this path induces probability measures that are arbitrarily close to the Haar measure and prove the simplest known average-case # P -hardness of random circuit sampling (RCS). RCS is the task of sampling from the output distribution of a quantum circuit whose local gates are random Haar unitaries, and is the lead candidate for demonstrating quantum supremacy in the "noisy intermediate scale quantum (NISQ)" computing era. Here we also prove exp(-Θ(n^4 )) robustness with respect to additive error. This overcomes issues that arise for extrapolations based on the truncations of the power series representation of the exponential function. (Dis)Proving the quantum supremacy conjecture requires an extension of this analysis to noise that is polynomially small in the system's size. This remains an open problem. Lastly, an efficient and private protocol for blind quantum computation is proposed that uses the Cayley deformations proposed herein for encryption. This is an efficient protocol that only requires classical communication between Alice and Bob. ** The talk is self-contained and does not require any pre-req beyond basic linear algebra (e.g, knowing what a unitary matrix is).

• Speaker: Mike Hartglass, Santa Clara University
• Title: Free products of finite-dimensional von Neumann algebras
• Date: 09/12/2019
• Time: 11:00 AM - 12:00 PM
• Place: C304 Wells Hall

I will present joint work with Brent Nelson, where we classify the structure of free products of von Neumann algebras equipped with arbitrary states. Our techniques use our other joint work of assigning a von Neumann algebra associated to a weighted graph. I will discuss this work and how it leads to computing finite-dimensional free products.

• Speaker: Corey Jones, The Ohio State University
• Title: The higher dimensional algebra of matrix product operators and quantum spin chains
• Date: 09/26/2019
• Time: 11:30 AM - 12:30 PM
• Place: C304 Wells Hall

In the context of 1D quantum spin chains, matrix product operators provide a way to study non-local operators such as translation in terms of quasi-local information. They have been used to describe a generalized form of symmetry for 1D systems on the boundary of 2D topological phases. In this talk, we will introduce some concepts of higher dimensional algebra, and a broad hypotheses about higher categories and spatially extended quantum systems. We will then explain how the collection of matrix product operators assembles into a higher (symmetric monoidal 2-) category, and discuss some implications of this. Based on joint work with David Penneys.

• Speaker: Charles Smart, U Chicago
• Title: TBA
• Date: 11/07/2019
• Time: 11:30 AM - 12:30 PM
• Place: C304 Wells Hall

No abstract available.

• Speaker: Kari Eifler, Texas A&M University
• Title: TBA
• Date: 11/21/2019
• Time: 11:30 AM - 12:30 PM
• Place: C304 Wells Hall

TBA