# Perimeter Institute Quantum Discussions

This series consists of weekly discussion sessions on foundations of quantum Theory and quantum information theory. The sessions start with an informal exposition of an interesting topic, research result or important question in the field. Everyone is strongly encouraged to participate with questions and comments.

## Seminar Series Events/Videos

Currently there are no upcoming talks in this series.

## Synchronous correlations, Bell inequalities, and categories of nonlocal games

Wednesday May 24, 2017
Speaker(s):

Given two sets X and Y, we consider synchronous correlations in a two-party nonlocal game with inputs X and outputs Y as a notion of generalized function between these sets (akin to a quantum graph homomorphism). We examine some structures in categories of synchronous classical, quantum, and nonsignalling strategies.

## Percolation transition vs. erasure thresholds for surface codes on graphs

Wednesday Apr 26, 2017
Speaker(s):

For a family of finite rate stabilizer codes, one can define two distinct error correction thresholds: the usual "block" threshold for the entire code, and the single-qubit threshold, where we only care about the stability of a single encoded qubit corresponding to a randomly chosen conjugate pair of logical X and Z operators.  Our main result is that in the case of erasures, for hyperbolic surface codes related to a {p,q} tiling of the hyperbolic plane, it is the latter threshold that coincides exactly with the infinite-graph edge percolation transition.  I will also discuss likely general

## "Quantum advantage with shallow circuits"

Wednesday Apr 19, 2017
Speaker(s):

We prove that constant-depth quantum circuits are more powerful than their classical counterparts. We describe an explicit (i.e., non-oracular) computational problem which can be solved with certainty by a constant-depth quantum circuit composed of one- and two-qubit gates. In contrast, we prove that any classical probabilistic circuit composed of bounded fan-in gates that solves the problem with high probability must have depth logarithmic in the input size. This is joint work with Sergey Bravyi and Robert Koenig (arXiv:1704.00690).

## Fighting noise with topology

Wednesday Mar 08, 2017
Speaker(s):

As we get closer to build a quantum computer, the main remaining challenge is handling the noise that aflicts quantum systems.

Topological methods, in their various forms, have become the main contestants in the quest for succesfully overcoming noise. A good deal of their strength and versatility is due to their rather unique physical flavour, which keeps giving rise to surprising developments.

## Quantum Field Theory in the Quantum Information Age

Thursday Feb 23, 2017
Speaker(s):

Quantum Field Theories are interacting quantum systems described by an infinite number of degrees of freedom, necessarily living on an infinite-dimensional Hilbert space. Hence, many concepts from Quantum Information Theory have to be adapted before they can be applied to this setting. However, the task is worthwhile as we obtain new tools to understand the entanglement structure of theories describing the fundamental forces of nature. I will outline two approaches along this route, one bottom-down and one bottom-up strategy.

## Quantum error-correction and black holes

Wednesday Feb 22, 2017
Speaker(s):

It is commonly believed that quantum information is not lost in a black hole. Instead, it is encoded into non-local degrees of freedom in some clever way; like a quantum error-correcting code. In this talk, I will discuss recent attempts to resolve some paradoxes in quantum gravity by using the theory of quantum error-correction. First, I will introduce a simple toy model of the AdS/CFT correspondence based on tensor networks and demonstrate that the correspondence between the AdS gravity and CFT is indeed a realization of quantum codes.

## Quantum supremacy of fault-tolerant quantum computation in a pre-threshold region

Wednesday Jan 25, 2017
Speaker(s):

Demonstrating quantum supremacy, a complexity-guaranteed quantum advantage against over the best classical algorithms by using less universal quantum devices, is an important near-term milestone for quantum information processing. Here we develop a threshold theorem for quantum supremacy with noisy quantum circuits in the pre-threshold region, where quantum error correction does not work directly.

## Recovery maps in quantum thermodynamics

Wednesday Jan 11, 2017
Speaker(s):

A research line that has been very active recently in quantum information is that of recoverability theorems. These, roughly speaking, quantify how well can quantum information be restored after some general CPTP map, through particular 'recovery maps'. In this talk, I will outline what this line of work can teach us about quantum thermodynamics.

## Non-holonomic tomography and detecting state-preparation and measurement correlated errors

Wednesday Dec 14, 2016
Speaker(s):

Quantum tomography is an important tool for characterizing the parameters of unknown states, measurements, and gates.  Standard quantum tomography is the practice of estimating these parameters with known measurements, states, or both, respectively.  In recent years, it has become important to address the issue of working with systems where the devices'' used to prepare states and make measurements both have significant errors.  Of particular concern to me is whether such state-preparation and measurement errors are correlated with each other.  In this talk, I will share a soluti

## The ABCs of color codes

Monday Dec 12, 2016
Speaker(s):

To build a fully functioning quantum computer, it is necessary to encode quantum information to protect it from noise. Topological codes, such as the color code, naturally protect against local errors and represent our best hope for storing quantum information. Moreover, a quantum computer must also be capable of processing this information. Since the color code has many computationally valuable transversal logical gates, it is a promising candidate for a future quantum computer architecture.

## LECTURES ON-DEMAND

### Gabriela González, Louisiana State University

Speaker: Gabriela Gonzalez