# 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.

## 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 solut

## 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.

## What does the effective resistance of electrical circuits have to do with quantum algorithms?

Friday Dec 09, 2016
Speaker(s):

I will answer the question in the title. I will also describe a new quantum algorithm for Boolean formula evaluation and an improved analysis of an existing quantum algorithm for st-connectivity. Joint work with Stacey Jeffery.

Wednesday Nov 16, 2016
Speaker(s):

Information theory establishes the fundamental limits on data transmission, storage, and processing. Quantum information theory unites information theoretic ideas with an accurate quantum-mechanical description of reality to give a more accurate and complete theory with new and more powerful possibilities for information processing. The goal of both classical and quantum information theory is to quantify the optimal rates of interconversion of different resources. These rates are usually characterized in terms of entropies.

## A toy theory of quantum speed-ups based on the stabilizer formalism

Wednesday Nov 09, 2016
Speaker(s):

A central question in quantum computation is to identify which problems can be solved faster on a quantum computer. A Holy Grail of the field would be to have a theory of quantum speed-ups that delineates the physical mechanisms sustaining quantum speed-ups and helps in the design of new quantum algorithms. In this talk, we present such a toy theory for the study of a class of quantum algorithms for algebraic problems, including Shor’s celebrated factoring algorithm. Our theory is an extension of Gottesman’s stabilizer formalism based on elements of group and hypergroup theory.

## Fault-tolerant quantum error correction with non-abelian anyons

Wednesday Nov 02, 2016
Speaker(s):

Non-abelian anyons have drawn much interest due to their suspected existence in two-dimensional condensed matter systems and for their potential applications in quantum computation. In particular, a quantum computation can in principle be realized by braiding and fusing certain non-abelian anyons. These operations are expected to be intrinsically robust due to their topological nature. Provided the system is kept at a

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## Foliated Quantum Codes, with a chance of Anyonic Time

Wednesday Jun 29, 2016
Speaker(s):

Raussendorf introduced a powerful model of fault tolerant measurement based quantum computation, which can be understood as a layering (or “foliation”) of a multiplicity of Kitaev’s toric code. I will discuss our generalisation of Raussendorf’s construction to an arbitrary CSS code. We call this a Foliated Quantum Code. Decoding this foliated construction is not necessarily straightforward, so I will discuss an example in which we foliate a family of finite-rate quantum turbo codes, and present the results of numerical simulations of the decoder performance.

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## The accuracy of finite quantum clocks: Fundamental constraints from dimension and thermodynamic considerations

Wednesday Apr 27, 2016
Speaker(s):

In this talk I will introduce recent research into quantum clocks of finite dimension, with the focus on their accuracy, as determined by their dimension, coherence, and power consumption.

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## How to Verify a Quantum Computation

Wednesday Mar 30, 2016
Speaker(s):

We give a new theoretical solution to a leading-edge experimental challenge, namely to the verification of quantum computations in the regime of high computational complexity. Our results are given in the language of quantum interactive proof systems. Specifically, we show that any language in BQP has a quantum interactive proof system with a polynomial-time classical verifier (who can also prepare random single-qubit pure states), and a quantum polynomial-time prover. Here, soundness is unconditional---i.e it holds even for computationally unbounded provers.

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## Protected gates for topological quantum field theories

Wednesday Jan 20, 2016
Speaker(s):

We study restrictions on locality-preserving unitary logical gates for topological quantum codes in two spatial dimensions. A locality-preserving operation is one which maps local operators to local operators --- for example, a constant-depth quantum circuit of geometrically local gates, or evolution for a constant time governed by a geometrically-local bounded-strength Hamiltonian. Locality-preserving logical gates of topological codes are intrinsically fault tolerant because spatially localized errors remain localized, and hence sufficiently dilute errors remain correctable.

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