Fall 2017 Spring
2018 Fall
2018 Fall 2020
(See also: The IQC-QuICS Math and Computer Science Seminar.)
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Email |
Office |
Office
hours |
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3100G
Atlantic Building |
Mon
3:00-4:00 pm |
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3100K
Atlantic Building |
By
appointment |
This
research-interaction seminar focuses on mathematical aspects of quantum
information, with a view towards quantum foundations, quantum cryptography,
quantum computing, and other topics in theoretical physics. The current
semester will tentatively focus on quantum resource theory and (graphical)
programming languages as central topics, but may
include other topics suggested by participants. No previous experience in
quantum theory is required, however linear algebra and (discrete) probability
is a must.
(Research Interaction Team participation does not require enrollment in
MATH489/689, however it is required to obtain credits.)
Coordinates: Monday, 29 January 2018,
4:15pm, Atlantic Building 3100A.
Title: Organizational meeting.
Moderators: Brad Lackey and Carl Miller.
Abstract: We'll discuss logistics, and then give some short
advertisements for papers that we'd like to discuss during the spring semester.
Suggestions and contributions are welcome!
Coordinates: Monday, 5 February 2018, 4:15pm, Atlantic Building
3100A.
Title: Constant-depth quantum circuits and nonlocal games.
Speaker: Carl Miller
Abstract: A recent paper of Bravyi, Gosset, and Koenig demonstrates a
constant-depth quantum circuit for solving a particular mathematical problem,
while at the same time showing that there is no constant-depth classical
circuit that can solve the same problem. The proof involves showing that such a
classical circuit would imply unreasonably effective strategies at certain
multiplayer games. In the talk I will examine some of the technical tools used
to achieve this result.
Reference: S. Bravyi, D. Gosset, R. Koenig, "Quantum advantage with
shallow circuits." arXiv:1704.00690. (2017)
Coordinates: Monday, 12 February 2018, 4:15pm, Atlantic Building
3100A.
Title: Morphisms in categories of nonlocal games.
Speaker: Brad Lackey
Abstract: Synchronous correlations are a class of nonlocal games that
behave like functions between finite sets. We examine categories whose
morphisms are games with synchronous classical, quantum, or general
nonsignaling correlations, characterizing when morphisms in these categories
are monic, epic, sections, or retractions.
Coordinates: Monday, 19 February 2018, 4:15pm, Atlantic Building
3100A.
Title: Morphisms in categories of nonlocal games (cont'd).
Speaker: Brad Lackey
Abstract: Synchronous correlations are a class of nonlocal games that
behave like functions between finite sets. We examine categories whose morphisms
are games with synchronous classical, quantum, or general nonsignaling
correlations, characterizing when morphisms in these categories are monic,
epic, sections, or retractions.
Coordinates: Monday, 26 February 2018, 4:15pm, Atlantic Building
3100A.
Title: The set of quantum correlations is not closed.
Speaker: Brad Lackey
Abstract: We review Slofstra's construction of a family of nonlocal
games that cannot be won with certainty using any finite-dimensional quantum
strategy, however can be played perfectly in the limit of such strategies. The
key methodology is to link a perfect strategy for such a game to a
finite-dimensional representation of a specific finitely-presented
group constructed from the game. Reference: Slofstra, arXiv:1703.08618.
Coordinates: Monday, 5 March 2018, 4:15pm, Atlantic Building 3100A.
Title: Graph Correlation Functions
Speaker: Aaron Ostrander
Abstract: Slofstra recently showed that the set of quantum correlations
is not closed; however, his construction (for the observables that exhibit
non-closure) requires advanced group theory. Following this result, Dykema et.
al. developed a graph theoretic proof of the non-closure of the set of quantum
correlations. We will begin going through the lemmas of arXiv:1709.05032 that are part of
this graph theoretic proof.
Coordinates: Monday, 12 March 2018, 4:15pm, Atlantic Building 3100A.
Title: Vectorial correlations and non-closure of the set of quantum
correlations
Speaker: Aaron Ostrander
Abstract: We will develop some lemmas about vectorial correlations.
Combining these with the lemmas we proved about graph correlation functions
last week, we will conclude the proof of non-closure of the set of correlations
by Dykema et. al.
Coordinates: Monday, 26 March 2018, 4:15pm, Atlantic Building 3100A.
Title: Quantum Cryptography from the Pretty Good Measurement
Speaker: Carl Miller
Abstract: The pretty good measurement is a formal way of choosing a strategy
to guess the value of a classical register given quantum side information. The
pretty good measurement is not always optimal, but can
be proven to be near-optimal in a precise sense. As a consequence, an adversary
who uses the pretty good measurement is almost as good as the strongest
possible adversary. In the talk, I will discuss how this simple construction
provides some short and elegant proofs of security in quantum cryptography.
Reference: arXiv:1707.06597.
Coordinates: Monday, 2 April 2018, 4:15pm, Atlantic Building 3100A.
Title: Schur-Weyl duality and its application to qubit purification
Speaker: Honghao Fu
Abstract: Schur-Weyl duality is one of the remarkable results in
representation theory, which connects the irreducible representations of the
symmetric group to the irreducible algebraic representation of the general
linear group of a complex vector space. It is also an important tool in the
study of quantum information. In this talk, I will give an overview of
Schur-Weyl duality which covers the background and some of the related topics.
Then I will give an example to show how it is applied in quantum Information.
The application is called qubit purification, which aims at producing one qubit
with high fidelity out of many copies of identical unknown depolarized qubits.
References:
Schur-Weyl Duality: http://math.uchicago.edu/~may/REU2016/REUPapers/Stevens.pdf.
Qubit Purification: https://arxiv.org/pdf/quant-ph/9812075.pdf.
Coordinates: Monday, 9 April 2018, 4:15pm, Atlantic Building 3100A.
Title: Schur-Weyl duality and its application to qubit purification (Part
II)
Speaker: Honghao Fu
Abstract: In the second part of this talk, I am going to focus on the
application of Schur-Weyl duality in the qubit purification problem. In the
setup of this problem, we are given N copies of a depolarized qubit. The goal
of this problem is to maximize the fidelity of the output state over all the
possible procedures. The optimal qubit purification is known
and it is designed based on the Schur decomposition of the state of the qubits.
We are going to see Schur-Weyl duality is applied to decompose this state and
how the structure of the irreducible representation of the unitary group makes
the optimal procedure simple.
References:
Schur-Weyl Duality: http://math.uchicago.edu/~may/REU2016/REUPapers/Stevens.pdf.
Qubit Purification: https://arxiv.org/pdf/quant-ph/9812075.pdf.
Coordinates: Monday, 16 April 2018, 4:15pm, Atlantic Building 3100A.
Title: The ZX-calculus: Quantum theory with spiders
Speaker: Spencer Breiner
Abstract: In this talk I will give a brief introduction to the
ZX-calculus, a formal system of diagrams and graphical manipulations which can
be used to give proofs about quantum processes. The first half of the talk will
connect the mathematical structures involved--monoidal categories,
Frobenius/Hopf algebras--with their physical interpretation in quantum theory.
In the remaining time I will demonstrate by example how these methods can help
to simplify and clarify quantum analyses.
Coordinates: Monday, 23 April 2018, 4:15pm, Atlantic Building 3100A.
Title: Point games and Coin Flipping protocols
Speaker: Aarthi Sundaram
Abstract: Kitaev's point game formalism was used by Mochon
(arXiv:0711.4114) to show the existence of a quantum weak coin flipping
protocol with arbitrarily small bias and is a fundamental result in quantum
cryptography. Though this result has been used as a black-box
in a number of other follow-up results, the novel techniques used in this proof
(especially Kitaev's point game formalism) are not well understood. It is
believed that a complete grasp of these techiniques could shed more light on
the role of entanglement in quantum protocols as well as find other
applications where point games can be used. One direction to find this
understanding may lie in finding a graphical calculus representation for point
games. As a first step in that direction, I will discuss our current grasp of
this formalism based on the work done by Aharanov et al. (arXiv:1402.7166) to
simplify and clarify some parts of Mochon's original proof.
Coordinates: Monday, 30 April 2018, 4:15pm, Atlantic Building 3100A.
Title: The two conjuctive fragments of linear logic
Speaker: Brad Lackey
Abstract: We present the two simple fragments of linear logic coming
from the additive conjunction and multiplicative conjunction (and their
associated units). Specifically we look at the syntax
of these related logics, and their algebraic and categorical semantics. Our
goal is to highlight the relationship between these systems and operational
quantum theories, quantum resource theories, and graphical languages for
quantum programming. This is ongoing joint work with Aarthi Sundaram.
Coordinates: Monday, 7 May 2018, 4:15pm, Atlantic Building 3100A.
Title: Quantum computation and 3-manifold invariants
Speaker: Gorjan Alagic
Abstract: Topological quantum computation (TQC) is an alternative model
of quantum computation, where computations are described via topological braids
rather than unitary circuits. As it turns out, there are other models which
also have this property, but where the underlying topological objects are
higher-dimensional analogues of braids. Understanding this model has led to
interesting results, such as quantum algorithms for approximating certain
3-manifold invariants and simulating so-called "topological quantum field
theories" in (2+1) dimensions. In this talk, I will give a brief introduction
to this area and a high-level overview of some of the main results.