Fall 2017 Spring 2018 Fall 2018 Fall 2020
(See also: The IQC-QuICS
Math and Computer Science Seminar.)
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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. In previous semesters we examined
various applications of algebra, analysis, and geometry to quantum foundations,
quantum cryptography, quantum computing, and other topics in theoretical
physics. 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.)
The seminar is finished for the fall semester. Have
a great holiday break!
B. Coecke and A. Kissinger, Picturing Quantum Processes.
Cambridge University Press, 2017.
G.M. D'Ariano, G. Chiribella, and P. Perinotti, Quantum Theory from First Principles. Cambridge University Press, 2017.
J. Watrous, The Theory of Quantum Information.
Cambridge University Press, 2018. (Available online.)
Z. Brakerski, P. Christiano, U. Mahadev, U. Vazirani, T.
Vidick. "Certifiable
Randomness from a Single Quantum Device."
S. Bravyi, D. Gosset, R. Koenig. "Quantum advantage with
shallow circuits."
S. Breiner, A. Kalev, C. Miller. "Parallel Self-Testing of the GHZ State with a Proof by Diagrams."
Coladangelo, J. Stark. "Unconditional separation of finite and infinite-dimensional quantum correlations."
K. Goh, J. Kaniewski, E. Wolfe, T. Vertesi, X. Wu, Y. Cai, Y. Liang, V. Scarani. "Geometry of the set of quantum correlations."
M. Lupini, et al. "Perfect strategies for non-signalling games."
W. Slofstra. "The set of quantum correlations is not closed."
L.P. Thinh, A. Varvitsiotis, and Y. Cai, "Structure of the set of
quantum correlators via semidefinite programming."
Coordinates: Monday, 27 August 2018, 4:00-5:00pm,
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 fall
semester. Suggestions and contributions are welcome!
Coordinates: Monday, 10 September 2018,
4:00-5:00pm, Atlantic Building 3100A.
Title: Operational Quantum Theory.
Speaker: Brad Lackey.
Abstract: I will talk about the basics of operational
quantum theory, which presents quantum theory as a general probability theory
focussing on systems and transformations. The natural language for this
formalism is category theory. In this first lecture I will rapidly cover the
most basic features of categories, build the framework for describing
operational quantum theories, and discuss how these elements are represented in
traditional quantum information science.
Coordinates: Monday, 17 September 2018,
4:00-5:00pm, Atlantic Building 3100A.
Title: Operational Quantum Theory, cont'd.
Speaker: Brad Lackey.
Abstract: Building on our description of operational
quantum theories as categories we will discuss the physical concepts of
causality, locality, and purity in the language of symmetric monoidal
categories. Finally I will mention a set of additional axioms that singles out
traditional quantum mechanics as a generalized probability theory.
Coordinates: Monday, 1 October 2018,
4:00-5:00pm, Atlantic Building 3100A.
Title: A picture-proof of quantum self-testing.
Speaker: Carl Miller.
Abstract: While diagrams are commonly used as an aid in
proofs in quantum information, it is less common to see proofs themselves
represented as pictures. Yet, some formal arguments can be more simply
represented as pictures rather than equations. Graphical languages for quantum
information have been developed (e.g., in the book "Picturing Quantum
Processes" by B. Coecke and A. Kissinger) in which every picture-element
has a formal meaning. In our work we use formal visual arguments to prove a new
result on quantum self-testing: we show that N copies of the GHZ state can be
self-tested by three non-communicating parties. I will discuss this proof and
give an introduction to diagrammatic quantum information along the way.
Reference: S. Breiner, A. Kalev, C. Miller. "Parallel Self-Testing of
the GHZ State with a Proof by Diagrams."
Coordinates: Monday, 8 October 2018,
4:00-5:00pm, Atlantic Building 3100A.
Title: Qubitization.
Speaker: Yuan Su.
Abstract: A unitary matrix can be block-diagonalized
using the singular value decompostion of its submatrix. This property is
sometimes referred to as "qubitization", which has wide applications
in quantum computing. In this talk, I state and prove a particular version of
qubitization, where the submatrix of the unitary admits an eigendecomposition.
References:
[1] Guang Hao Low and Isaac L. Chuang, Hamiltonian simulation by
qubitization, arXiv:1610.06546.
[2] Andras Gilyen, Yuan Su, Guang Hao Low, and Nathan Wiebe,
Quantum singular value transformation and beyond: exponential improvements for
quantum matrix arithmetics, arXiv:1806.01838.
Coordinates: Monday, 15 October 2018,
4:00-5:00pm, Atlantic Building 3100A.
Title: Geometry of the set of quantum correlations.
Speaker: Xingyao Wu.
Abstract: The distinction between quantum correlation and
classical correlation is usually studied with Bell inequalities. However, if we
consider the geometry of quantum set in the probability space, Bell
inequalities do not tell too much about it. In this work, we study the geometry
of the set of quantum correlations arising from the convexity of the set
itself. We study the scenario of two inputs and two outputs for two parties and
derive nontrivial properties of the set in this case. We also show that even
more complex features appear in Bell scenarios with more inputs or more
parties. Finally, we discuss the limitations that the geometry of the quantum
set imposes on the task of self-testing.
Reference:
K. Goh, J. Kaniewki, E. Wolfe, T. Vertesi, X. Wu, Y. Cai, Y.-C.
Liang, V. Scarani. Physical Review A 97, 022104. (2018)
Coordinates: Monday, 22 October 2018,
4:00-5:00pm, Atlantic Building 3100A.
Title: Black-box random number generation with a single
quantum device.
Speaker: Carl Miller.
Abstract: Random number generation protocols have been
constructed that are strictly "device-independent" -- that is, they
make no assumptions about the accuracy of the devices used. Such protocols make
use of Bell violation experiments, and their security depends on physical
assumptions (such as timing or non-communication). I will discuss a major
breakthrough result that removes the need for the finer physical assumptions
behind device-independent randomness, and relies instead on a computational
hardness assumption. This result shows that, in principle, it is possible for a
classical user to generate randomness simply by remote interaction with an
untrusted client. The proof relies on the hardness of the Learning With Errors
problem (LWE), which is used in postquantum cryptography.
Reference: Z. Brakerski, P. Christiano, U. Mahadev, U. Vazirani,
T. Vidick. Certifiable Randomness from a Single Quantum Device. arXiv:1804.00640.
(2018)
Coordinates: Monday, 29 October 2018,
4:00-5:00pm, Atlantic Building 3100A.
Title: Quantum-inspired recommender system algorithm
Speaker: Daochen Wang.
Abstract: This summer, 18-year-old Ewin Tang published a
classical algorithm for recommendation systems that is "exponentially
faster" than existing classical algorithms. Her work was inspired by a
quantum algorithm for the same task which had been one of few quantum machine
learning algorithms that didn’t suffer from numerous caveats. I’ll talk about
the general structure of Tang’s algorithm and why it can be said to be
“inspired” by the quantum algorithm. If time allows, I’ll also give some proofs
of the main results that justify Tang’s algorithm.
References: arXiv:1603.08675, arXiv:1807.04271.
Coordinates: Monday, 5 November 2018,
4:00-5:00pm, Atlantic Building 3100A.
Title: Groups, convex geometry, and programming a quantum
annealer
Speaker: Brad Lackey.
Abstract: To program a quantum annealer for solving
constrained optimization problems, one must construct objective functions whose
minima encode the hard constraints imposed by the underlying problem. For such
"penalty models" we desire the additional property that the gap in
the objective value between states that meet and fail the constraints is
maximized amongst the allowable objective functions. We discuss why this is a
desirable property and mathematical methods to find optimal penalty models
using convex geometry and group theory. Our central example will be constraints
on the Hamming weight of bitstrings.
Reference: arXiv:1704.07290.
Coordinates: Monday, 12 November 2018,
4:00-5:00pm, Atlantic Building 3100A.
Title: A Quick Introduction to Quantum Copy Protection
and Money
Speaker: Diane Tchuindjo.
Abstract: The question of whether there can be unclonable
quantum money that anyone can verify is one that has remained open for the last
40 years. Moving away from money, one can ask a more generalized question: can
quantum states be used as copy-protected programs, that is, one that lets the
user evaluate a function f but not create more programs for f? This talk will
aim to formally define quantum money and copy-protection schemes, investigate
their basic properties, and provide preliminaries from cryptography and quantum
information. The goal of the talk is to provide a framework that can be used to
study specific schemes.
Coordinates: Monday, 19 November 2018,
4:00-5:00pm, Atlantic Building 3100A.
Title: Quantum secret sharing using GHZ states
Speaker: Sixian Liu.
Abstract: If n researchers participate in a nuclear bomb
project, they share the classified information. However, they think there is a
spy in the group, so they decide that the nuclear bomb can be accessed only by
working collaboratively with any k of them (i.e., (k-1) people cannot access
the bomb). How can this be achieved? I will talk about how GHZ states can be
used to share the quantum secret between two parties, so that they need to work
together to reconstruct the original information, and how to prevent an
eavesdropper. At the end, we will see how this technique can be generalized to
higher dimensions. The talk is mainly based on the paper Hillery, M., Buzek,
V., Berthiaume, A.: Quantum secret sharing. Phys. Rev. A 59(3), 1829-1834
(1999).
Coordinates: Monday, 26 November 2018,
4:00-5:00pm, Atlantic Building 3100A.
Title: Characterizing the set of quantum correlations by
semidefinite programming tools
Speaker: Honghao Fu.
Abstract: The study of quantum correlations started with
John Bell's discovery of nonlocality and has led to real-world applications in
cryptography, randomness certification and other fields. However, the structure
of the set of quantum correlations is not well understood. Even to determine if
a given correlation is quantum can be difficult in general. In this talk, I am
going to introduce tools from semidefinite programming which can be used to
determine if a given correlation is in the quantum set or an extreme point of
the quantum set. Related basic concepts of semidefinite programming and quantum
correlation will also be covered.
Coordinates: Monday, 3 December 2018,
4:00-5:00pm, Atlantic Building 3100A.
Title: Some homological tools for the quantum mechanic
Speaker: Thomas Mainiero (Rutgers).
Abstract: That guy who retired at 25 to practice reading
auras of upside-down cerebral crystal nudists might have accidentally said
something relevant to physics: space can emerge from entanglement. Indeed, the
vague idea that non-trivial topologies/geometries might be related to entangled
states is not new. Cohomology is a great way to detect global/topologically
non-trivial quantities. We'll introduce chain complexes associated to
multipartite states, and describe how the cohomology of such complexes output
obstructions to factorizability of the state in the form of operators that
exhibit non-local correlations. We'll also outline how the Euler
characteristics of these complexes are related to mutual information. Such
homological techniques are computationally accessible probes of a
non-commutative space associated to a multipartite state; other geometric
probes might provide further measures of entanglement.