The Quantum Information and Computing Seminar at the University of Delaware meets on Wednesdays at 11am. Unless specified otherwise, the meetings are held in person in Ewing 336. In Spring 2024, the seminar meets at 11:30am on Mondays.
May 6th, 2024
Jurij Volcic, Drexel University
Title: Self-testing: from quantum information theory to operator algebras
Abstract: Self-testing is the strongest form of quantum functionality verification, which allows one to deduce the quantum state and measurements of an entangled system from its classically observed statistics. From a mathematical perspective (which will be the perspective of this talk), self-testing is an intriguing uniqueness phenomenon, pertaining to functional analysis, moment problems, convexity and representation theory. This talk addresses basic motivation and ideas behind self-testing, and discusses which states and measurements can be self-tested. In particular, the talk focuses on how tuples of projections adding to a scalar multiple of identity, and Jordan algebras find its way into this corner of quantum information theory. Based on joint work with Ranyiliu Chen and Laura Mančinska.
February 12th, 2024
Walter van Suijlekom, Radboud University Nijmegen
Title: Geometric spaces at finite resolution
Abstract: After a gentle introduction to the spectral approach to geometry, we extend the framework in order to deal with two types of approximation of metric spaces. On the one hand, we consider spectral truncations of geometric spaces, while on the other hand, we consider metric spaces up to finite resolution. In our approach, the traditional role played by operator algebras is taken over by so-called operator systems. Essentially, this is the minimal structure required on a space of operators to be able to speak of positive elements, states, pure states, etc.
We illustrate our methods in concrete examples obtained by spectral truncations of the circle and of metric spaces up to finite resolution. The former yield operator systems of finite-dimensional Toeplitz matrices, and the latter give suitable subspaces of the compact operators. We also analyze the cones of positive elements and the pure-state spaces for these operator systems, which turn out to possess a very rich structure.
November 27th, 2023
Hamza Fawzi, University of Cambridge
Title: Entropy constraints for ground state optimization
Abstract: We study the use of von Neumann entropy constraints for obtaining lower bounds on the ground energy of quantum many-body systems. Known methods for obtaining certificates on the ground energy typically use consistency of local observables and are expressed as semidefinite programming relaxations. The local marginals defined by such a relaxation do not necessarily satisfy entropy inequalities that follow from the existence of a global state. Here, we propose to add such entropy constraints that lead to tighter convex relaxations for the ground energy problem. We give analytical and numerical results illustrating the advantages of such entropy constraints and study the limitations of the entropy constraints we construct. Joint work with Omar Fawzi and Samuel Scalet (arXiv:2305.06855).
November 13th, 2023
Meenakshi McNamara, Purdue University
Title: The quantum b-fold chromatic number and quantum graph products
Abstract: Quantum chromatic numbers are defined on classical graphs using non-local games. These may be extended to be invariants of quantum graphs using quantum-to-classical games. As generalizations of classical graphs using operator algebras, quantum graphs appear in connection to quantum information theory. We define several types of products of quantum graphs, and bound the resulting quantum chromatic numbers of the product graphs. Additionally, in studying the lexicographic product of quantum graphs we define a quantum version of the b-fold chromatic number in order to obtain quantum bounds analogous to the classical case. In a similar manner to the classical case, the quantum b-fold chromatic number is interesting in its own right and through its connection to an associated definition of a quantum fractional chromatic number that we define as well. We will end this talk by discussing properties of these newly defined variations on quantum coloring. This is joint work with Rolando de Santiago and Priyanga Ganesan.
October 30th, 2023
Yuan Chieh-Chen, University of Delaware
Title: The Opportunities and Challenges of Solving Differential Equations in Quantum Computing: An Invitation, Some results and Perspectives
Abstract: Quantum computing has brought several algorithms with quantum advantages. Thanks to HHL algorithms for solving linear equations, it's natural to extend the classical discretization algorithms for solving differential equations in quantum computers. However, those algorithms generally require a higher number of qubits, which is not feasible now. In this talk, we will first introduce some basic concepts and knowledge about quantum computing. Then, we will first compare different methods for solving differential equations in quantum computing. Next, we will focus on the method using variational quantum circuits. Finally, we will discuss how to use the Koopman theory in dynamical systems to speed up the optimization part in the classical part of the variational quantum algorithms. Furthermore, we will explore the perspectives of learning the entire dynamics or operator learning using Koopman operator theory.
October 23rd, 2023
Elizabeth Werner, Case Western Reserve University
Title: On the geometry of projective tensor products
Abstract: We study the volume ratio of the projective tensor products l_p^n\otimes_{\pi} l_q^n \otimes_{\pi} l_r^n, 1\leq p <\leq q \leq r \leq \infty. We obtain asymptotic formulas that are sharp in almost all cases. From the Bourgain-Milman bound on the volume ratio of Banach spaces in terms of their cotype 2 constant, we obtain information on the cotype of these 3-fold projective tensor products. Our results naturally generalize to k-fold products. Based on joint work with O. Giladi, J. Prochno, C. Sch ̈utt and N. Tomczak-Jaegermann.
May 2nd, 2023
Milan Mosonyi, Quantum Information National Laboratory, Hungary
(Seminar cancelled due to illness)
February 9th, 2023
Daniel Spiegel, University of Colorado at Boulder
Title: Topological Results on Pure State Space Inspired by Parametrized Quantum Phases
Abstract: The study of parametrized many-body gapped Hamiltonians and their topological phases represents a fast-growing frontier at the intersection of mathematical physics and condensed matter physics. In the limit of infinite system size, observable quantities are represented by elements of a uniformly hyperfinite C*-algebra A and the object of study is a continuous function into the space P(A) of pure states of A. With a continuous family of pure states, questions arise of how to do classical C*-algebraic maneuvers like the GNS construction and Kadison transitivity theorem in a way that depends continuously on the input data. I will present new theorems pertaining to both the norm and weak* topologies on P(A) to address these questions and others that have arisen in the study of parametrized many-body quantum systems.
November 16th, 2022
Karol Zyczkowski, Jagiellonian Univesity
Title: Thirty-six entangled officers of Euler: quantum solution of a classically impossible problem
Abstract: A quantum combinatorial designs is composed of quantum states, arranged with a certain symmetry and balance. They determine distinguished quantum measurements and can be applied for quantum information processing. Negative solution to the famous problem of $36$ officers of Euler implies that there are no two orthogonal Latin squares of order six. We show that the problem has a solution, provided the officers are entangled, and construct orthogonal quantum Latin squares of this size. The solution can be visualized on a chessboard of size six, which shows that 36 officers are splitted in nine groups, each containing of four entangled states. It allows us to construct a pure nonadditive quhex quantum error detection code.
November 9th, 2022
Roy Araiza, University of Urbana
Title: An index for inclusions of operator systems
November 2nd, 2022
Douglas Farenick, University of Regina
Title: Toeplitz Separability, Entanglement, and Complete Positivity via Operator System Duality
Abstract: A recent duality theorem of Connes and van Suijllekom, when formulated for the operator system category, casts light on some phenomena related to finite Toeplitz matrices, including the structure of linear isometries, automatic complete positivity, and the separability of positive block Toeplitz matrices. The key lies in the duality theorem, which I shall explain in this lecture, and on the theoery of extremal completely positive linear maps on unital C$^*$-algebras with values in the type I factor $B(H)$.
This lecture is based on collaborative work with Michelle McBurney.
October 12th, 2022
Title: Extension of Positive Maps and (real) entanglement theory
Abstract: Arveson's extension theorem guarantees that every completely positive map defined on an operator system can be extended to a completely positive map defined on the whole C*-algebra containing it. An analogous statement where complete positivity is replaced by positivity is known to be false. A natural question is whether extendibility could still hold for positive maps satisfying stronger conditions, such as being unital and norm 1. In this talk I will present various counterexamples showing that positive norm-one unital maps defined on an operator subsystem of a matrix algebra cannot be extended to a positive map on the full matrix algebra. Since positive maps are used to detect entanglement in quantum information theory, I will discuss a connection between extendibility of positive maps and entanglement theory. In particular, we discuss how the concept of entanglement in quantum mechanics defined on real Hilbert spaces is drastically different from the one defined on complex Hilbert spaces.
This is a joint work with Giulio Chiribella, Ken Davidson and Vern Paulsen.
October 5th, 2022
Alexandru Chirvasitu, University of Buffalo
Title: Universal constructions in categories of quantum actions
Abstract: A continuous action $\pi:\mathbb{G}\times\mathbb{X}\to\mathbb{X}$ of a topological group on a topological space has a universal compactification, i.e. the category of equivariant morphisms from $\mathbb{X}$ into compact Hausdorff $\mathbb{G}$-spaces has an initial object.
The analogous result holds in the non-commutative setting, whereby one substitutes a $C^*$-algebra $A$ for $\mathbb{X}$, a locally compact {\it quantum} group for $\mathbb{G}$ (a kind of operator-algebraic multiplier Hopf algebra $C_0(\mathbb{G})$), and a coaction
\[
\rho:A\to M(C_0(\mathbb{G})\otimes A)
\]
for $\pi$ (where $M(-)$ denotes the multiplier algebra construction). I will unpack enough of the language to make sense of this statement, and discuss related category-theoretic results on categories of quantum compactifications.
April 26th, 2022
Marianna Safronova, University of Delaware
Title: What would you do with a 1000 qubits?
December 8th, 2021
Henry Yuen, Columbia University
Title: TBA
Abstract: TBA
November 17th, 2021
Milan Mosonyi, Budapest University of Technology and Economics
Title: Rényi divergences in quantum information theory III
Abstract: TBA
November 10rd, 2021
Milan Mosonyi, Budapest University of Technology and Economics
Title: Rényi divergences in quantum information theory II
Abstract: TBA
November 3rd, 2021
Milan Mosonyi, Budapest University of Technology and Economics
Title: Rényi divergences in quantum information theory I
Abstract: We discuss various quantum Rényi divergences (minimal, maximal, (\alpha,z)) and their role in binary quantum state discrimination.
October 6th, 2021 (the talk is in person, in Ewing 336)
Travis Russell, US Military Academy
Title: An operator system approach to quantum correlations
Abstract: In this talk, I will explain a novel approach to Tsirelson's problem using the theory of operator systems. Tsirelson's problem relates to whether the commuting operator model of quantum mechanics produces different statistics than the tensor product model of quantum mechanics in non-local measurement scenarios. These questions have been shown to be equivalent to Connes' embedding problem from the theory of von Neumann algebras. After tremendous effort by physicists, mathematicians, and computer scientists, Tsirelson's problem was finally resolved in a recent paper. Nevertheless, interest in understanding Tsirelson's problem in greater detail remains. After exploring some background in the theory of operator systems, I will explain how to characterize quantum correlations using only abstract operator system theory, building upon existing C*-algebraic and operator theoretic characterizations in the literature. This new characterization yields an equivalent restatement of Tsirelson's problem in the language of abstract operator systems.
September 25th, 2021
Ruslan Shaydulin, Argonne National Laboratory.
Title: Towards Practical Advantage in Quantum Optimization
Abstract: Hybrid quantum-classical algorithms such as the quantum approximate optimization algorithm (QAOA) are attracting a lot of attention as one of the most promising approaches for leveraging near-term quantum computers for practical applications. These algorithms combine a parameterized quantum evolution with a classical routine that produces high-quality parameters. Such approaches have a number of challenges associated with them, as the near-term hardware is limited by its error rates, connectivity and small number of available qubits. In this talk I will discuss a number of recent results that attempt to address these challenges. I will present a formal connection between the symmetry group of the objective function and the symmetries of the QAOA ansatz, and show how this connection can be leveraged to reduce the cost of finding QAOA parameters purely classically, predicting QAOA performance and to mitigate the errors of near-term hardware.