Fall 2017 Spring 2018 Fall 2018 **Fall 2020**

In this seminar, we are interested in all aspects of
research at the intersection between quantum information science and
mathematics. Goals for talks include:

· Studying recent research results in quantum information from a
mathematical angle;

· Finding examples (old and new) in which existing tools from
mathematics can be adapted for application in quantum information;

· Studying quantum algorithms for mathematical problems.

This seminar is associated with QuICS and the UMD math department. Participation from other departments is
encouraged. Graduate students can sign
up for the seminar for credit (as MATH 689).

All meetings are online. Our weekly time slot is Monday, 2:00-3:00pm.

**Time**: Monday, August 31st, 2020, 2:00-3:00pm.

**Title**: Organizational meeting.

**Speaker**: Carl Miller

**Abstract**: We will discuss logistics and possible research
themes for the coming semester.

**Link:** https://umd.zoom.us/j/93284680492?pwd=RHEvWGtoSk03T2FLblh0bkFldHNYQT09

**Time**: Monday, September 14th, 2020,
2:00-3:00pm.

**Title**: Pictorial Proofs Using ZX-Calculus

**Speaker**: Yusuf Alnawakhtha

**Abstract**: In this talk, we will
briefly explore the use of monoidal categories in quantum information. Namely
we will introduce the ZX-Calculus which is a diagrammatic formalism that
strives to enhance intuition by providing pictorial proofs and we will provide examples
of how some proofs can be simplified using this framework. Later in the talk,
we will go over a recent application of ZX-Calculus in fault tolerant quantum
computing and how it was used to provide the intuition for this result.

**Link:** https://umd.zoom.us/j/93284680492?pwd=RHEvWGtoSk03T2FLblh0bkFldHNYQT09

**References**:

[1] Coecke, Bob. "Quantum picturalism."
Contemporary physics 51.1 (2010): 59-83.

[2] de Beaudrap,
Niel, Xiaoning Bian, and Quanlong Wang.
"Fast and effective techniques for T-count reduction via spider nest
identities." arXiv preprint arXiv:2004.05164
(2020).

**Time**: Monday, September 21st, 2020,
2:00-3:00pm.

**Title: **Quantum randomness and the geometry of the Schatten matrix norm

**Speaker**: Carl Miller

**Abstract:** One of the most successful
recent applications of quantum information has been the generation of
"certified" random numbers.
The unique properties of quantum devices allow the generation of numbers
that are provably random, offering a potential major benefit to cryptography
and other fields. Constructing the right
theory to prove quantum randomness can be challenging. Quantum devices and adversaries are modeled
by complex vector spaces whose dimensions may be arbitrarily large,
and proving security in such a setting leads to some difficult mathematical
problems. This talk will be a
retrospective look at one successful approach to quantum randomness that is
based on the convexity of the Schatten matrix norm.

**Link:** https://umd.zoom.us/j/93284680492?pwd=RHEvWGtoSk03T2FLblh0bkFldHNYQT09

**Time**: Monday, October 5th, 2020, 2:00-3:00pm.

**Title:** Symmetries, graph properties, and quantum speedups

**Speaker**: Daochen Wang

**Abstract:** Aaronson and Ambainis (2009)
and Chailloux (2018) showed that fully symmetric (partial) functions do not
admit exponential quantum query speedups. This raises a natural question: how
symmetric must a function be before it cannot exhibit a large quantum speedup?

In this work, we prove that hypergraph symmetries in the adjacency matrix model
allow at most a polynomial separation between randomized and quantum query
complexities. We also show that, remarkably, permutation groups constructed out
of these symmetries are essentially the only permutation groups that prevent
super-polynomial quantum speedups. We prove this by fully characterizing the
primitive permutation groups that allow super-polynomial quantum speedups.

In contrast, in the adjacency list model for bounded-degree graphs (where graph
symmetry is manifested differently), we exhibit a property testing problem that
shows an exponential quantum speedup. These results resolve open questions
posed by Ambainis, Childs, and Liu (2010) and Montanaro and de Wolf (2013)

**Link:** https://umd.zoom.us/j/93284680492?pwd=RHEvWGtoSk03T2FLblh0bkFldHNYQT09

**Reference:** Ben-David, S., Childs, A. M., Gilyén,
A., Kretschmer, W., Podder, S., & Wang, D. (2020). Symmetries, graph
properties, and quantum speedups. arXiv preprint arXiv:2006.12760.

**Time:** Monday, October 19th, 2020, 2:00-3:00pm.

**Title:** Quantum Query Complexity of Symmetric Oracle Problems

**Speaker:** Shih-Han Hung

**Abstract:** In this talk, I will present quantum query complexity of
symmetric oracle problems. In particular, we will be exploring the query
complexity of quantum learning problems in which the oracles form a group G of
unitary matrices, and a description of the optimal success probability of a
t-query quantum algorithm in terms of group characters. More generally, in the
coset identification problem, for a subgroup H of group G, the task is to
determine which coset the group element belongs to. The authors provide
character-theoretic formulas for the optimal success probability achieved by a
t-query algorithm for this problem. It generalizes a number of well-known
quantum algorithms including the Bernstein-Vazirani problem, the van Dam
problem and finite field polynomial interpolation.

**Link:** https://umd.zoom.us/j/93284680492?pwd=RHEvWGtoSk03T2FLblh0bkFldHNYQT09

**References:**

[1] Daniel Copeland, James Pommersheim, Quantum query complexity of symmetric
oracle problems, https://arxiv.org/abs/1812.09428.

[2] Orest Bucicovschi, Daniel Copeland, David A. Meyer, and James Pommersheim.
Single-query quantum algorithms for symmetric problems, https://arxiv.org/abs/1503.05548.

**Time:** Monday, November 9th, 2020, 2:00-3:00pm.

**Title:** Computations with Greater Quantum Depth Are Strictly More
Powerful (Relative to an Oracle).

**Speaker:** Matthew Coudron

**Abstract:** A conjecture of Jozsa (arXiv:quant-ph/0508124)
states that any polynomial-time quantum computation can be simulated by
polylogarithmic-depth quantum computation interleaved with polynomial-depth
classical computation. Separately, Aaronson conjectured that there exists an
oracle O such that BQP^O ≠ (BPP^(BQNC))^O. These conjectures are intriguing
allusions to the unresolved potential of combining classical and low-depth
quantum computation. In this work we show that the Welded Tree Problem, which
is an oracle problem that can be solved in quantum polynomial time as shown by
Childs et al. (arXiv:quant-ph/0209131),
cannot be solved in BPP^(BQNC), nor can it be solved in the class that Jozsa
describes. This proves Aaronson's oracle separation conjecture and provides a
counterpoint to Jozsa's conjecture relative to the Welded Tree oracle problem.
More precisely, we define two complexity classes, HQC and JC whose languages
are decided by two different families of interleaved quantum-classical
circuits. HQC contains BPP^(BQNC) and is therefore relevant to Aaronson's conjecture,
while JC captures the model of computation that Jozsa considers. We show that
the Welded Tree Problem gives an oracle separation between either of {JC, HQC}
and BQP. Therefore, even when interleaved with arbitrary polynomial-time
classical computation, greater "quantum depth" leads to strictly
greater computational ability in this relativized setting.

**Link:** https://umd.zoom.us/j/93284680492?pwd=RHEvWGtoSk03T2FLblh0bkFldHNYQT09

**Time:** Monday, December 7th, 2020,
2:00-3:00pm.

**Title:** Bounding the Accuracy of Distributed Quantum Sensing

**Speaker:** Jessica Thompson

**Abstract:** A potential application of quantum information is to
distributed sensing. The goal of a sensing problem can be described as
calculating a specific value by measuring signals with a collection of sensors.
With a classical signal, the accuracy in which the quantity can be determined
is inversely bounded by the square root of the number of sensors; this bound is
called the standard quantum limit. However, the use of quantum resources, such
as entanglement and squeezed light, allows one to surpass this limit. For
specific protocols, the accuracy is bounded by the quantum Cramér-Rao
bound, which relies on the quantum Fisher Information of the system. In this
talk, we will discuss the various quantum protocols for distributed quantum
sensing and the calculation of this bound, in regards to
their accuracy.

**Link:** https://umd.zoom.us/j/93284680492?pwd=RHEvWGtoSk03T2FLblh0bkFldHNYQT09

**References:**

[1] Zhuang,
Quntao, Zheshen Zhang, and
Jeffrey H. Shapiro. "Distributed quantum sensing using continuous-variable
multipartite entanglement." Physical Review A 97.3 (2018): 032329.

[2] Liu, Jing, et al. "Quantum
Fisher information matrix and multiparameter estimation." Journal of
Physics A: Mathematical and Theoretical 53.2 (2019): 023001.

J. Watrous. *The Theory of Quantum Information.
* Cambridge University Press, 2018.

S. Wehner, D. Elkouss,
R. Hanson. *Quantum
internet: A vision for the road ahead. * Science 362, Issue 6412 (2018).

National Academies of Sciences, Engineering, and
Medicine. *Quantum Computing: Progress
and Prospects.* The National
Academies Press, 2019. (Available
here – online version is free.)