Current graduate students

CS/Math Seminar - Kunal Marwaha - University of Chicago

200 University Ave. Waterloo ON. QNC 1201 + ZOOM

We study a variant of QMA where quantum proofs have non-negative amplitudes in both completeness and soundness. This class was introduced by Jeronimo and Wu [STOC '23] to understand QMA(2). We show that this variant is very powerful even without considering multiple unentangled quantum provers. In fact, QMA+ with some constant gap is equal to NEXP, even though QMA+ with some other constant gap is equal to QMA.

The Clifford theory of the n-qubit Clifford group

Quantum-Nano Centre, 200 University Ave West, Room QNC 1201 Waterloo, ON CA N2L 3G1

The n-qubit Pauli group and its normalizer the n-qubit Clifford group have applications in quantum error correction and device characterization. Recent applications have made use of the representation theory of the Clifford group. We apply the tools of (the coincidentally named) Clifford theory to examine the representation theory of the Clifford group using the much simpler representation theory of the Pauli group. We find an unexpected correspondence between irreducible characters of the n-qubit Clifford group and those of the (n + 1)-qubit Clifford group. This talk will rely on the explanation of Clifford theory given last week.

IQC Seminar - Zahra Khanian, Technical University of Munich

200 University Ave W. Waterloo On Can QNC 1201

In the seminal 1948 paper "a mathematical theory of communication", Shannon introduced the concept of a classical source as a random variable and established its optimal compression rate, given by Shannon entropy. Nearly five decades later, Schumacher rigorously defined the notion of a quantum source and its compressibility. Schumacher's definition involved a quantum system and correlations with a purifying reference system. In our work, we build upon Schumacher's quantum source model, extending it to the most general form allowed by quantum mechanics. This extension involves considering the source and the reference in a mixed state, along with the presence of additional systems treated as side information. We address and solve various problems posed by these modifications, determining the optimal compression rates. While our work contributes significant progress in quantum source compression, we point out remaining open questions that require further exploration.

A quick introduction to Clifford theory

Quantum-Nano Centre, 200 University Ave West, Room QNC 1201 Waterloo, ON CA N2L 3G1

Clifford theory studies the connection between representations of a group and those of its normal subgroups. In recent work, I examined the Clifford theory of the Clifford group to determine parts of its character table for future applications. The goal of this talk is to introduce the representation theory and Clifford theory of finite groups sufficiently to understand next week's talk when I will explain the Clifford theory of the n-qubit Clifford group. Note that these are two distinct Cliffords. I may also briefly discuss the applications of Clifford theory in quantum error correction, time permitting.

Research Advancement Centre, 475 Wes Graham Way, Room RAC 2009, Waterloo, ON, CA N2L 6R2