Current undergraduate students

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.

CS Math Seminar - Kewen Wu, UC Berkeley (ZOOM + in person)

200 University Ave W. Waterloo On. N2G 4K3 QNC 1201

Motivated by limitations on the depth of near-term quantum devices, we study the depth-computation trade-off in the query model, where the depth corresponds to the number of adaptive query rounds and the computation per layer corresponds to the number of parallel queries per round. We achieve the strongest known separation between quantum algorithms with r versus r−1 rounds of adaptivity. We do so by using the k-fold Forrelation problem introduced by Aaronson and Ambainis (SICOMP'18). For k=2r, this problem can be solved using an r round quantum algorithm with only one query per round, yet we show that any r−1 round quantum algorithm needs an exponential (in the number of qubits) number of parallel queries per round.

Our results are proven following the Fourier analytic machinery developed in recent works on quantum-classical separations. The key new component in our result are bounds on the Fourier weights of quantum query algorithms with bounded number of rounds of adaptivity. These may be of independent interest as they distinguish the polynomials that arise from such algorithms from arbitrary bounded polynomials of the same degree.

Joint work with Uma Girish, Makrand Sinha, Avishay Tal

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

Unruh phenomena and thermalization for qudit detectors

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

The Unruh effect is the flat space analogue to Hawking radiation, describing how an observer in flat spacetime perceives the quantum vacuum state to be in a thermal state when moving along a constantly accelerated trajectory. This effect is often described operationally using the qubit-based Unruh-DeWitt detector.

We study Unruh phenomena for more general qudit detectors coupled to a quantized scalar field, noting the limitations to the utility of the detailed balance condition as an indicator for Unruh thermality of higher-dimensional qudit detector models. We illustrate these limitations using two types of qutrit detector models based on the spin-1 representations of SU(2) and the non-Hermitian generalization of the Pauli observables (the Heisenberg-Weyl operators).

[2309.04598] Unruh phenomena and thermalization for qudit detectors (arxiv.org)

Tight bounds for Pauli channel learning with and without entanglement

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

Quantum entanglement is a crucial resource for learning properties from nature, but a precise characterization of its advantage can be challenging. In this work, we consider learning algorithms without entanglement as those that only utilize separable states, measurements, and operations between the main system of interest and an ancillary system. Interestingly, these algorithms are equivalent to those that apply quantum circuits on the main system interleaved with mid-circuit measurements and classical feedforward. Within this setting, we prove a tight lower bound for Pauli channel learning without entanglement that closes the gap between the best-known upper bound. In particular, we show that Θ(n^2/ε^2) rounds of measurements are required to estimate each eigenvalue of an n-qubit Pauli channel to ε error with high probability when learning without entanglement. In contrast, a learning algorithm with entanglement only needs Θ(1/ε^2) copies of the Pauli channel. Our results strengthen the foundation for an entanglement-enabled advantage for Pauli noise characterization. We will talk about ongoing experimental progress in this direction.

Reference: Mainly based on [arXiv: 2309.13461]

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

Two randomly selected audience members will get the opportunity to present their work on the whiteboard for 20-minutes each.