Faculty

A polar decomposition for quantum channels: insightful tools to navigate through noisy quantum circuits

Arnaud Carignan-Dugas, Institute for Quantum Computing

Inevitably, assessing the overall performance of a quantum computer must rely on characterizing some of its elementary constituents and, from this information, formulate a broader statement concerning more complex constructions thereof.

Journal club presentation:

"Experimental superposition of orders of quantum gates" by Procopio et. al.

(Nature Comms 6, 7913 (2015)

Arash Ahmadi, Institute for Quantum Computing

Quantum computers achieve a speed-up by placing quantum bits (qubits) in superpositions of different states. However, it has recently been appreciated that quantum mechanics also allows one to ‘superimpose different operations’.

Chinmay Nirkhe, University of California, Berkeley

We study approximate quantum low-density parity-check (QLDPC) codes, which are approximate quantum error-correcting codes specified as the ground space of a frustration-free local Hamiltonian, whose terms do not necessarily commute. Such codes generalize stabilizer QLDPC codes, which are exact quantum error-correcting codes with sparse, low-weight stabilizer generators (i.e. each stabilizergenerator acts on a few qubits, and each qubit participates in a few stabilizer generators).

Three Results in Quantum Physics

Master's Candidate: Jaron Huq

Nicole Yunger Halpern, Harvard University Department of Physics

Thermodynamics has shed light on engines, efficiency, and time’s arrow since the Industrial Revolution. But the steam engines that powered the Industrial Revolution were large and classical. Much of today’s technology and experiments are small-scale, quantum, and out-of-equilibrium. Nineteenth-century thermodynamics requires updating for the 21st century. Guidance has come from the mathematical toolkit of quantum information theory.

Adina Luican-Mayer, University of Ottawa

Innovative technologies have a history of capitalizing on the discovery of new physical phenomena, often at the confluence of advances in material characterization techniques and innovations in design and controlled synthesis of high-quality materials. Pioneered by the discovery of graphene, atomically thin materials (2D materials) hold the promise for realizing physical systems with distinct properties, previously inaccessible.

Tobias Fritz, Perimeter Institute

Similar to how commutative algebra studies rings and their ideals, the protagonists of real algebra are ordered rings. Their interplay between algebra and geometry is studied in terms of Positivstellen- stze, real analogs of the Nullstellensatz, which go back to Artin's solution of Hilbert's 17th problem. I will describe some of the state of the art in this eld, and then introduce a new Positivstellensatz which unies and generalizes several of the existing ones.