Usually, a quantum algorithm uses products of unitaries to complete a task. Lack of technique and intuition in algorithm design has hindered the development of quantum algorithm.
A long-standing puzzle in quantum complexity theory is to understand the power of the class MIP* of multiprover interactive proofs with shared entanglement. This question is closely related to the study of entanglement through non-local games, which dates back to the pioneering work of Bell.
“Quantum physics” has taken its position with “rocket science” in pop culture as a shorthand for frighteningly complicated science. Quantum physics has also taken on a sort of magical connotation in fiction, with features like entanglement, superposition, and tunneling, spurring imagination. But where does the science draw the line? How much is joyful speculation, and how much is disregard for reality? And if it’s always seen as either magical or scary, how does that affect the perception of quantum science?
In 2011 Harry Buhrman, Serge Fehr, Christian Schaffner and Florian Speelman proposed a new measure of complexity for finite Boolean functions, called "The Garden-hose complexity". This measure can be viewed as a type of distributed space complexity where two players with private inputs compute a Boolean function co-operatively. While its motivation mainly came from the applications to position based quantum cryptography, the playful definition of the model is quite appealing in itself.
Recently, Silas Beane, David Kaplan, Natalie Klco and I considered the entanglement power of the S-‐matrix describing low-‐energy hadronic interactions, and the implications of particular limits. We found that vanishing entanglement power occurs at points of emergent global symmetries, which are seen to be consistent with nature and also recent lattice quantum chromodynamics (QCD) calculations. I will discuss aspects of these results.
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.
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.
In the area of quantum state learning, one is given a small number of "samples" of a quantum state, and the goal is use them to determine a feature of the state. Examples include learning the entire state ("quantum state tomography"), determining whether it equals a target state ("quantum state certification"), or estimating its von Neumann entropy. These are problems which are not only of theoretical interest, but are also commonly used in current-day implementation and verification of quantum technologies.
Significant global efforts are currently underway to build quantum computers. The two main goals for near-term quantum computers are finding and solving interesting problems in the presence of noise and developing techniques to mitigate errors. In this talk, I will outline and motivate an abstraction layer needed to reliably operate quantum computers under realistic noise models, namely, a cycle consisting of all the primitive gates applied to a quantum computer within a specified time period.
As a more general form of quantum superposition, quantum coherence represents one of the most fundamental features that set the difference of quantum mechanics from the classical realm. In this talk, we will use the tool of semidefinite programming to study two fundamental tasks relating quantum coherence, i.e., coherence distillation of quantum states and coherence cost of quantum processes.