Approximate Degree in Classical and Quantum Computing by Mark Bun

Approximate Degree in Classical and Quantum Computing by Mark Bun

The ability (or inability) to represent or approximate Boolean functions by polynomials is a central concept in complexity theory, underlying interactive and probabilistically checkable proof systems, circuit lower bounds, quantum complexity theory, and more. In this book, the authors survey what is known about a particularly natural notion of approximation by polynomials, capturing pointwise approximation over. This book covers recent progress on proving approximate degree lower and upper bounds and describes some applications of the new bounds to oracle separations, quantum query and communication complexity, and circuit complexity. The authors explain how several of these advances have been unlocked by a particularly simple and elegant technique, called dual block composition, for constructing solutions to this dual linear program. They also provide concise coverage of even more recent lower bound techniques based on a new complexity measure called spectral sensitivity. Finally, they show how explicit constructions of approximating polynomials have been inspired by quantum query algorithms. This book provides a comprehensive review of the foundational and recent developments of an important topic in both classical and quantum computing. The reader has a considerable body of knowledge condensed in an accessible form to quickly understand the principles and further their own research.

SKU	Unavailable
ISBN 13	9781638281405
ISBN 10	1638281408
Title	Approximate Degree in Classical and Quantum Computing
Author	Mark Bun
Series	Foundations And Trends® In Theoretical Computer Science
Condition	Unavailable
Binding Type	Paperback
Publisher	now publishers Inc
Year published	2023-01-01
Number of pages	212
Cover note	Book picture is for illustrative purposes only, actual binding, cover or edition may vary.
Note	Unavailable