Part 2 The polynomial method: Quantum query complexity | Yassine Hamoudi (U California Berkeley)

Lecture 2 notes The polynomial method https://www.ias.edu/sites/default/files/Hamoudi%20Lecture2.pdf Problem session 2 https://www.ias.edu/sites/default/files/Hamoudi%20Lecture2.pdf Quantum query complexity offers one of the most fruitful models of computation for the study of quantum algorithms. It has featured many significant quantum speedups, from the Bernstein-Vazirani algorithm to the recent Yamakawa-Zhandry supremacy breakthrough. The limits of quantum queries have been questioned since the early days of quantum computing. This led to the development of two fundamental lower bound techniques: the polynomial and the adversary methods. The focus of this course will be to introduce these methods and to present some of their new variants, such as the compressed oracle technique. We will also consider the role of duals in these methods and how they can lead to tight bounds or even new algorithms. #YassineHamoudi, #IASPCMI, #quantumcomputing, #linearalgebra, #quantumcomputer, #quantumcomputers, #quantum, #pcmi, #quantumcomputation, -- The 2023 Program: Quantum Computation Organizers: David Gosset, University of Waterloo; Aram Harrow, MIT; Stacey Jeffery, CWI and QuSoft; Ryan O'Donnell, Carnegie Mellon University; and Thomas Vidick, Caltech. Very recently we have seen experiments at the boundary of the "quantum computing advantage", where quantum computers can massively outperform classical ones at certain tasks. These advances highlight the need for further mathematical understanding of the computational power of near-term quantum devices. The goal of the 2023 GSS is to dive deeply into the mathematics relevant for building near-term quantum computers, analyzing their power, and putting them to use. Minicourses will include: overviews of quantum learning, information theory, and linear-algebraic algorithms; recent advances in quantum error-correcting codes; and, the complexity theory of random circuits and Hamiltonians. Structure: The Graduate Summer School at PCMI consists of a series of several interwoven minicourses on different aspects of the main research theme of that summer. These courses are taught by leading experts in the field, chosen not only for their stature in the field but their pedagogical abilities. Each minicourse comprises three to five lectures. Each course is accompanied by a daily problem session, structured to help students develop facility with the material. 2023 Schedule Week 1 Andras: Quantum Fourier transform beyond Shor's algorithm Omar: Quantum information theory Srinivasan: Overview of quantum learning theory Week 2 Ewin: Quantum and quantum-inspired linear algebra Nicolas: Quantum LDPC codes Yassine: Quantum query complexity Week 3 Bill: Computational complexity of near-term quantum experiments Jeongwan: Topological aspects of quantum codes Sandy: Quantum Hamiltonian complexity — The GSS takes place within the broader structure of PCMI, so there are many researchers at all levels in the field in attendance, as well as participants in the other PCMI programs. ias.edu/PCMI