Introduction to quantum computing from the perspective of quantum dynamics. The class is aimed at early graduate students in physics and chemistry, and assumes a familiarity with basic quantum mechanics. We start with an introduction to mixed states and to many-qubit Hilbert spaces. We then discuss how the evolution of any quantum system can be described in terms of elementary operations on qubits, and when it is that this evolution becomes hard to describe using a classical computer (i.e. when entanglement grows). Following this, we discuss the implications of randomness in the quantum measurement process for the power of quantum computers. The notes end with a discussion of quantum singular value transformations.Â
Lecturer: Sam Garratt
Lectures (+ recordings)
6/13 Introduction
6/17 Universal quantum computation
6/20 Entanglement growth (most states are highly entangled)
6/24 Measurements (most entangled states are useless)
6/27 Quantum algorithms (useful circuits)
References
General: Nielsen and Chuang,
Quantum computation and quantum information
Circuits from CNOT and single-qubit unitaries
Barenco et al. [Phys. Rev. A 52, 3457 (1995)]
Universal QC from Clifford circuits + magic
Bravyi, Kitaev [Phys. Rev. A 71, 022316 (2005)]