PHYS 112

Quantum mechanics is the basic "operating system" for the laws of physics. At the most fundamental level, it is a theory of information, controlling what it means to know something about the state of a physical system, and how its information content changes when the system is manipulated and measured.

The importance of quantum mechanics has been recognized in fields far outside of basic physics. In information technology, the application of quantum mechanics promises a revolution, with potential dividends including unbreakable cryptography, fast computation, and simulation of quantum systems that are intractable for classical computers, such as nuclei and molecules. Achieving this promise also presents enormous technical challenges. Over the last few decades, there has been steady progress towards quantum technology with real-world applications. Naturally, there have also been a lot of hype and more than a few spurious claims.

In Spring 2027, for the first time at Brandeis, we will have a course on quantum information and computation!

This course is aimed at a broad audience of undergraduate and graduate students from physics, chemistry, math, computer science, and engineering (and perhaps beyond). YOU DO NOT HAVE TO KNOW ANY QUANTUM MECHANICS -- OR EVEN ANY PHYSICS -- TO TAKE THIS COURSE! You will be taught all the physics (and information theory) you need. The prereqs are:

• a solid foundation in linear algebra (at the level of MATH 15a)

• some basic numerical programming ability (in the language or system of your choice: python, Mathematica, Matlab, etc.)

We will establish the basic elements of quantum information and computation, along with some of their potential real-world realizations and applications, and provide a foundation for more in-depth study. Topics covered will include:

• Classical information theory: Shannon theory, error correcting codes, cryptography

• Linear algebra review: complex vector spaces; bases; Hermitian, unitary, & isometric operators & matrices; rank & nullity; eigenvalues & eigenvectors; trace & determinant; orthogonal projectors; direct sum & product

• Fundamentals of quantum mechanics: states, measurements, entanglement, decoherence; qubits, photon polarization, Bloch sphere; channels

• Non-classicality of quantum mechanics; Bell's theorem

• Quantum information theory: von Neuman entropy, relative entropy; fundamental inequalities; Holevo information; superdense coding

• Teleportation

• Cryptography & key distribution

• Circuits & algorithms: Grover search; digital & analogue simulation; algorithmic complexity classes, quantum advantage. We will run actual circuits on IBM's quantum computer.

• Error correction; fault tolerant computation

• Hardware implementations: photonics, superconducting qubits, other platforms

The course will meet TuTh 3:55-5:15. (Depending on enrollment, there may also be recitation sections.)

Please see the syllabus below for more details, and contact me if you have any questions (mph@brandeis.edu).