## Introduction to Quantum Computing

Meet the machine from the future, exponentially more powerful than classical computers. Quantum computing and quantum information could potentially revolutionize IT and many branches of science. It has remained only an academic interest until the recent hardware breakthroughs and the surge in commercial interest. Startup companies such as D-wave and IonQ are popping up in the news. Google, IBM, Intel, Microsoft are all heavily investing on quantum computing hardware with their own approaches. But what are quantum computers? What can they do and where does its power come from? What are the prototype systems built so far in the laboratory? How far are we from a universal quantum computer? How to write a quantum code and run it? How can quantum mechanics help secure communications? And what on earth is quantum teleportation? We will seek to answer some of these questions in this course.

**Location:** Exploratory Hall 1004

**Time:** 1:30-2:45pm, Tuesday and Thursday

**Instructor:** Erhai Zhao

**Prerequisites:** Linear algebra (matrices, vector space), complex numbers, and University Physics (160 and 260). Previous exposure to quantum mechanics is a plus but not required. Physics, Electrical Engineering, Computer science and all other majors are welcome.

For Physics Majors (390): this course will count as an upper level elective credit.

For Graduate Students (590): you will be assigned harder homework problems and required to do a research project.

**Textbook:** *Quantum Computing: A Gentle Introduction*, E. Rieffel & W. Polak

**Topics (tentative):**

- Classical bits, Turing machine, problems hard to solve on classical computers
- The postulates of quantum mechanics; example of photon
- The quantum bit (qubit). States, superposition, ket and bra notation, bloch sphere
- Operations on qubits, measurements, eigenvalues and probability, example of spin
- Multiple qubits, entanglement, “spooky action at a distance”
- Quantum gates and quantum circuits, unitary evolution
- Physical realization: superconducting qubits, ion traps, quantum dots etc.
- Quantum Fourier transform, Shor’s algorithm for factoring large numbers
- Search a needle in the haystack: Grover’s algorithm
- Race to quantum supremacy with 75 qubits: Google, Microsoft, Intel and IBM’s bet
- The D-wave controversy: testing quantum annealing with 108 qubits
- Hands-on project: how to write a quantum code and run it on IBM Q
- Advanced topics: error correction, topological quantum computing
- Impact of quantum information on science and technology

** Grades (tentative):** Weekly homework (1/3), midterm exam (1/3), final exam(1/3)