## 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 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

**Lecture Topics:**

The full contents of the course (lecture notes, supplementary materials, homework solutions, practice exams) are available for registered students on Blackboard.

Sample lecture notes on quantum Fourier transform and period finding.

- Complexity of computing. Turing machine, easy vs hard problems on classical computers.
- Single qubit, experiments with photons, Dirac notation, quantum weirdness.
- Vector space of qubit states. Bloch sphere.
- Quantum gates for single qubit. Pauli & Hadamard gate. Unitary transformations, K, R, T and phase gate.
- Hermitian operators. Eigenvalues, probability, measurement.
- Summary: postulates of quantum mechanics.
- Two-qubit states. Tensor product. Bell states. Entanglement.
- Two-qubit transformations. Tensor operators. Controlled not. Swap. None-cloning.
- Measurement of two-bit systems. EPR pair. Bell theorem & inequality. “Spooky action at a distance” with Alice, Bob and Eve.
- Three and more qubits. GHZ. Toffloli gate. Quantum circuits. Reversible computing. Quantum functions/oracles.
- Application: Teleportation. Dense coding.
- Quantum parallelism, Walsh-Dadamard. Deutsch’s algorithm.
- More query problems: Deutsch-Josza, Simon.
- Quantum Fourier transform and its circuit realization.
- Integer factorization & period finding. Shor’s algorithm for factoring large numbers
- Search problem. Grover’s algorithm. Grover diffusion and amplitude amplification.
- Physical realization: superconducting qubits, ion traps etc.
- Race to quantum supremacy: Google, Microsoft, Intel, IBM, and start-ups.
- Getting to know IBM Q.
- Programming with Qiskit.
- Hands-on project: realizing your quantum algorithm and run it on a quantum computer.
- Advanced topics (that we do not have time to talk about)!

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