## Research Areas at VCU

At a high level, the Quantum Computing Lab at VCU focuses primarily on the following two areas of research in theoretical computer science.

### Computational Complexity Theory

Computational complexity theory
is an area of computer science which studies the resources required, such as computing time or memory, to complete a given task. A specific focus of our group is on the subarea of *Quantum Hamiltonian Complexity*, which can be viewed as the study of physically motivated quantum generalizations of the Boolean Satisfiability Problem. Such ``quantum satisfiability problems'' are appealing in that they encode properties of physical quantum systems when cooled to low temperatures. The setting of *low* temperature, in particular, is interesting, as it is the regime in which certain exotic phenomena, such as superconductivity and superfluidity, manifest themselves. Here is a video demonstration, for example, of helium-4 undergoing a phase transition into the superfluid phase as it is cooled to near absolute zero.

### Algorithms

Algorithms are the heart and soul of much of computer science; they are what make Google's search engine, GPS directions, and just about every piece of software on your computer possible. Our lab pursues two main lines of algorithmic research. The first is the study of *classical* algorithms, such as exact or approximation algorithms, for computational problems arising in the setting of quantum mechanics. A standard such problem is that of estimating ground state energies of many-body quantum systems, also known as the Local Hamiltonian Problem. The second is the study of *quantum* algorithms, wherein the goal is to exploit the counterintuitive properties of quantum mechanics (such as superposition and entanglement) on a quantum computer in order to design algorithms which outperform classical computers.

For more information on any of these topics, please feel free to drop by Dr. Gharibian's office (see People).