The quantum circuit model is a standard framework for formulating quantum algorithms, which is developed in analogy with the classical logic circuit model. Over the years, the applications of this model have expanded far beyond quantum computing, now serving as a standard tool in theoretical physics for modeling the time evolution and phases of quantum systems governed by local Hamiltonians. In this talk, I will first present an overview of the fundamental concepts and principles underlying the quantum circuit model. Then, I will discuss recent developments on the theory of quantum circuits with gates respecting a global symmetry or, equivalently, a global conservation law. As an example, I will show that using a single ancilla qubit, any Hamming-weight-conserving unitary transformation can be realized with XY interaction, which is a Hamming-weight-conserving interaction. More generally, in the case of Abelian symmetries, I will show that any symmetry-respecting unitary can be realized with local symmetry-respecting unitaries and a single ancilla qudit. Finally, I will briefly discuss the applications of symmetry-respecting quantum circuits for suppressing noise in quantum computers.
Iman Marvian is an assistant professor in the departments of Physics and Electrical & Computer Engineering at Duke University. He received his Ph.D. in Physics in 2012 at the University of Waterloo and Perimeter Institute for Theoretical Physics in Waterloo, Canada. Before moving to Duke, he worked as a postdoctoral researcher at the University of Southern California and MIT. Marvian has a broad research interest in quantum information and computation theory. He has worked on topics, such as quantum circuits, quantum algorithms, quantum resource theories and quantum thermodynamics, entanglement, symmetry-protected topological order, and error correction/suppression.