The construction of a scalable quantum computer architecture based on multiple interacting quantum walkers could, in principle, be used as an architecture for building a scaled quantum computer with no need for time-dependent control.Expand

It is proved that the Clifford group is a 3-design, showing that it is a better approximation to Haar-random unitaries than previously expected and characterizing how well random Clifford elements approximateHaar- random unitaries.Expand

This work proves that approximating the ground energy of the Bose-Hubbard model on a graph at fixed particle number is QMA-complete, and obtains a related result for a class of 2-local Hamiltonians defined by graphs that generalizes the XY model.Expand

Quantum walk is a versatile and intuitive framework for developing quantum algorithms. Applications of quantum walk include an example of exponential speedup over classical computation [6] and… Expand

We prove that approximating the ground energy of the antiferromagnetic XY model on a simple graph at fixed magnetization (given as part of the instance specification) is QMA-complete. To show this,… Expand

Certain continuous-time quantum walks can be viewed as scattering processes. These processes can perform quantum computations, but it is challenging to design graphs with desired scattering behavior.… Expand

A quantum walk is a time-homogeneous quantum-mechanical pr ocess on a graph defined by analogy to classical random walk. The quantum walker is a p article that moves from a given vertex to adjacent… Expand

This thesis analyzes the many-particles system corresponding to a multi-particle quantum walk, showing that the time evolution of such systems on a polynomial sized graph is universal for quantum computation, and thus determining how a particular state evolves is as hard as an arbitrary quantum computation.Expand