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Universal Computation by Multiparticle Quantum Walk
TLDR
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.
The Clifford group forms a unitary 3-design
  • Z. Webb
  • Mathematics
    Quantum Inf. Comput.
  • 9 October 2015
TLDR
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.
The Bose-Hubbard Model is QMA-complete
TLDR
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.
Universal computation by multi-particle quantum walk arXiv
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
Complexity of the XY antiferromagnet at fixed magnetization
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,
The Bose-Hubbard Model is QMA-complete
TLDR
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.
Momentum switches
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.
A Case of Hyperbolic Billiards
37 82 v 2 [ qu an tph ] 15 F eb 2 01 3 Universal computation by multi-particle quantum walk
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
The computational power of many-body systems
  • Z. Webb
  • Physics, Computer Science
  • 28 September 2016
TLDR
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.