Bose-Hubbard model for universal quantum walk-based computation

@article{Underwood2012BoseHubbardMF,
  title={Bose-Hubbard model for universal quantum walk-based computation},
  author={Michael S. Underwood and David L. Feder},
  journal={Physical Review A},
  year={2012},
  volume={85}
}
We present a novel scheme for universal quantum computation based on spinless interacting bosonic quantum walkers on a piecewise-constant graph, described by the two-dimensional Bose-Hubbard model. Arbitrary X and Z rotations are constructed, as well as an entangling two-qubit CPHASE gate and a SWAP gate. Quantum information is encoded in the positions of the walkers on the graph, as in previous quantum walk-based proposals for universal quantum computation, though in contrast to prior schemes… 

Figures from this paper

The Hubbard Model for Universal Quantum Computation
TLDR
It is shown that universal quantum computation can be implemented using interacting spinless (spin-polarized) fermions and a scheme for achieving universal quantum computing with the Hubbard model is proposed, which may be realized in the laboratory based on current experimental techniques.
Electric circuits for universal quantum gates and quantum Fourier transformation
  • M. Ezawa
  • Physics
    Physical Review Research
  • 2020
Universal quantum computation may be realized based on quantum walk, by formulating it as a scattering problem on a graph. In this paper, we simulate quantum gates through electric circuits,
Strongly correlated quantum walks with a 12-qubit superconducting processor
TLDR
The demonstration of quantum walks on a quantum processor, using superconducting qubits as artificial atoms and tomographic readout, paves the way to quantum simulation of many-body phenomena and universal quantum computation.
A Rout to Protect Quantum Gates constructed via quantum walks from Noises
TLDR
The decoherence effect is investigated and it is found that the coherence time can be enhanced by either increasing the number of sites on the graph or the ratio of the potential to the hopping strength, which is expected to motivate the design of the quantum gate with long coherenceTime.
Quantum computational supremacy in the sampling of bosonic random walkers on a one-dimensional lattice
We study the sampling complexity of a probability distribution associated with an ensemble ofidentical noninteracting bosons undergoing a quantum random walk on a one-dimensional lattice.With uniform
Complexity of Fermionic Dissipative Interactions and Applications to Quantum Computing
Interactions between particles are usually a resource for quantum computing, making quantum many-body systems intractable by any known classical algorithm. In contrast, noise is typically considered
Exciton propagation via quantum walks based on non-Hermitian coin flip operations
  • A. Thilagam
  • Physics, Mathematics
    Journal of Mathematical Chemistry
  • 2014
We examine the coherent propagation of the one-dimensional Frenkel exciton (correlated electron-hole pair system) based on a model of a quantum walker in multi-dimensional Hilbert space. The walk is
Limits on Classical Simulation of Free Fermions with Dissipation
Free-fermionic systems are a valuable, but limited, class of many-body problems efficiently simulable on a classical computer. We examine how classical simulability of noninteracting fermions is
Complexity phase diagram for interacting and long-range bosonic Hamiltonians
TLDR
A "complexity phase diagram" is demonstrated for the Bose-Hubbard model with long-range hopping that shows how the complexity of simulating time evolution varies according to various parameters appearing in the problem, such as the evolution time, the particle density, and the degree of locality.
...
...

References

SHOWING 1-10 OF 29 REFERENCES
Mesoscopic electron transport
Preface L.P. Kouwenhoven, et al. Introduction to Mesoscopic Electron Transport L.P. Kouwenhoven, et al. Geometric Phases in Mesoscopic Systems - From the Aharonov-Bohm Effect to Berry Phases A.
Theory of quantum computation
Short review article on quantum computation accepted for Supplement III, Encyclopaedia of Mathematics (publication expected Summer 2001). See also this http URL
Ann
Aaron Beck’s cognitive therapy model has been used repeatedly to treat depression and anxiety. The case presented here is a 34-year-old female law student with an adjustment disorder with mixed
Nature 415
  • 39
  • 2002
and M
  • Szegedy, in Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
  • 2005
Phys
  • Rev. Lett. 102, 180501
  • 2009
Phys
  • Rev. A 81, 042330
  • 2010
Phys
  • Rev. Lett. 90, 147901
  • 2003
Int
  • J. Quant. Inf. 1, 507
  • 2003
Phys
  • Rev. A 85, 022307
  • 2012
...
...