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Spin-1/2 particles moving on a 2D lattice with nearest-neighbor
interactions can realize an autonomous quantum computer
Dominik Janzing
abstract: What is the simplest Hamiltonian which can implement quantum computation
without requiring any control operations during the computation process? In a
previous paper we have constructed a 10-local finite-range interaction among
qubits on a 2D lattice having this property. Here we show that
pair-interactions among qutrits on a 2D lattice are sufficient, too, and can
also implement an ergodic computer where the result can be read out from the
time average state after some post-selection with high success probability.
Two of the 3 qutrit states are given by the two levels of a spin-1/2 particle
located at a specific lattice site, the third state is its absence. Usual
hopping terms together with an attractive force among adjacent particles induce
a coupled quantum walk where the particle spins are subjected to spatially
inhomogeneous interactions implementing holonomic quantum computing. The
holonomic method ensures that the implemented circuit does not depend on the
time needed for the walk.
Even though the implementation of the required type of spin-spin interactions
is currently unclear, the model shows that quite simple Hamiltonians are
powerful enough to allow for universal quantum computing in a closed physical
system.
- oai_identifier:
- oai:arXiv.org:quant-ph/0506270
- categories:
- quant-ph
- comments:
- More detailed explanations including description of a programmable
version. 44 pages, 12 figures, latex. To appear in PRA
- arxiv_id:
- quant-ph/0506270
- created:
- 2005-06-30
- updated:
- 2006-12-12
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