dorsal/arxiv
View SchemaSpin-1/2 particles moving on a 2D lattice with nearest-neighbor interactions can realize an autonomous quantum computer
| Authors | Dominik Janzing |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0506270 |
| URL | https://arxiv.org/abs/quant-ph/0506270 |
| DOI | 10.1103/PhysRevA.75.012307 |
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.
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"abstract": "What is the simplest Hamiltonian which can implement quantum computation\nwithout requiring any control operations during the computation process? In a\nprevious paper we have constructed a 10-local finite-range interaction among\nqubits on a 2D lattice having this property. Here we show that\npair-interactions among qutrits on a 2D lattice are sufficient, too, and can\nalso implement an ergodic computer where the result can be read out from the\ntime average state after some post-selection with high success probability.\n Two of the 3 qutrit states are given by the two levels of a spin-1/2 particle\nlocated at a specific lattice site, the third state is its absence. Usual\nhopping terms together with an attractive force among adjacent particles induce\na coupled quantum walk where the particle spins are subjected to spatially\ninhomogeneous interactions implementing holonomic quantum computing. The\nholonomic method ensures that the implemented circuit does not depend on the\ntime needed for the walk.\n Even though the implementation of the required type of spin-spin interactions\nis currently unclear, the model shows that quite simple Hamiltonians are\npowerful enough to allow for universal quantum computing in a closed physical\nsystem.",
"arxiv_id": "quant-ph/0506270",
"authors": [
"Dominik Janzing"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.75.012307",
"title": "Spin-1/2 particles moving on a 2D lattice with nearest-neighbor interactions can realize an autonomous quantum computer",
"url": "https://arxiv.org/abs/quant-ph/0506270"
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