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Universal Quantum Computation with Non-Interacting Fermions

David Feder, University of Calgary

(Session 12 : Sunday from 10:30am-11:00am)

Abstract. In measurement-based quantum computation, an algorithm proceeds entirely by making measurements on successive qubits comprising some highly entangled 'resource state.' The most well-studied resource state is the cluster state. Much recent work has been done to identify other suitable resource states, and particular effort has been expended on identifying experimentally implementable Hamiltonians that yield resource states as their gapped ground states. We show that for a particular choice of lattice model, the gapped ground state of non-interacting indistinguishable fermions is formally equivalent to a cluster state. Entanglement is a direct consequence of fermionic antisymmetry, and local unitary gates are implemented by turning on a small additional lattice. The quantum information is encoded entirely in the lattice positions of the fermions, rendering it impervious to many sources of decoherence. This suggests that resources for quantum information processing may be generic in Nature.