Identifying phases of quantum many-body systems that are universal for quantum computation.

School of Physical Sciences, The University of Queensland, St Lucia, Queensland 4072, Australia.
Physical Review Letters (Impact Factor: 7.73). 08/2009; 103(2):020506. DOI: 10.1103/PhysRevLett.103.020506
Source: PubMed

ABSTRACT Quantum computation can proceed solely through single-qubit measurements on an appropriate quantum state, such as the ground state of an interacting many-body system. We investigate a simple spin-lattice system based on the cluster-state model, and by using nonlocal correlation functions that quantify the fidelity of quantum gates performed between distant qubits, we demonstrate that it possesses a quantum (zero-temperature) phase transition between a disordered phase and an ordered "cluster phase" in which it is possible to perform a universal set of quantum gates.

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    ABSTRACT: We describe a many-body quantum system which can be made to quantum compute by the adiabatic application of a large applied field to the system. Prior to the application of the field quantum information is localized on one boundary of the device, and after the application of the field this information has propagated to the other side of the device with a quantum circuit applied to the information. The applied circuit depends on the many-body Hamiltonian of the material, and the computation takes place in a degenerate ground space with symmetry-protected topological order. Such adiabatic quantum transistors are universal adiabatic quantum computing devices which have the added benefit of being modular. Here we describe this model, provide arguments for why it is an efficient model of quantum computing, and examine these many-body systems in the presence of a noisy environment.
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    ABSTRACT: The two-dimensional cluster state, a universal resource for measurement-based quantum computation, is also the gapped ground state of a short-ranged Hamiltonian. Here, we examine the effect of perturbations to this Hamiltonian. We prove that, provided the perturbation is sufficiently small and respects a certain symmetry, the perturbed ground state remains a universal resource. We do this by characterising the operation of an adaptive measurement protocol throughout a suitable symmetry-protected quantum phase, relying on generic properties of the phase rather than any analytic control over the ground state.
    New Journal of Physics 07/2012; 14(11). · 4.06 Impact Factor


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