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: 7.51). 08/2009; 103(2):020506. DOI: 10.1103/PhysRevLett.103.020506
Source: PubMed


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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    • "Notice that H clu has a Z 2 × Z 2 symmetry generated by the following two operators (see e.g. [32] [33] [34] "
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    ABSTRACT: In this paper, we study the geometry of reduced density matrices for states with symmetry-protected topological (SPT) order. We observe ruled surface structures on the boundary of the convex set of low dimension projections of the reduced density matrices if a symmetry-breaking term is added to the boundary of the system, which signals the SPT order. This symmetry-breaking term does not represent a thermodynamic quantity. Consequently, the ruled surface can neither be revealed in a system without boundary, nor by a symmetry-breaking term representing a thermodynamic quantity. Although the ruled surfaces only appear in the thermodynamic limit where the ground-state degeneracy is exact, we analyze the precision of our numerical algorithm and show that a finite system calculation suffices to reveal the ruled surfaces.
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    • "Recently, ideas from quantum information and computation [3] give rise to new perspectives on examining phases of matter, such as topological phases and their classification [4]. Moreover, from the viewpoint of computational universality in measurement-based quantum computation (MBQC) [5] [6] [7] [8] [9], a few works have suggested that resource states can emerge from certain quantum phases of matter [10] [11] [12] [13] [14] and that the transition in the quantum computational capability results in a new notion of phase transitions [15] [16] [17]. Here, we construct two models to investigate their ground states and thermal states for providing universal quantum computational resource for MBQC. "
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    ABSTRACT: We construct two spin models on lattices (both two and three-dimensional) to study the capability of quantum computational power as a function of temperature and the system parameter. There exists a finite region in the phase diagram such that the thermal equilibrium states are capable of providing a universal fault-tolerant resource for measurement-based quantum computation. Moreover, in such a region the thermal resource states on the 3D lattices can enable topological protection for quantum computation. The two models behave similarly in terms of quantum computational power. However, they have different properties in terms of the usual phase transitions. The first model has a first-order phase transition only at zero temperature whereas there is no transition at all in the second model. Interestingly, the transition in the quantum computational power does not coincide with the phase transition in the first model.
    Physical Review A 02/2014; 89(5). DOI:10.1103/PhysRevA.89.052315 · 2.81 Impact Factor
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    • "These systems can be exactly diagonalized by a transformation of the spin model to a model with noninteracting fermions. Following the work of Doherty and Bartlett [23], but with additional attention to the boundary terms, suppose that one defines a code with the following ðn À 1Þ encoded Pauli operators: "
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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.
    Physical Review X 07/2012; 3(2). DOI:10.1103/PhysRevX.3.021015 · 9.04 Impact Factor
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