Southwest Quantum Information and Technology

Thirteenth Annual Meeting, February 17-20, 2011
Boulder, Colorado

Full Program | Thursday | Friday | Saturday | Sunday | All Sessions

SESSION 12: Quantum Computation
Session Chair:
10:30am-11:00am	David Feder, University of Calgary
	Universal Quantum Computation with Non-Interacting Fermions
	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.
11:00am--11:30am	Robert Raussendorf, University of British Columbia
	The 2D AKLT state is universal for measurement-based quantum computation
	Abstract. We demonstrate that the two-dimensional AKLT state on a honeycomb lattice is a universal resource for measurement-based quantum computation [1]. Our argument proceeds by reduction of the AKLT state to a 2D cluster state, which is already known to be universal, and consists of two steps. First, we devise a local POVM by which the AKLT state is mapped to a random planar graph state. Second, we show numerically that the connectivity properties of these random graphs are governed by percolation, and that typical graphs are in the connected phase. The corresponding graph states can then be transformed to 2D cluster states by standard techniques. Joint work with Tzu-Chieh Wei and Ian Affleck. An analogous result has been obtained by A. Miyake in [2]. [1] TC Wei, I. Affleck and R.Raussendorf, arXiv:1009.2840, [2] A. Miyake, arXiv:1009.3491
11:30am-12:00pm	Wim van Dam, University of California, Santa Barbara
	Noise Thresholds for Higher Dimensional Systems using the Discrete Wigner Function
	Abstract. This work analyzes the non-stabilizer states and non-stabilizer operations that must be present in any quantum circuit if it is to perform better-than-classical quantum computation. That such a non-stabilizer resource is necessary for universal quantum computation is a consequence of the Gottesman-Knill theorem. In particular, we find states and operations that are maximally non-stabilizer in the sense that they require the highest amount of depolarizing noise to make them become stabilizer states and operations respectively. In doing so we make novel use of a theoretical construction known as the discrete Wigner function (DWF). We find d-level (qudit) states whose negativity (in terms of the DWF quasiprobabilites) is maximal, answering a conjecture of Wootters. We find non-Clifford gates, acting on d-level systems, which require very high amounts (rapidly approaching 100 percent as dimension, d, increases) of depolarizing noise to become decomposable in terms of Clifford gates. In previous literature the convex hull of Clifford gates was called the Clifford polytope. This work describes the qudit version of the Clifford polytope, and bounding inequalities that describe this object are derived using a simple argument. Our results have implications for the question of qudit magic state distillation.