Workshop dates: May 24 - 27, 2016
Location: University of British Columbia, Vancouver, Canada
Juan Bermejo-Vega, Freie Universitaet Berlin, Berlin, Germany: Abelian Hypergroups and Quantum Computation
Abstract: Motivated by a connection, described here for the first time, between the hidden normal subgroup problem (HNSP) and abelian hypergroups (algebraic objects that model collisions of physical particles), we develop a stabilizer formalism using abelian hypergroups and an associated classical simulation theorem (a la Gottesman-Knill). Using these tools, we develop the first provably efficient quantum algorithm for finding hidden subhypergroups of nilpotent abelian hypergroups and, via the aforementioned connection, a new, hypergroup-based algorithm for the HNSP on nilpotent groups. We also give efficient methods for manipulating non-unitary, non-monomial stabilizers and an adaptive Fourier sampling technique of general interest.
Joint work with Kevin Zatloukal. Reference: arXiv:1509.05806.
Dan Browne, University College London, London, UK: TBA
Abstract: TBA, but will be about Wigner functions and qubits
Nicolas Delfosse, UC Riverside + Caltech, CA, USA: A simple proof of the equivalence between contextuality and negativity of the Wigner function for qudits.
Abstract: Contextuality and negativity of the Wigner function are two notions of non-classicality for quantum systems. Howard, Wallman, Veitch and Emerson proved recently that these 2 notions coincides for systems of qudits. This equivalence promotes contextuality as a ressource that magic states must possess in order to obtain a quantum speed-up. In this talk, we will compare different notions of contextuality for systems of qudits. Then, we will present a simple proof of the equivalence between contextuality and negativity of the Wigner function.
Based on join work with Juan Bermejo-Vega, Dan E. Browne, Cihan Okay, Robert Raussendorf
Vadym Kliuchnikov, Microsoft Research, Redmond, USA: Exact synthesis of single-qubit unitaries over Clifford-cyclotomic gate sets
Abstract: Whiteboard talk explaining a simple case and illustrating all the theoretical concepts present in our recent works arXiv:1501.04944, arXiv:1504.03383, arXiv:1504.04350.
Cihan Okay, University of Western Ontario, London, Canada: TBA
Abstract: TBA
Sam Roberts, University of Sydney, Sydney, Australia: Symmetry protected topological order in the 3D cluster state
Abstract: Characterising physically realistic spin systems that are useful for quantum computation and also robust to noise is a central problem in quantum information theory. The cluster state in 3-dimensions is the gapped ground state of a local Hamiltonian which exhibits some remarkable properties, including infinite entanglement length at nonzero temperatures [Phys. Rev. A 71, 062313, (2005)]. A natural question to ask is whether there is an ordered phase where some of these properties are insensitive to perturbations. We find a symmetry of the cluster state which puts it in a nontrivial symmetry protected topological (SPT) phase. A consequence of this order is that the ground state of the cluster Hamiltonian retains its infinite entanglement length even when perturbed, provided the perturbations respect the symmetry and are sufficiently small.
Joel Wallman, University of Waterloo, Waterloo, Canada: Characterizing Universal Gate Sets via Dihedral Benchmarking
Abstract: We describe a practical experimental protocol for robustly characterizing the error rates of non-Clifford gates associated with dihedral groups, including gates in SU(2) associated with arbitrarily small angle rotations. Our dihedral benchmarking protocol is a generalization of randomized benchmarking that relaxes the usual unitary 2-design condition. Combining this protocol with existing randomized benchmarking schemes enables an efficient means of characterizing universal gate sets for quantum information processing in a way that is independent of state-preparation and measurement errors. In particular, our protocol enables direct benchmarking of the T gate (sometime called Pi/8-gate) even for the gate-dependent error model that is expected in leading approaches to fault-tolerant quantum computation.
Beni Yoshida, Perimeter Institute, Waterloo, Canada: Gapped boundaries, group cohomology and fault-tolerant logical gates
Abstract: We establish the connection among classifications of gapped boundaries in topological phases of matter, bosonic symmetry-protected topological (SPT) phases and fault-tolerantly implementable logical gates in quantum error-correcting codes. We begin by presenting constructions of gapped boundaries for the d-dimensional quantum double model by using d-cocycles functions (d \geq 2). We point out that the system supports m-dimensional excitations (m < d), which we shall call fluctuating charges, that are superpositions of point-like electric charges characterized by m-dimensional bosonic SPT wavefunctions. There exist gapped boundaries where electric charges or magnetic fluxes may not condense by themselves, but may condense only when accompanied by fluctuating charges. Magnetic fluxes and codimension-2 fluctuating charges exhibit non-trivial multi-excitation braiding statistics, involving more than two excitations. The statistical angle can be computed by taking slant products of underlying cocycle functions sequentially. We find that excitations that may condense into a gapped boundary can be characterized by trivial multi-excitation braiding statistics, generalizing the notion of the Lagrangian subgroup. As an application, we construct fault-tolerantly implementable logical gates for the d-dimensional quantum double model by using d-cocycle functions. Namely, corresponding logical gates belong to the dth level of the Clifford hierarchy, but are outside of the (d-1)th level, if cocycle functions have non-trivial sequences of slant products.
Nikolas Breuckmann, Universitaet Aachen, Germany: Local Decoding in 4D Homological Codes
Oleg Kabernik, University of British Columbia, Vancouver, Canada: Reduced state spaces
Petr Lisonek, Simon Fraser University, Vancouver, Canada: Quantum codes from generalized quadrangles
Robert Raussendorf, University of British Columbia, Vancouver, Canada: Cohomological classification of contextual quantum computations
David Stephen, University of British Columbia, Vancouver, Canada: Universal 1D MBQC in SPT phases
Stefan Trandafir, Simon Fraser University, Vancouver, Canada: Kochen-Specker Proofs on Incidence Structures
Dongsheng Wang, University of British Columbia, Vancouver, Canada: Resource state classification for MBQC
Scientific organizer: Robert Raussendorf (UBC)