24 research outputs found
Quantum computation with abelian anyons on the honeycomb lattice
We consider a two-dimensional spin system that exhibits abelian anyonic
excitations. Manipulations of these excitations enable the construction of a
quantum computational model. While the one-qubit gates are performed
dynamically the model offers the advantage of having a two-qubit gate that is
of topological nature. The transport and braiding of anyons on the lattice can
be performed adiabatically enjoying the robust characteristics of geometrical
evolutions. The same control procedures can be used when dealing with
non-abelian anyons. A possible implementation of the manipulations with optical
lattices is developed.Comment: 4 pages, 3 figures, REVTEX, improved presentation and implementatio
Quantum gates with topological phases
We investigate two models for performing topological quantum gates with the
Aharonov-Bohm (AB) and Aharonov-Casher (AC) effects. Topological one- and
two-qubit Abelian phases can be enacted with the AB effect using charge qubits,
whereas the AC effect can be used to perform all single-qubit gates (Abelian
and non-Abelian) for spin qubits. Possible experimental setups suitable for a
solid state implementation are briefly discussed.Comment: 2 figures, RevTex
Topological Features in Ion Trap Holonomic Computation
Topological features in quantum computing provide controllability and noise
error avoidance in the performance of logical gates. While such resilience is
favored in the manipulation of quantum systems, it is very hard to identify
topological features in nature. This paper proposes a scheme where holonomic
quantum gates have intrinsic topological features. An ion trap is employed
where the vibrational modes of the ions are coherently manipulated with lasers
in an adiabatic cyclic way producing geometrical holonomic gates. A crucial
ingredient of the manipulation procedures is squeezing of the vibrational
modes, which effectively suppresses exponentially any undesired fluctuations of
the laser amplitudes, thus making the gates resilient to control errors.Comment: 9 pages, 4 figures, REVTE
Negative Quasi-Probability as a Resource for Quantum Computation
A central problem in quantum information is to determine the minimal physical
resources that are required for quantum computational speedup and, in
particular, for fault-tolerant quantum computation. We establish a remarkable
connection between the potential for quantum speed-up and the onset of negative
values in a distinguished quasi-probability representation, a discrete analog
of the Wigner function for quantum systems of odd dimension. This connection
allows us to resolve an open question on the existence of bound states for
magic-state distillation: we prove that there exist mixed states outside the
convex hull of stabilizer states that cannot be distilled to non-stabilizer
target states using stabilizer operations. We also provide an efficient
simulation protocol for Clifford circuits that extends to a large class of
mixed states, including bound universal states.Comment: 15 pages v4: This is a major revision. In particular, we have added a
new section detailing an explicit extension of the Gottesman-Knill simulation
protocol to deal with positively represented states and measurement (even
when these are non-stabilizer). This paper also includes significant
elaboration on the two main results of the previous versio
Quantum Holonomies for Quantum Computing
Holonomic Quantum Computation (HQC) is an all-geometrical approach to quantum
information processing. In the HQC strategy information is encoded in
degenerate eigen-spaces of a parametric family of Hamiltonians. The
computational network of unitary quantum gates is realized by driving
adiabatically the Hamiltonian parameters along loops in a control manifold. By
properly designing such loops the non-trivial curvature of the underlying
bundle geometry gives rise to unitary transformations i.e., holonomies that
implement the desired unitary transformations. Conditions necessary for
universal QC are stated in terms of the curvature associated to the non-abelian
gauge potential (connection) over the control manifold. In view of their
geometrical nature the holonomic gates are robust against several kind of
perturbations and imperfections. This fact along with the adiabatic fashion in
which gates are performed makes in principle HQC an appealing way towards
universal fault-tolerant QC.Comment: 16 pages, 2 figures, REVTE
Vortex Loops and Majoranas
We investigate the role that vortex loops play in characterizing eigenstates
of interacting Majoranas. We first give some general results, and then we focus
on ladder Hamiltonian examples to test further ideas. Two methods yield exact
results: i.) We utilize the mapping of spin Hamiltonians to quartic
interactions of Majoranas and show under certain conditions the spectra of
these two examples coincide. ii) In cases with reflection-symmetric
Hamiltonians, we use reflection positivity for Majoranas to characterize
vortices. Aside from these exact results, two additional methods suggest wider
applicability of these results: iii.) Numerical evidence suggests similar
behavior for certain systems without reflection symmetry. iv.) A perturbative
analysis also suggests similar behavior without the assumption of reflection
symmetry.Comment: 28 page