28 research outputs found
Local invariants of braiding quantum gates -- associated link polynomials and entangling power
For a generic n-qubit system, local invariants under the action of SL(2,C)⊗n characterize non-local properties of entanglement. In general, such properties are not immediately apparent and hard to construct. Here we consider two-qubit Yang-Baxter operators and show that their eigenvalues completely determine the non-local properties of the system. Moreover, we apply the Turaev procedure to these operators and obtain their associated link/knot polynomials. We also compute their entangling power and compare it with that of a generic two-qubit operator
Quark-antiquark potential in defect conformal field theory
We consider antiparallel Wilson lines in N = 4 super Yang-Mills in the presence of a codimension-1 defect. We compute the Wilson lines’ expectation value both at weak coupling, in the gauge theory, and at strong coupling, by finding the string configurations which are dual to this operator. These configurations display a Gross-Ooguri transition between a connected, U-shaped string phase and a phase in which the string breaks into two disconnected surfaces. We analyze in detail the critical configurations separating the two phases and compare the string result with the gauge theory one in a certain double scaling limit
Braiding quantum gates from partition algebras
Unitary braiding operators can be used as robust entangling quantum gates. We introduce a solution-generating technique to solve the (d,m,l)-generalized Yang-Baxter equation, for m/2 64l 64m, which allows to systematically construct such braiding operators. This is achieved by using partition algebras, a generalization of the Temperley-Lieb algebra encountered in statistical mechanics. We obtain families of unitary and non-unitary braiding operators that generate the full braid group. Explicit examples are given for a 2-, 3-, and 4-qubit system, including the classification of the entangled states generated by these operators based on Stochastic Local Operations and Classical Communication
Topological Quantum Computation on Supersymmetric Spin Chains
Quantum gates built out of braid group elements form the building blocks of topological quantum computation. They have been extensively studied in SU(2)k quantum group theories, a rich source of examples of non-Abelian anyons such as the Ising (k=2), Fibonacci (k=3) and Jones-Kauffman (k=4) anyons. We show that the fusion spaces of these anyonic systems can be precisely mapped to the product state zero modes of certain Nicolai-like supersymmetric spin chains. As a result, we can realize the braid group on the product state zero modes of these supersymmetric systems. These operators kill all the other states in the Hilbert space, thus preventing the occurrence of errors while processing information, making them suitable for quantum computing
Dynamical tachyons on fuzzy spheres
We study the spectrum of off-diagonal fluctuations between displaced fuzzy
spheres in the BMN plane wave matrix model. The displacement is along the plane
of the fuzzy spheres. We find that when two fuzzy spheres intersect at angles
classical tachyons develop and that the spectrum of these modes can be computed
analytically. These tachyons can be related to the familiar Nielsen-Olesen
instabilities in Yang-Mills theory on a constant magnetic background. Many
features of the problem become more apparent when we compare with maximally
supersymmetric Yang-Mills on a sphere, of which this system is a truncation. We
also set up a simple oscillatory trajectory on the displacement between the
fuzzy spheres and study the dynamics of the modes as they become tachyonic for
part of the oscillations. We speculate on their role regarding the possible
thermalization of the system.Comment: 34 pages, 4 figures; v2: 35 pages, expanded sec. 4.3, added
reference
Conformal and non-conformal hyperloop deformations of the 1/2 BPS circle
We construct new large classes of BPS Wilson hyperloops in three-dimensional N=4 quiver Chern-Simons-matter theory on S3. The main strategy is to start with the 1/2 BPS Wilson loop of this theory, choose any linear combination of the supercharges it preserves, and look for deformations built out of the matter fields that still preserve that supercharge. This is a powerful generalization of a recently developed approach based on deformations of 1/4 and 1/8 BPS bosonic loops, which itself was far more effective at discovering new operators than older methods relying on complicated ansatze. We discover many new moduli spaces of BPS hyperloops preserving varied numbers of supersymmetries and varied subsets of the symmetries of the 1/2 BPS operator. In particular, we find new bosonic operators preserving 2 or 3 supercharges as well as new families of loops that do not share supercharges with any bosonic loops, including subclasses of both 1/8 and 1/4 BPS loops that are conformal
Operator product expansion of higher rank Wilson loops from D-branes and matrix models
In this paper we study correlation functions of circular Wilson loops in
higher dimensional representations with chiral primary operators of N=4 super
Yang-Mills theory. This is done using the recently established relation between
higher rank Wilson loops in gauge theory and D-branes with electric fluxes in
supergravity. We verify our results with a matrix model computation, finding
perfect agreement in both the symmetric and the antisymmetric case.Comment: 28 pages, latex; v2: minor misprints corrected, references adde
Instantons and Matter in N=1/2 Supersymmetric Gauge Theory
We extend the instanton calculus for N=1/2 U(2) supersymmetric gauge theory
by including one massless flavor. We write the equations of motion at leading
order in the coupling constant and we solve them exactly in the
non(anti)commutativity parameter C. The profile of the matter superfield is
deformed through linear and quadratic corrections in C. Higher order
corrections are absent because of the fermionic nature of the back-reaction.
The instanton effective action, in addition to the usual 't Hooft term,
includes a contribution of order C^2 and is N=1/2 invariant. We argue that the
N=1 result for the gluino condensate is not modified by the presence of the new
term in the effective action.Comment: 33 pages, harvmac; v2: minor changes, added references; v3: added
analysis of the instanton measure in section
Quarkonium dissociation by anisotropy
We compute the screening length for quarkonium mesons moving through an
anisotropic, strongly coupled N=4 super Yang-Mills plasma by means of its
gravity dual. We present the results for arbitrary velocities and orientations
of the mesons, as well as for arbitrary values of the anisotropy. The
anisotropic screening length can be larger or smaller than the isotropic one,
and this depends on whether the comparison is made at equal temperatures or at
equal entropy densities. For generic motion we find that: (i) mesons dissociate
above a certain critical value of the anisotropy, even at zero temperature;
(ii) there is a limiting velocity for mesons in the plasma, even at zero
temperature; (iii) in the ultra-relativistic limit the screening length scales
as with \epsilon =1/2, in contrast with the isotropic result
\epsilon =1/4.Comment: 39 pages, 26 figures; v2: minor changes, added reference
Orbifolding the Twistor String
The D-instanton expansion of the topological B-model on the supermanifold
CP(3|4) reproduces the perturbative expansion of N=4 Super Yang-Mills theory.
In this paper we consider orbifolds in the fermionic directions of CP(3|4).
This operation breaks the SU(4) R-symmetry group, reducing the amount of
supersymmetry of the gauge theory. As specific examples we take N=1 and N=2
orbifolds and obtain the corresponding superconformal quiver theories. We
discuss the D1 instanton expansion in this context and explicitly compute some
amplitudes.Comment: 24 pages, 8 figures; v2: minor correction