ContactDepartment of PhysicsUniversity of Basel Klingelbergstrasse 82 CH4056 Basel, Switzerland

Short CV
2009  2013  PhD under the supervision of Prof. Dr. D. Loss, University of Basel, Switzerland 
2007  2009  Master in Physics, ETH Zurich, Switzerland 
2004  2007  Bachelor in Physics, ETH Zurich, Switzerland 
Publications
Show all abstracts.1.  Topological Order and Reflection Positivity 
Arthur Jaffe and Fabio L. Pedrocchi. Europhysics Letters 105, 40002 (2014); arxiv:1310.5370.
The focus of this paper is twofold. First, we observe that Hamiltonians displaying both topological order and reflection positivity have an interesting property: expectations in different groundstate vectors of a given local operator WA have the same sign. Secondly, we illustrate this result with a specific Majorana Hamiltonian, related to the toric code which is widely studied in quantum information theory. We show that expectations of reflectionsymmetric loops in ground states of this Hamiltonian are vortexfree or vortexfull.
 
2.  Vortex Loops and Majorana Fermions 
Stefano Chesi, Arthur Jaffe, Daniel Loss, and Fabio L. Pedrocchi. J. Math. Phys. 54, 112203 (2013); arXiv:1305.6270.
We investigate the role that vortex loops play in characterizing eigenstates
of certain systems of halfinteger spins with nearestneighbor interaction on a
trivalent lattice. In particular we focus on ground states (and other lowlying
states). We test our ideas on a "spin ladder" In certain cases we show how the
vortex configuration of the ground state is determined by the relative signs of
the coupling constants. Two methods yield exact results: i.) We utilize the
equivalence of spin Hamiltonians with quartic interactions of Majorana
fermions, and analyze that fermionic Hamiltonian. ii) We use reflection
positivity for Majorana fermions to characterize vortices in ground states for
reflectionsymmetric couplings. Two additional methods suggest potential 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.
 
3.  LongRange Interaction of SingletTriplet Qubits via Ferromagnets 
Luka Trifunovic, Fabio L. Pedrocchi, and Daniel Loss. arXiv:1305.2451
We propose a mechanism of a longrange coherent interaction between two
singlettriplet qubits dipolarly coupled to a dogboneshaped ferromagnet. An
effective qubitqubit interaction Hamiltonian is derived and the coupling
strength is estimated. Furthermore we derive the effective coupling between two
spin1/2 qubits that are coupled via dipolar interaction to the ferromagnet and
that lie at arbitrary positions and deduce the optimal positioning. We consider
hybrid systems consisting of spin1/2 and ST qubits and derive the effective
Hamiltonian for this case. We then show that operation times vary between 1MHz
and 100MHz and give explicit estimates for GaAs, Silicon, and NVcenter based
spin qubits. Finally, we explicitly construct the required sequences to
implement a CNOT gate. The resulting quantum computing architecture retains all
the single qubit gates and measurement aspects of earlier approaches, but
allows qubit spacing at distances of order 1$\,\mu$m for twoqubit gates,
achievable with current semiconductor technology.
 
4.  Reflection Positivity for Majorana Fermions 
Arthur Jaffe and Fabio L. Pedrocchi. Annales Henri Poincare; arXiv:1305.1792.
We establish reflection positivity for Gibbs trace states defined by a
certain class of Hamiltonians that describe the interaction of Majorana
fermions on a lattice. These Hamiltonians may include manybody interactions,
as long as the signs of the associated coupling constants satisfy certain
restrictions. We show that reflection positivity holds on an even subalgebra of
Majorana fermions.
 
5.  LongDistance Entanglement of Spin Qubits via Ferromagnet 
Luka Trifunovic, Fabio L. Pedrocchi, and Daniel Loss. Phys. Rev. X 3, 041023 (2013); arXiv:1302.4017.
We propose a mechanism of coherent coupling between distant spin qubits
interacting dipolarly with a ferromagnet. We derive an effective twospin
interaction Hamiltonian and find a regime where dynamics is coherent. Finally,
we present a sequence for the implementation of the entangling CNOT gate and
estimate the corresponding operation time to be a few tens of nanoseconds. A
particularly promising application of our proposal is to atomistic spinqubits
such as siliconbased qubits and NVcenters in diamond to which existing
coupling schemes do not apply.
 
6.  Dynamic Generation of Topologically Protected SelfCorrecting Quantum Memory 
Daniel Becker, Tetsufumi Tanamoto, Adrian Hutter, Fabio L. Pedrocchi, and Daniel Loss. Phys. Rev. A 87,042340 (2013); arXiv:1302.3998.
We propose a scheme to dynamically realize a thermally stable quantum memory
based on the toric code. The code is generated from qubit systems with typical
twobody interactions (Ising, XY, Heisenberg) using periodic, NMRlike, pulse
sequences. It allows one to encode the logical qubits without measurements and
to protect them dynamically against the time evolution of the physical qubits.
Thermal stability is achieved by weakly coupling the qubits to additional
cavity modes that mediate longrange attractive interactions between the
stabilizer operators of the toric code. We investigate how the fidelity, with
which the toric code is realized, depends on the period length T of the pulse
sequence and the magnitude of possible pulse errors. We derive an optimal
period T_opt that maximizes the fidelity.
 
7.  Enhanced thermal stability of the toric code through coupling to a bosonic bath 
Fabio L. Pedrocchi, Adrian Hutter, James R. Wootton, and Daniel Loss. Phys. Rev. A 88, 062313 (2013); arXiv:1309.0621; arXiv:1209.5289.
We propose and study a model of a quantum memory that features selfcorrecting properties and a lifetime growing arbitrarily with system size at nonzero temperature. This is achieved by locally coupling a 2D L x L toric code to a 3D bath of bosons hopping on a cubic lattice. When the stabilizer operators of the toric code are coupled to the displacement operator of the bosons, we solve the model exactly via a polaron transformation and show that the energy penalty to create anyons grows linearly with L. When the stabilizer operators of the toric code are coupled to the bosonic density operator, we use perturbation theory to show that the energy penalty for anyons scales with ln(L). For a given error model, these energy penalties lead to a lifetime of the stored quantum information growing respectively exponentially and polynomially with L. Furthermore, we show how to choose an appropriate coupling scheme in order to hinder the hopping of anyons (and not only their creation) with energy barriers that are of the same order as the anyon creation gaps. We argue that a toric code coupled to a 3D Heisenberg ferromagnet realizes our model in its lowenergy sector. Finally, we discuss the delicate issue of the stability of topological order in the presence of perturbations. While we do not derive a rigorous proof of topological order, we present heuristic arguments suggesting that topological order remains intact when perturbative operators acting on the toric code spins are coupled to the bosonic environment.
 
8.  Majorana states in inhomogeneous spin ladders 
Fabio L. Pedrocchi, Stefano Chesi, Suhas Gangadharaiah, and Daniel Loss. Phys. Rev. B 86, 205412 (2012); arXiv:1204.3044.
We propose an inhomogeneous open spin ladder, related to the Kitaev honeycomb
model, which can be tuned between topological and nontopological phases. In
extension of Lieb's theorem, we show numerically that the ground state of the
spin ladder is either vortex free or vortex full. We study the robustness of
Majorana end states (MES) which emerge at the boundary between sections in
different topological phases and show that while the MES in the homogeneous
ladder are destroyed by singlebody perturbations, in the presence of
inhomogeneity at least twobody perturbations are required for destabilizing
MES. Furthermore, we prove that x, y, or z inhomogeneous magnetic fields are
not able to destroy the topological degeneracy. Finally, we present a
trijunction setup where MES can be braided. A network of such spin ladders
provides thus a promising platform for realization and manipulation of Majorana
end states.
 
9.  Absence of spontaneous magnetic order of lattice spins coupled to itinerant interacting electrons in one and two dimensions 
Daniel Loss, Fabio L. Pedrocchi, and Anthony J. Leggett. Phys. Rev. Lett. 107, 107201 (2011); arXiv:1107.1223.
We extend the MerminWagner theorem to a system of lattice spins which are
spincoupled to itinerant and interacting charge carriers. We use the
Bogoliubov inequality to rigorously prove that neither (anti) ferromagnetic
nor helical longrange order is possible in one and two dimensions at any
finite temperature. Our proof applies to a wide class of models including any
form of electronelectron and singleelectron interactions that are independent
of spin. In the presence of Rashba or Dresselhaus spinorbit interactions (SOI)
magnetic order is allowed and intimately connected to equilibrium spin
currents. However, in the special case when Rashba and Dresselhaus SOIs are
tuned to be equal, magnetic order is excluded again. This opens up a new
possibility to control magnetism in magnetic semiconductors electrically.
 
10.  Physical solutions of the Kitaev honeycomb model 
Fabio L. Pedrocchi, Stefano Chesi, and Daniel Loss. Phys. Rev. B 84, 165414 (2011); arXiv:1105.4573.
We investigate the exact solution of the honeycomb model proposed by Kitaev and derive an explicit formula for the projector onto the physical subspace. The physical states are simply characterized by the parity of the total occupation of the fermionic eigenmodes. We consider a general lattice on a torus and show that the physical fermion parity depends in a nontrivial way on the vortex configuration and the choice of boundary conditions. In the vortexfree case with a constant gauge field we are able to obtain an analytical expression of the parity. For a general configuration of the gauge field the parity can be easily evaluated numerically, which allows the exact diagonalization of large spin models. We consider physically relevant quantities, as in particular the vortex energies, and show that their true value and associated states can be substantially different from the one calculated in the unprojected space, even in the thermodynamic limit.
 
11.  Quantum memory coupled to cavity modes 
Fabio L. Pedrocchi, Stefano Chesi, and Daniel Loss. Phys. Rev. B 83, 115415 (2011); arXiv:1011.3762.
Inspired by spinelectric couplings in molecular magnets, we introduce in the
Kitaev honeycomb model a linear modification of the Ising interactions due to
the presence of quantized cavity fields. This allows to control the properties
of the lowenergy toric code Hamiltonian, which can serve as a quantum memory,
by tuning the physical parameters of the cavity modes, like frequencies, photon
occupations, and coupling strengths. We study the properties of the model
perturbatively by making use of the SchriefferWolff transformation and show
that, depending on the specific setup, the cavity modes can be useful in
several ways. They allow to detect the presence of anyons through frequency
shifts and to prolong the lifetime of the memory by enhancing the anyon
excitation energy or mediating longrange anyonanyon interactions with tunable
sign. We consider both resonant and largely detuned cavity modes.
