451 research outputs found
Minimum construction of two-qubit quantum operations
Optimal construction of quantum operations is a fundamental problem in the
realization of quantum computation. We here introduce a newly discovered
quantum gate, B, that can implement any arbitrary two-qubit quantum operation
with minimal number of both two- and single-qubit gates. We show this by giving
an analytic circuit that implements a generic nonlocal two-qubit operation from
just two applications of the B gate. We also demonstrate that for the highly
scalable Josephson junction charge qubits, the B gate is also more easily and
quickly generated than the CNOT gate for physically feasible parameters.Comment: 4 page
Ettingshausen effect due to Majorana modes
The presence of Majorana zero-energy modes at vortex cores in a topological
superconductor implies that each vortex carries an extra entropy , given
by , that is independent of temperature. By utilizing this
special property of Majorana modes, the edges of a topological superconductor
can be cooled (or heated) by the motion of the vortices across the edges. As
vortices flow in the transverse direction with respect to an external imposed
supercurrent, due to the Lorentz force, a thermoelectric effect analogous to
the Ettingshausen effect is expected to occur between opposing edges. We
propose an experiment to observe this thermoelectric effect, which could
directly probe the intrinsic entropy of Majorana zero-energy modes.Comment: 16 pages, 3 figure
Preparing ground states of quantum many-body systems on a quantum computer
Preparing the ground state of a system of interacting classical particles is
an NP-hard problem. Thus, there is in general no better algorithm to solve this
problem than exhaustively going through all N configurations of the system to
determine the one with lowest energy, requiring a running time proportional to
N. A quantum computer, if it could be built, could solve this problem in time
sqrt(N). Here, we present a powerful extension of this result to the case of
interacting quantum particles, demonstrating that a quantum computer can
prepare the ground state of a quantum system as efficiently as it does for
classical systems.Comment: 7 pages, 1 figur
Anatomy of fermionic entanglement and criticality in Kitaev spin liquids
We analyze in detail the effect of nontrivial band topology on the area-law behavior of the entanglement entropy in Kitaev's honeycomb model. By mapping the translationally invariant 2D spin model onto 1D fermionic subsystems, we identify those subsystems responsible for universal entanglement contributions in the gapped phases and those responsible for critical entanglement scaling in the gapless phases. For the gapped phases, we analytically show how the topological edge states contribute to the entanglement entropy and provide a universal lower bound for it. For the gapless semimetallic phases and topological phase transitions, the identification of the critical subsystems shows that they fall always into the Ising or the XY universality classes. As our study concerns the fermionic degrees of freedom in the honeycomb model, qualitatively similar results are expected to apply also to generic topological insulators and superconductors
Non-Abelian statistics as a Berry phase in exactly solvable models
We demonstrate how to directly study non-Abelian statistics for a wide class
of exactly solvable many-body quantum systems. By employing exact eigenstates
to simulate the adiabatic transport of a model's quasiparticles, the resulting
Berry phase provides a direct demonstration of their non-Abelian statistics. We
apply this technique to Kitaev's honeycomb lattice model and explicitly
demonstrate the existence of non-Abelian Ising anyons confirming the previous
conjectures. Finally, we present the manipulations needed to transport and
detect the statistics of these quasiparticles in the laboratory. Various
physically realistic system sizes are considered and exact predictions for such
experiments are provided.Comment: 10 pages, 3 figures. To appear in New Journal of Physic
Necessary Condition for the Quantum Adiabatic Approximation
A gapped quantum system that is adiabatically perturbed remains approximately
in its eigenstate after the evolution. We prove that, for constant gap, general
quantum processes that approximately prepare the final eigenstate require a
minimum time proportional to the ratio of the length of the eigenstate path to
the gap. Thus, no rigorous adiabatic condition can yield a smaller cost. We
also give a necessary condition for the adiabatic approximation that depends on
local properties of the path, which is appropriate when the gap varies.Comment: 5 pages, 1 figur
Markov entropy decomposition: a variational dual for quantum belief propagation
We present a lower bound for the free energy of a quantum many-body system at
finite temperature. This lower bound is expressed as a convex optimization
problem with linear constraints, and is derived using strong subadditivity of
von Neumann entropy and a relaxation of the consistency condition of local
density operators. The dual to this minimization problem leads to a set of
quantum belief propagation equations, thus providing a firm theoretical
foundation to that approach. The minimization problem is numerically tractable,
and we find good agreement with quantum Monte Carlo for the spin-half
Heisenberg anti-ferromagnet in two dimensions. This lower bound complements
other variational upper bounds. We discuss applications to Hamiltonian
complexity theory and give a generalization of the structure theorem of Hayden,
Jozsa, Petz and Winter to trees in an appendix
Strong Anisotropy in Spin Suceptibility of Superfluid 3He-B Film Caused by Surface Bound States
Spin susceptibility of superfluid 3He-B film with specular surfaces is
calculated. It is shown that, when the magnetic field is applied in a direction
perpendiculr to the film, the suseptibility is significantly enhanced by the
contribution from the surface bound states. No such enhancement is found for
the magnetic field parallel to the film. A simplified model with spatially
constant order parameter is used to elucidate the magnetic properties of the
surface bound states. The Majorana nature of the zero energy bound state is
also mentioned.Comment: 4 pages, 4 figure
Experimental quantum tossing of a single coin
The cryptographic protocol of coin tossing consists of two parties, Alice and
Bob, that do not trust each other, but want to generate a random bit. If the
parties use a classical communication channel and have unlimited computational
resources, one of them can always cheat perfectly. Here we analyze in detail
how the performance of a quantum coin tossing experiment should be compared to
classical protocols, taking into account the inevitable experimental
imperfections. We then report an all-optical fiber experiment in which a single
coin is tossed whose randomness is higher than achievable by any classical
protocol and present some easily realisable cheating strategies by Alice and
Bob.Comment: 13 page
Parafermionic edge zero modes in Z_n-invariant spin chains
A sign of topological order in a gapped one-dimensional quantum chain is the
existence of edge zero modes. These occur in the Z_2-invariant Ising/Majorana
chain, where they can be understood using free-fermion techniques. Here I
discuss their presence in spin chains with Z_n symmetry, and prove that for
appropriate coupling they are exact, even in this strongly interacting system.
These modes are naturally expressed in terms of parafermions, generalizations
of fermions to the Z_n case. I show that parafermionic edge zero modes do not
occur in the usual ferromagnetic and antiferromagnetic cases, but rather only
when the interactions are chiral, so that spatial-parity and time-reversal
symmetries are broken.Comment: 22 pages. v2: small changes, added reference
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