449219
Simulation of Topological Field Theories¶by Quantum Computers
Abstract: Quantum computers will work by evolving a high tensor power of a small (e.g. two) dimensional Hilbert space by local gates, which can be implemented by applying a local Hamiltonian H for a time t. In contrast to this quantum engineering, the most abstract reaches of theoretical physics has spawned “topological models” having a finite dimensional internal state space with no natural tensor product structure and in which the evolution of the state is discrete, H≡ 0. These are called topological quantum field theories (TQFTs). These exotic physical systems are proved to be efficiently simulated on a quantum computer. The conclusion is two-fold:1. TQFTs cannot be used to define a model of computation stronger than the usual quantum model “BQP”.2. TQFTs provide a radically different way of looking at quantum computation. The rich mathematical structure of TQFTs might suggest a new quantum algorithm.
54954168
From String Nets to Nonabelions
We discuss Hilbert spaces spanned by the set of string nets, i.e. trivalent graphs, on a lattice. We suggest some routes by which such a Hilbert space could be the low-energy subspace of a model of quantum spins on a lattice with short-ranged interactions. We then explain conditions which a Hamiltonian acting on this string net Hilbert space must satisfy in order for the system to be in the DFib (Doubled Fibonacci) topological phase, that is, be described at low energy by an SO(3)3 × SO(3)3 doubled Chern-Simons theory, with the appropriate non-abelian statistics governing the braiding of the low-lying quasiparticle excitations (nonabelions). Using the string net wavefunction, we describe the properties of this phase. Our discussion is informed by mappings of string net wavefunctions to the chromatic polynomial and the Potts model.
18058928
Density of the SO(3) TQFT Representation of Mapping Class Groups
We show that for an odd prime r>3 and an integer g>1, in the projective representation given by the SO(3) Witten-Reshitikhin-Turaev theory at an rth root of unity, the image of the mapping class group of a surface of genus g is dense.
11394439
Identifying topological order by entanglement entropy
Topological entanglement entropy provides a robust measure for detecting the long-range entanglement that characterizes quantum ground states displaying topological order. A new method for calculating this entropy isolates minimally entangled states from the ground states of a topological phase—offering a reliable test for identifying topological spin liquids.
119138174
On Metaplectic Modular Categories and Their Applications
For non-abelian simple objects in a unitary modular category, the density of their braid group representations, the #P-hard evaluation of their associated link invariants, and the BQP-completeness of their anyonic quantum computing models are closely related. We systematically study such properties of the non-abelian simple objects in the metaplectic modular categories SO(m)2 for an odd integer m ≥ 3. The simple objects with quantum dimensions $${\sqrt{m}}$$m have finite image braid group representations, and their link invariants are classically efficient to evaluate. We also provide classically efficient simulations of their braid group representations. These simulations of the braid group representations can be regarded as qudit generalizations of the Knill–Gottesmann theorem for the qubit case. The simple objects of dimension 2 give us a surprising result: while their braid group representations have finite images and are efficiently simulable classically after a generalized localization, their link invariants are #P-hard to evaluate exactly. We sharpen the #P-hardness by showing that any sufficiently accurate approximation of their associated link invariants is already #P-hard.
19017470
Topological properties of Abelian and non-Abelian quantum Hall states classified using patterns of zeros
It has been shown that different Abelian and non-Abelian fractional quantum Hall states can be characterized by patterns of zeros described by sequences of integers ${{S}_{a}}$. In this paper, we will show how to use the data ${{S}_{a}}$ to calculate various topological properties of the corresponding fraction quantum Hall state, such as the number of possible quasiparticle types and their quantum numbers, as well as the actions of the quasiparticle tunneling and modular transformations on the degenerate ground states on torus.
17172847
Topological graph polynomials and quantum field theory Part I: heat kernel theories
We investigate the relationship between the universal topological polynomials for graphs in mathematics and the parametric representation of Feynman amplitudes in quantum field theory. In this first paper we consider translation invariant theories with the usual heat-kernel-based propagator. We show how the Symanzik polynomials of quantum field theory are particular multivariate versions of the Tutte polynomial, and how the new polynomials of noncommutative quantum field theory are particular versions of the Bollob\'as-Riordan polynomials.
118521941
Relativistic quantum effects of Dirac particles simulated by ultracold atoms
Quantum simulation is a powerful tool to study a variety of problems in physics, ranging from high-energy physics to condensed-matter physics. In this article, we review the recent theoretical and experimental progress in quantum simulation of Dirac equation with tunable parameters by using ultracold neutral atoms trapped in optical lattices or subject to light-induced synthetic gauge fields. The effective theories for the quasiparticles become relativistic under certain conditions in these systems, making them ideal platforms for studying the exotic relativistic effects. We focus on the realization of one, two, and three dimensional Dirac equations as well as the detection of some relativistic effects, including particularly the well-known Zitterbewegung effect and Klein tunneling. The realization of quantum anomalous Hall effects is also briefly discussed.
118630803
Particle-in-cell mode beam dynamics simulation of the low energy beam transport for the SSC-linac injector
A new SSC-linac system (injector into separated sector cyclotron) is being designed in the HIRFL (heavy ion research facility of Lanzhou). As part of SSC-Linac, the LEBT (low energy beam transport) consists of seven solenoids, four quadrupoles, a bending magnet and an extra multi-harmonic buncher. The total length of this segment is about 7 meters. The beam dynamics in this LEBT has been studied using three-dimensional PIC (particle-in-cell) code BEAMPATH. The simulation results show that the continuous beam from the ion source is first well analyzed by a charge-to-mass selection system, and the beam of the selected charge-to-mass ratio is then efficiently pre-bunched by a multi-harmonic buncher and optimally matched into the RFQ (radio frequency quadrupole) for further acceleration. The principles and effects of the solenoid collimation channel are discussed, and it could limit the beam emittance by changing the aperture size.
118600395
Analysis of strong decays of the charmed mesons D(2550), D(2600), D(2750) and D(2760)
In this article, we study the strong decays of the newly observed charmed mesons D(2550), D(2600), D(2750), and D(2760) with the heavy quark effective theory in the leading order approximation, and tentatively identify the (D(2550),D(2600)) as the 2S doublet (0{sup -},1{sup -}) and the (D(2750),D(2760)) as the 1D doublet (2{sup -},3{sup -}), respectively. The identification of the D(2750) and D(2760) as the same particle with J{sup P}=3{sup -} is disfavored.
118873737
Laminar plasma dynamos
A new kind of dynamo utilizing flowing laboratory plasmas has been identified. The conversion of plasma kinetic energy to magnetic energy is verified numerically by kinematic dynamo simulations for magnetic Reynolds numbers above 210. As opposed to intrinsically-turbulent liquid-sodium dynamos, the proposed plasma dynamo corresponds to laminar flow topology. Modest plasma parameters (1–20 eV temperatures, 1019–1020 m−3 densities in 0.3–1.0 m scale-lengths driven by velocities on the order of the Alfven critical ionization velocity) self-consistently satisfy the conditions needed for the magnetic field amplication. Growth rates for plasma dynamos are obtained numerically with different geometry and magnetic Reynolds numbers. Magnetic-field-free coaxial plasma guns can be used to sustain the plasma flow and the dynamo.