We propose and analyze the effect of anyonic interferometers that are designed such that the probe anyons traveling in a given path through the interferometer twist or braid around each other. These "twisted" interferometers are found to provide operational utility that may not be available from anyon braiding operations and standard (untwisted) anyonic interferometry measurements. In particular, it enables Ising anyons to generate "magic states," which can be used to implement pi/8-phase gates. We consider the possible implementations of such twisted interferometers in quantum Hall systems, 2D p_x + i p_y superconductors, and 2D Majorana heterostructures, and discuss obstacles and challenges associated with implementation.
We describe measurement-only topological quantum computation using both projective and interferometrical measurement of topological charge. We demonstrate how anyonic teleportation can be achieved using "forced measurement" protocols for both types of measurement. Using this, it is shown how topological charge measurements can be used to generate the braiding transformations used in topological quantum computation, and hence that the physical transportation of computational anyons is unnecessary. We give a detailed discussion of the anyonics for implementation of topological quantum computatio…
Proposals to measure non-Abelian anyons in a superconductor by quantum interference of vortices suffer from the predominantly classical dynamics of the normal core of an Abrikosov vortex. We show how to avoid this obstruction using coreless Josephson vortices, for which the quantum dynamics has been demonstrated experimentally. The interferometer is a flux qubit in a Josephson junction circuit, which can nondestructively read out a topological qubit stored in a pair of anyons --- even though the Josephson vortices themselves are not anyons. The flux qubit does not couple to intra-vortex excita…
We examine interferometric measurements of the topological charge of (non-Abelian) anyons. The target's topological charge is measured from its effect on the interference of probe particles sent through the interferometer. We find that superpositions of distinct anyonic charges a and a' in the target decohere (exponentially in the number of probes particles used) when the probes have nontrivial monodromy with the charges that may be fused with a to give a'.
Since the anyonic excitations in the Kitaev toric model are perfectly localized quasiparticles, it is possible to generate dynamically the ground state and the excitations of the model Hamiltonian to simulate the anyonic interferometry. We propose a scheme in circuit QED to simulate the interferometry. The qubit-cavity interaction can be engineered to realize effective state control as well as the controlled dynamics of qubits, which are sufficient to prepare the ground states, create and remove the anyonic excitation, and simulate the anyonic interferometry. The simplicity and high fidelity o…
Recently a pair of experiments demonstrated a simulation of Abelian anyons in a spin network of single photons. The experiments were based on an Abelian discrete gauge theory spin lattice model of Kitaev. Here we describe how to use linear optics and single photons to simulate non-Abelian anyons. The scheme makes use of joint qutrit-qubit encoding of the spins and the resources required are three pairs of parametric down converted photons and 14 beam splitters.
Strongly correlated quantum systems can exhibit exotic behavior called topological order which is characterized by non-local correlations that depend on the system topology. Such systems can exhibit remarkable phenomena such as quasi-particles with anyonic statistics and have been proposed as candidates for naturally fault-tolerant quantum computation. Despite these remarkable properties, anyons have never been observed in nature directly. Here we describe how to unambiguously detect and characterize such states in recently proposed spin lattice realizations using ultra-cold atoms or molecules…
Three manifold topology is used to analyze the effect of anyonic interferometers in which the probe anyons' path along an arm crosses itself, leading to a "twisted" or braided space-time trajectory for the probe anyons. In the case of Ising non-Abelian anyons, twisted interferometry is shown to be able to generate a topologically protected $π/8$-phase gate, which cannot be generated from quasiparticle braiding.
We develop the general quantum measurement theory of non-Abelian anyons through interference experiments. The paper starts with a terse introduction to the theory of anyon models, focusing on the basic formalism necessary to apply standard quantum measurement theory to such systems. This is then applied to give a detailed analysis of anyonic charge measurements using a Mach-Zehnder interferometer for arbitrary anyon models. We find that, as anyonic probes are sent through the legs of the interferometer, superpositions of the total anyonic charge located in the target region collapse when they …
We demonstrate that twisted equivariant differential K-theory of transverse complex curves accommodates exotic charges of the form expected of codimension=2 defect branes, such as of D7-branes in IIB/F-theory on A-type orbifold singularities, but also of their dual 3-brane defects of class-S theories on M5-branes. These branes have been argued, within F-theory and the AGT correspondence, to carry special SL(2)-monodromy charges not seen for other branes, but none of these had previously been identified in the expected brane charge quantization law given by K-theory. Here we observe that it is …
The distinct methods for measuring topological charge in a non-abelian anyonic system have been discussed in the literature: projective measurement of a single point-like quasiparticle and interferometric measurement of the total topological charge of a group of quasiparticles. Projective measurement by definition is only applied near a point and will project to a topological charge sector near that point. Thus, if it is to be applied to a \emph{group} of anyons to project to a \emph{total} charge, then the anyons must first be fused one by one to obtain a single anyon carrying the collective …
Preparation of a non-classically correlated state is the first step of any quantum-enhanced interferometric protocol. An efficient method is the one-axis twisting, which entangles a collection of initially uncorrelated particles by means of two-body interactions. Here we investigate the limits of the quantum improvement which can be reached with this method in realistic experimental conditions. We demonstrate that the usefulness of this entangling mechanism is a result of fine structures introduced into the quantum state. The scale at which these structures vary allows us to identify the minim…
Quasi-particles are elementary excitations of condensed matter quantum phases. Demonstrating that they keep quantum coherence while propagating is a fundamental issue for their manipulation for quantum information tasks. Here, we consider anyons, the fractionally charged quasi-particles 20 of the Fractional Quantum Hall Effect occurring in two-dimensional electronic conductors in high magnetic fields. They obey anyonic statistics, intermediate between fermionic and bosonic. Surprisingly, anyons show large quantum coherence when transmitted through the localized states of electronic Fabry-Pérot…
In an adiabatic rapid passage experiment, the Bloch vector of a two-level system (qubit) is inverted by slowly inverting an external field to which it is coupled, and along which it is initially aligned. In twisted rapid passage, the external field is allowed to twist around its initial direction with azimuthal angle $ϕ(t)$ at the same time that it is inverted. For polynomial twist: $ϕ(t) \sim Bt^{n}$. We show that for $n \geq 3$, multiple avoided crossings can occur during the inversion of the external field, and that these crossings give rise to strong interference effects in the qubit trans…
We have investigated the properties of a model of 1D anyons interacting through a $δ$-function repulsive potential. The structure of the quasi-periodic boundary conditions for the anyonic field operators and the many-anyon wavefunctions is clarified. The spectrum of the low-lying excitations including the particle-hole excitations is calculated for periodic and twisted boundary conditions. Using the ideas of the conformal field theory we obtain the large-distance asymptotics of the density and field correlation function at the critical temperature T=0 and at small finite temperatures. Our expr…
Interferometric Braiding of Anyons in Chern Insulators
Ludwig-Maximilians-Universität München（慕尼黑大学）；Munich Center for Quantum Science and Technology (MCQST)（慕尼黑量子科学与技术中心）；Université Libre de Bruxelles（布鲁塞尔自由大学）；Collège de France（法兰西公学院）；Sorbonne Université（索邦大学）；International Solvay Institutes（国际索尔维研究所）
