Solovay-Kitaev Decomposition Strategy for Single-Qubit Channels

Inspired by the Solovay-Kitaev decomposition for approximating unitary operations as a sequence of operations selected from a universal quantum computing gate set, we introduce a method for approximating any single-qubit channel using single-qubit gates and the controlled-NOT (CNOT). Our approach uses the decomposition of the single-qubit channel into a convex combination of "quasiextreme" channels. Previous techniques for simulating general single-qubit channels would require as many as 20 CNOT gates, whereas ours only needs one, bringing it within the range of current experiments

Fractional Quantum Hall Effect in Topological Flat Bands with Chern Number Two

Recent theoretical works have demonstrated various robust Abelian and non-Abelian fractional topological phases in lattice models with topological flat bands carrying Chern number C=1. Here we study hard-core bosons and interacting fermions in a three-band triangular-lattice model with the lowest topological flat band of Chern number C=2. We find convincing numerical evidence of bosonic fractional quantum Hall effect at the $\nu=1/3$ filling characterized by three-fold quasi-degeneracy of ground states on a torus, a fractional Chern number for each ground state, a robust spectrum gap, and a gap in quasihole excitation spectrum. We also observe numerical evidence of a robust fermionic fractional quantum Hall effect for spinless fermions at the $\nu=1/5$ filling with short-range interactions.Comment: 5 pages, 7 figures, with Supplementary Materia

A new approach to the study of the ground-state properties of 2D Ising spin glass

A new approach known as flat histogram method is used to study the +/-J Ising spin glass in two dimensions. Temperature dependence of the energy, the entropy, and other physical quantities can be easily calculated and we give the results for the zero-temperature limit. For the ground-state energy and entropy of an infinite system size, we estimate e0 = -1.4007 +/- 0.0085 and s0 = 0.0709 +/- 0.006, respectively. Both of them agree well with previous calculations. The time to find the ground-states as well as the tunneling times of the algorithm are also reported and compared with other methods.Comment: 11 pages, 4 figure

Detach and Adapt: Learning Cross-Domain Disentangled Deep Representation

While representation learning aims to derive interpretable features for describing visual data, representation disentanglement further results in such features so that particular image attributes can be identified and manipulated. However, one cannot easily address this task without observing ground truth annotation for the training data. To address this problem, we propose a novel deep learning model of Cross-Domain Representation Disentangler (CDRD). By observing fully annotated source-domain data and unlabeled target-domain data of interest, our model bridges the information across data domains and transfers the attribute information accordingly. Thus, cross-domain joint feature disentanglement and adaptation can be jointly performed. In the experiments, we provide qualitative results to verify our disentanglement capability. Moreover, we further confirm that our model can be applied for solving classification tasks of unsupervised domain adaptation, and performs favorably against state-of-the-art image disentanglement and translation methods.Comment: CVPR 2018 Spotligh

Non-Abelian Quantum Hall Effect in Topological Flat Bands

Inspired by recent theoretical discovery of robust fractional topological phases without a magnetic field, we search for the non-Abelian quantum Hall effect (NA-QHE) in lattice models with topological flat bands (TFBs). Through extensive numerical studies on the Haldane model with three-body hard-core bosons loaded into a TFB, we find convincing numerical evidence of a stable $\nu=1$ bosonic NA-QHE, with the characteristic three-fold quasi-degeneracy of ground states on a torus, a quantized Chern number, and a robust spectrum gap. Moreover, the spectrum for two-quasihole states also shows a finite energy gap, with the number of states in the lower energy sector satisfying the same counting rule as the Moore-Read Pfaffian state.Comment: 5 pages, 7 figure

Fractional Quantum Hall Effect of Hard-Core Bosons in Topological Flat Bands

Recent proposals of topological flat band (TFB) models have provided a new route to realize the fractional quantum Hall effect (FQHE) without Landau levels. We study hard-core bosons with short-range interactions in two representative TFB models, one of which is the well known Haldane model (but with different parameters). We demonstrate that FQHE states emerge with signatures of even number of quasi-degenerate ground states on a torus and a robust spectrum gap separating these states from higher energy spectrum. We also establish quantum phase diagrams for the filling factor 1/2 and illustrate quantum phase transitions to other competing symmetry-breaking phases.Comment: 4 pages, 6 figure