Low-noise conditional operation of singlet-triplet coupled quantum dot qubits

We theoretically study the influence of charge noise on a controlled phase gate, implemented using two proximal double quantum dots coupled electrostatically. Using the configuration interaction method, we present a full description of the conditional control scheme and quantitatively calculate the gate error arising from charge fluctuations. Our key finding is that the existence of noise-immune sweet spots depends on not only the energy detuning but also the device geometry. The conditions for sweet spots with minimal charge noise are predicted analytically and verified numerically. Going beyond the simple sweet-spot concept we demonstrate the existence of other optimal situations for fast and low-noise singlet-triplet two-qubit gates.Comment: 4 pages, 4 figure

Topological flat band models with arbitrary Chern numbers

We report the theoretical discovery of a systematic scheme to produce topological flat bands (TFBs) with arbitrary Chern numbers. We find that generically a multi-orbital high Chern number TFB model can be constructed by considering multi-layer Chern number C=1 TFB models with enhanced translational symmetry. A series of models are presented as examples, including a two-band model on a triangular lattice with a Chern number C=3 and an $N$-band square lattice model with $C=N$ for an arbitrary integer $N$. In all these models, the flatness ratio for the TFBs is larger than 30 and increases with increasing Chern number. In the presence of appropriate inter-particle interactions, these models are likely to lead to the formation of novel Abelian and Non-Abelian fractional Chern insulators. As a simple example, we test the C=2 model with hardcore bosons at 1/3 filling and an intriguing fractional quantum Hall state is observed.Comment: 8 pages, 7 figure

Quantum theory of the charge stability diagram of semiconductor double quantum dot systems

We complete our recently introduced theoretical framework treating the double quantum dot system with a generalized form of Hubbard model. The effects of all quantum parameters involved in our model on the charge stability diagram are discussed in detail. A general formulation of the microscopic theory is presented, and truncating at one orbital per site, we study the implication of different choices of the model confinement potential on the Hubbard parameters as well as the charge stability diagram. We calculate the charge stability diagram keeping three orbitals per site and find that the effect of additional higher-lying orbitals on the subspace with lowest-energy orbitals only can be regarded as a small renormalization of Hubbard parameters, thereby justifying our practice of keeping only the lowest-orbital in all other calculations. The role of the harmonic oscillator frequency in the implementation of the Gaussian model potential is discussed, and the effect of an external magnetic field is identified to be similar to choosing a more localized electron wave function in microscopic calculations. The full matrix form of the Hamiltonian including all possible exchange terms, and several peculiar charge stability diagrams due to unphysical parameters are presented in the appendix, thus emphasizing the critical importance of a reliable microscopic model in obtaining the system parameters defining the Hamiltonian.Comment: 19 pages, 15 figure

Scalable High-Dimensional Multivariate Linear Regression for Feature-Distributed Data

Feature-distributed data, referred to data partitioned by features and stored across multiple computing nodes, are increasingly common in applications with a large number of features. This paper proposes a two-stage relaxed greedy algorithm (TSRGA) for applying multivariate linear regression to such data. The main advantage of TSRGA is that its communication complexity does not depend on the feature dimension, making it highly scalable to very large data sets. In addition, for multivariate response variables, TSRGA can be used to yield low-rank coefficient estimates. The fast convergence of TSRGA is validated by simulation experiments. Finally, we apply the proposed TSRGA in a financial application that leverages unstructured data from the 10-K reports, demonstrating its usefulness in applications with many dense large-dimensional matrices