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We report individual confinement and two-axis qubit operations of two electron spin qubits in GaAs gate-defined sextuple quantum dot array with integrated micro-magnet. As a first step toward multiple qubit operations, we demonstrate coherent manipulations of three singlet-triplet qubits showing underdamped Larmor and Ramsey oscillations in all double dot sites. We provide an accurate measure of site site-dependent field gradients and rms electric and magnetic noise, and we discuss the adequacy of simple rectangular micro-magnet for practical use in multiple quantum dot arrays. We also discuss current limitations and possible strategies for realizing simultaneous multi multi-qubit operations in extended linear arrays.

Fast and high-fidelity quantum state detection is essential for building robust spin-based quantum information processing platforms in semiconductors. The Pauli spin blockade (PSB)-based spin-to-charge conversion and its variants are widely used for the spin state discrimination of two-electron singlet-triplet (ST$_0$) qubits; however, the single-shot measurement fidelity is limited by either the low signal contrast, or the short lifetime of the triplet state at the PSB energy detuning, especially due to strong mixing with singlet states at large magnetic field gradients. Ultimately, the limited single-shot measurement fidelity leads to low visibility of quantum operations. Here, we demonstrate an alternative method to achieve spin-to-charge conversion of ST$_0$ qubit states using energy selective tunneling between doubly occupied quantum dots (QDs) and electron reservoirs. We demonstrate a single-shot measurement fidelity of 90% and an S-T$_0$ oscillation visibility of 81% at a field gradient of 100 mT (~ 500 $MHz\cdot h \cdot(g^{*}\cdot \mu_B)^{-1}$); this allows single-shot readout with full electron charge signal contrast and, at the same time, long and tunable measurement time with negligible effect of relaxation even at strong magnetic field gradients. Using an rf-sensor positioned opposite to the QD array, we apply this method to two ST$_0$ qubits and show high-visibility readout of two individual single-qubit gate operations is possible with a single rf single-electron transistor sensor. We expect our measurement scheme for two-electron spin states can be applied to various hosting materials and provides a simplified and complementary route for multiple qubit state detection with high accuracy in QD-based quantum computing platforms.

We report raster scan multiplexed charge-stability diagram measurements for tuning multiple gate-defined quantum dots in GaAs/AlGaAs heterostructures. We evaluate the charge sensitivity of the quantum point contact (QPC) in both radio frequency (rf)-reflectometry and direct current (dc)-transport modes, where we measure the signal-to-noise ratio (SNR) of 40 for rf-QPC with integration time per pixel of 10ms , corresponding to 1.14ms for resolving single electron transition in few electron regime. The high SNR for reasonable integration time allows fast two-dimensional (2D) scanning, which we use to facilitate double and triple quantum dot tuning process. We configure highly stable raster scan multiplexed quantum dot tuning platform using a switching matrix and transformer-coupled alternating current (ac) ramp sources with software control. As an example of high-throughput multiple quantum dot tuning, we demonstrate systematic triple quantum dot (TQD) formation using this platform in which a multiplexed combination of 2D scans enables the identification of few electron regime in multiple quantum dots in just a few minutes. The method presented here is general, and we expect that the tuning platform is applicable to more complex multiple quantum dot arrays, allowing efficient quantum dot system Hamiltonian parameter calibration.

In this paper, we present a numerical algorithm for the accurate and efficient computation of the convolution of the frequency domain layered media Green's function with a given density function. Instead of compressing the convolution matrix directly as in the classical fast multipole method, fast direct solvers, and fast H-matrix algorithms, the new algorithm considers a translated form of the original matrix so that many existing building blocks from the highly optimized free-space fast multipole method can be easily adapted to the Sommerfeld integral representations of the layered media Green's function. An asymptotic analysis is performed on the Sommerfeld integrals for large orders to provide an estimate of the decay rate in the new "multipole" and "local" expansions. In order to avoid the highly oscillatory integrand in the original Sommerfeld integral representations when the source and target are close to each other, or when they are both close to the interface in the scattered field, mathematically equivalent alternative direction integral representations are introduced. The convergence of the multipole and local expansions and formulas and quadrature rules for the original and alternative direction integral representations are numerically validated., Comment: 27 pages

In this paper, we develop fast multipole methods for 3D Helmholtz kernel in layered media. Two algorithms based on different forms of Taylor expansion of layered media Green's function are developed. A key component of the first algorithm is an efficient algorithm based on discrete complex image approximation and recurrence formula for the calculation of the layered media Green's function and its derivatives, which are given in terms of Sommerfeld integrals. The second algorithm uses symmetric derivatives in the Taylor expansion to reduce the size of precomputed tables for the derivatives of layered media Green's function. Numerical tests in layered media have validated the accuracy and O(N) complexity of the proposed algorithms.

The classification of shapes is of great interest in diverse areas ranging from medical imaging to computer vision and beyond. While many statistical frameworks have been developed for the classification problem, most are strongly tied to early formulations of the problem - with an object to be classified described as a vector in a relatively low-dimensional Euclidean space. Statistical shape data have two main properties that suggest a need for a novel approach: (i) shapes are inherently infinite dimensional with strong dependence among the positions of nearby points, and (ii) shape space is not Euclidean, but is fundamentally curved. To accommodate these features of the data, we work with the square-root velocity function of the curves to provide a useful formal description of the shape, pass to tangent spaces of the manifold of shapes at different projection points which effectively separate shapes for pairwise classification in the training data, and use principal components within these tangent spaces to reduce dimensionality. We illustrate the impact of the projection point and choice of subspace on the misclassification rate with a novel method of combining pairwise classifiers.

Electron pairing due to a repulsive Coulomb interaction in a triple quantum dot (TQD) is experimentally studied. It is found that electron pairing in two dots of a TQD is mediated by the third dot, when the third dot strongly couples with the other two via Coulomb repulsion so that the TQD is in the twofold degenerate ground states of (1, 0, 0) and (0, 1, 1) charge configurations. Using the transport spectroscopy that monitors electron transport through each individual dot of a TQD, we analyze how to achieve the degeneracy in experiments, how the degeneracy is related to electron pairing, and the resulting nontrivial behavior of electron transport. Our findings may be used to design a system with nontrivial electron correlations and functionalities., Comment: 5 pages, 5 figures

A periodizing scheme and the method of fundamental solutions are used to solve acoustic wave scattering from doubly-periodic three-dimensional multilayered media. A scattered wave in a unit cell is represented by the sum of the near and distant contribution. The near contribution uses the free-space Green's function and its eight immediate neighbors. The contribution from the distant sources is expressed using proxy source points over a sphere surrounding the unit cell and its neighbors. The Rayleigh-Bloch radiation condition is applied to the top and bottom layers. Extra unknowns produced by the periodizing scheme in the linear system are eliminated using a Schur complement. The proposed numerical method avoids using singular quadratures and the quasi-periodic Green's function or complicated lattice sum techniques. Therefore, the proposed scheme is robust at all scattering parameters including Wood anomalies. The algorithm is also applicable to electromagnetic problems by using the dyadic Green's function. Numerical examples with 10-digit accuracy are provided. Finally, reflection and transmission spectra are computed over a wide range of incident angles for device characterization.