Characterizing the Structure of Topological Insulator Thin Films

We describe the characterization of structural defects that occur during molecular beam epitaxy of topological insulator thin films on commonly used substrates. Twinned domains are ubiquitous but can be reduced by growth on smooth InP (111)A substrates, depending on details of the oxide desorption. Even with a low density of twins, the lattice mismatch between (Bi,Sb)2Te3 and InP can cause tilts in the film with respect to the substrate. We also briefly discuss transport in simultaneously top and back electrically gated devices using SrTiO3 and the use of capping layers to protect topological insulator films from oxidation and exposure

Supervised learning with quantum enhanced feature spaces

Machine learning and quantum computing are two technologies each with the potential for altering how computation is performed to address previously untenable problems. Kernel methods for machine learning are ubiquitous for pattern recognition, with support vector machines (SVMs) being the most well-known method for classification problems. However, there are limitations to the successful solution to such problems when the feature space becomes large, and the kernel functions become computationally expensive to estimate. A core element to computational speed-ups afforded by quantum algorithms is the exploitation of an exponentially large quantum state space through controllable entanglement and interference. Here, we propose and experimentally implement two novel methods on a superconducting processor. Both methods represent the feature space of a classification problem by a quantum state, taking advantage of the large dimensionality of quantum Hilbert space to obtain an enhanced solution. One method, the quantum variational classifier builds on [1,2] and operates through using a variational quantum circuit to classify a training set in direct analogy to conventional SVMs. In the second, a quantum kernel estimator, we estimate the kernel function and optimize the classifier directly. The two methods present a new class of tools for exploring the applications of noisy intermediate scale quantum computers [3] to machine learning.Comment: Fixed typos, added figures and discussion about quantum error mitigatio

Low temperature saturation of phase coherence length in topological insulators

Implementing topological insulators as elementary units in quantum technologies requires a comprehensive understanding of the dephasing mechanisms governing the surface carriers in these materials, which impose a practical limit to the applicability of these materials in such technologies requiring phase coherent transport. To investigate this, we have performed magneto-resistance (MR) and conductance fluctuations\ (CF) measurements in both exfoliated and molecular beam epitaxy grown samples. The phase breaking length ($l_{\phi}$) obtained from MR shows a saturation below sample dependent characteristic temperatures, consistent with that obtained from CF measurements. We have systematically eliminated several factors that may lead to such behavior of $l_{\phi}$ in the context of TIs, such as finite size effect, thermalization, spin-orbit coupling length, spin-flip scattering, and surface-bulk coupling. Our work indicates the need to identify an alternative source of dephasing that dominates at low $T$ in topological insulators, causing saturation in the phase breaking length and time

Probabilistic error cancellation for dynamic quantum circuits

Probabilistic error cancellation (PEC) is a technique that generates error-mitigated estimates of expectation values from ensembles of quantum circuits. In this work we extend the application of PEC from unitary-only circuits to dynamic circuits with measurement-based operations, such as mid-circuit measurements and classically-controlled (feedforward) Clifford operations. Our approach extends the sparse Pauli-Lindblad noise model to measurement-based operations while accounting for non-local measurement crosstalk in superconducting processors. Our mitigation and monitoring experiments provide a holistic view for the performance of the protocols developed in this work. These capabilities will be a crucial tool in the exploration of near-term dynamic circuit applications.Comment: Minor updates to v

Interplay between ferromagnetism, surface states, and quantum corrections in a magnetically doped topological insulator

The breaking of time-reversal symmetry by ferromagnetism is predicted to yield profound changes to the electronic surface states of a topological insulator. Here, we report on a concerted set of structural, magnetic, electrical and spectroscopic measurements of \MBS thin films wherein photoemission and x-ray magnetic circular dichroism studies have recently shown surface ferromagnetism in the temperature range 15 K $\leq T \leq 100$ K, accompanied by a suppressed density of surface states at the Dirac point. Secondary ion mass spectroscopy and scanning tunneling microscopy reveal an inhomogeneous distribution of Mn atoms, with a tendency to segregate towards the sample surface. Magnetometry and anisotropic magnetoresistance measurements are insensitive to the high temperature ferromagnetism seen in surface studies, revealing instead a low temperature ferromagnetic phase at $T \lesssim 5$ K. The absence of both a magneto-optical Kerr effect and anomalous Hall effect suggests that this low temperature ferromagnetism is unlikely to be a homogeneous bulk phase but likely originates in nanoscale near-surface regions of the bulk where magnetic atoms segregate during sample growth. Although the samples are not ideal, with both bulk and surface contributions to electron transport, we measure a magnetoconductance whose behavior is qualitatively consistent with predictions that the opening of a gap in the Dirac spectrum drives quantum corrections to the conductance in topological insulators from the symplectic to the orthogonal class.Comment: To appear in Phys. Rev.