No abstract

We propose and investigate a new method of quantum process tomography (QPT) which we call projected least squares (PLS). In short, PLS consists of first computing the least-squares estimator of the Choi matrix of an unknown channel, and subsequently projecting it onto the convex set of Choi matrices. We consider four experimental setups including direct QPT with Pauli eigenvectors as input and Pauli measurements, and ancilla-assisted QPT with mutually unbiased bases (MUB) measurements. In each case, we provide a closed form solution for the least-squares estimator of the Choi matrix. We propose a novel, two-step method for projecting these estimators onto the set of matrices representing physical quantum channels, and a fast numerical implementation in the form of the hyperplane intersection projection algorithm. We provide rigorous, non-asymptotic concentration bounds, sampling complexities and confidence regions for the Frobenius and trace-norm error of the estimators. For the Frobenius error, the bounds are linear in the rank of the Choi matrix, and for low ranks, they improve the error rates of the least squares estimator by a factor d2, where d is the system dimension. We illustrate the method with numerical experiments involving channels on systems with up to 7 qubits, and find that PLS has highly competitive accuracy and computational tractability.

We propose and investigate a new method of quantum process tomography (QPT) which we call projected least squares (PLS). In short, PLS consists of first computing the least-squares estimator of the Choi matrix of an unknown channel, and subsequently projecting it onto the convex set of Choi matrices. We consider four experimental setups including direct QPT with Pauli eigenvectors as input and Pauli measurements, and ancilla-assisted QPT with mutually unbiased bases (MUB) measurements. In each case, we provide a closed form solution for the least-squares estimator of the Choi matrix. We propose a novel, two-step method for projecting these estimators onto the set of matrices representing physical quantum channels, and a fast numerical implementation in the form of the hyperplane intersection projection algorithm. We provide rigorous, non-asymptotic concentration bounds, sampling complexities and confidence regions for the Frobenius and trace-norm error of the estimators. For the Frobenius error, the bounds are linear in the rank of the Choi matrix, and for low ranks, they improve the error rates of the least squares estimator by a factor d 2 , where d is the system dimension. We illustrate the method with numerical experiments involving channels on systems with up to 7 qubits, and find that PLS has highly competitive accuracy and computational tractability.

Abstract. The fracturing of glaciers and ice shelves in Antarctica influences their dynamics, and may introduce as-yet poorly understood feedbacks and hysteresis into the ice sheet system. Therefore, data on the evolving distribution of crevasses is required to better understand the evolution of the ice sheet, though such data has traditionally been difficult and time consuming to generate. Here, we present an automated method of mapping crevasses on grounded and floating ice with the application of convolutional neural networks to Sentinel-1 synthetic aperture radar backscatter images acquired between 2015 and 2022. We apply this method across Antarctica to produce a 7-and-a-half year record of composite fracture maps at monthly intervals and 50 m spatial resolution, showing the distribution of crevasses around the majority of the ice sheet margin. We develop a method of quantifying changes to the density of ice shelf fractures using the timeseries of crevasse maps, and show increases in crevassing on the Thwaites and Pine Island ice shelves over the observational period, with observed changes elsewhere in the Amundsen Sea dominated by the advection of existing crevasses. Using stress fields computed using the BISICLES ice sheet model, we show that much of this structural change has occurred in strongly buttressing regions of these ice shelves, indicating a recent and ongoing link between fracturing and the developing dynamics of the Amundsen Sea Sector.

<p>The majority of ice mass loss in West Antarctica is due to the ejection of grounded ice into the sea via ice-dynamic processes. Structural changes that impact the flow speed of marine-terminating glaciers can, therefore, impact their contribution to global sea level rise. Thwaites Glacier is among those for which these considerations are particularly important, due to its potential connection to the stability of the West Antarctic ice sheet, and the structural changes that have been observed at its terminus in recent years. However, the interactions between ice structural properties and flow speed are not well established, partly due to the limited availability of coincident observations.</p><p>We present weekly ice velocity measurements, derived using Sentinel-1 radar data, showing the recent onset of episodic dynamic variability in the form of two large-magnitude ~30%-45% acceleration/deceleration events between 2017 and 2021, occurring across the majority of the remnant of Thwaites Glacier's floating ice tongue, before a relaxation to the 2015/16 mean speed. Using deep learning methods, we measured a synchronous decrease in the structural integrity of the ice tongue and its eastern shear margin during the study period, and the upstream propagation of these regions of damaged ice. The pattern of change seen in the concurrent damage and ice velocity observations suggests a link between the two, which we explore in the work. The existence of this link is further supported by ice flow modelling, carried out using the BISICLES ice sheet model, in which the spatial pattern and concentration of observed damage are closely reproduced when forced with the observed speed changes.</p><p>Our results add to the growing body of evidence that the extent and degree of damaged ice has a significant distributed effect on ice velocity, and further demonstrate that damage processes must be integrated in ice sheet models in order to make accurate predictions of long-term behaviour and sea level contribution.</p>