On the Principles of Differentiable Quantum Programming Languages

Variational Quantum Circuits (VQCs), or the so-called quantum neural-networks, are predicted to be one of the most important near-term quantum applications, not only because of their similar promises as classical neural-networks, but also because of their feasibility on near-term noisy intermediate-size quantum (NISQ) machines. The need for gradient information in the training procedure of VQC applications has stimulated the development of auto-differentiation techniques for quantum circuits. We propose the first formalization of this technique, not only in the context of quantum circuits but also for imperative quantum programs (e.g., with controls), inspired by the success of differentiable programming languages in classical machine learning. In particular, we overcome a few unique difficulties caused by exotic quantum features (such as quantum no-cloning) and provide a rigorous formulation of differentiation applied to bounded-loop imperative quantum programs, its code-transformation rules, as well as a sound logic to reason about their correctness. Moreover, we have implemented our code transformation in OCaml and demonstrated the resource-efficiency of our scheme both analytically and empirically. We also conduct a case study of training a VQC instance with controls, which shows the advantage of our scheme over existing auto-differentiation for quantum circuits without controls.Comment: Codes are available at https://github.com/LibertasSpZ/adcompil

KESSLER: A MACHINE LEARNING LIBRARY FOR SPACECRAFT COLLISION AVOIDANCE

As megaconstellations are launched and the space sector grows, space debris pollution is posing an increasing threat to operational spacecraft. Low Earth orbit is a junkyard of dead satellites, rocket bodies, shrapnels, and other debris that travel at very high speed in an uncontrolled manner. Collisions at orbital speeds can generate fragments and potentially trigger a cascade of more collisions endangering the whole population, a scenario known since the late 1970s as the Kessler syndrome. In this work we present Kessler: an open-source Python package for machine learning (ML) applied to collision avoidance. Kessler provides functionalities to import and export conjunction data messages (CDMs) in their standard format and predict the evolution of conjunction events based on explainable ML models. In Kessler we provide Bayesian recurrent neural networks that can be trained with existing collections of CDM data and then deployed in order to predict the contents of future CDMs in a given conjunction event, conditioned on all CDMs received up to now, with associated uncertainty estimates about all predictions. Furthermore Kessler includes a novel generative model of conjunction events and CDM sequences implemented using probabilistic programming, simulating the CDM generation process of the Combined Space Operations Center (CSpOC). The model allows Bayesian inference and also the generation of large datasets of realistic synthetic CDMs that we believe will be pivotal to enable further ML approaches given the sensitive nature and public unavailability of real CDM data

Towards Automated Satellite Conjunction Management with Bayesian Deep Learning

After decades of space travel, low Earth orbit is a junkyard of discarded rocket bodies,dead satellites, and millions of pieces of debris from collisions and explosions.Objects in high enough altitudes do not re-enter and burn up in the atmosphere, butstay in orbit around Earth for a long time. With a speed of 28,000 km/h, collisionsin these orbits can generate fragments and potentially trigger a cascade of morecollisions known as the Kessler syndrome. This could pose a planetary challenge,because the phenomenon could escalate to the point of hindering future spaceoperations and damaging satellite infrastructure critical for space and Earth scienceapplications. As commercial entities place mega-constellations of satellites in orbit,the burden on operators conducting collision avoidance manoeuvres will increase.For this reason, development of automated tools that predict potential collisionevents (conjunctions) is critical. We introduce a Bayesian deep learning approachto this problem, and develop recurrent neural network architectures (LSTMs) thatwork with time series of conjunction data messages (CDMs), a standard data formatused by the space community. We show that our method can be used to modelall CDM features simultaneously, including the time of arrival of future CDMs,providing predictions of conjunction event evolution with associated uncertainties