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A large team of researchers working with Google Inc. and affiliated with a host of institutions in the U.S., one in Germany and one in the Netherlands has implemented a quantum approximate optimization algorithm (QAOA) on a 53-qubit noisy intermediate-scale quantum (NISQ) device. In their paper published in the journal Nature Physics,, the group describes their method of studying the performance of their QAOA on Google's Sycamore superconducting 53-qubit quantum processor and what they learned from it. Boaz Barak with Harvard University has published a News & Views piece on the work done by the team in the same journal issue.

"With each interaction, Alexa is training to hear better, to interpret more precisely, to trigger actions that map to the user's commands more accurately, and to build a more complete model of their preferences, habits and desires. What is required to make this possible? Put simply: each small moment of convenience - be it answering a question, turning on a light, or playing a song - requires a vast planetary network, fueled by the extraction of non-renewable materials, labor, and data. The scale of resources required is many magnitudes greater than the energy and labor it would take a human to operate a household appliance or flick a switch. A full accounting for these costs is almost impossible, but it is increasingly important that we grasp the scale and scope if we are to understand and govern the technical infrastructures that thread through our lives. III The Salar, the world's largest flat surface, is located in southwest Bolivia at an altitude of 3,656 meters above sea level. It is a high plateau, covered by a few meters of salt crust which are exceptionally rich in lithium, containing 50% to 70% of the world's lithium reserves. 4 The Salar, alongside the neighboring Atacama regions in Chile and Argentina, are major sites for lithium extraction. This soft, silvery metal is currently used to power mobile connected devices, as a crucial material used for the production of lithium-Ion batteries. It is known as 'grey gold.' Smartphone batteries, for example, usually have less than eight grams of this material. 5 Each Tesla car needs approximately seven kilograms of lithium for its battery pack. 6 All these batteries have a limited lifespan, and once consumed they are thrown away as waste. Amazon reminds users that they cannot open up and repair their Echo, because this will void the warranty. The Amazon Echo is wall-powered, and also has a mobile battery base. This also has a limited lifespan and then must be thrown away as waste. According to the Ay

Numerical results show that school closure alone would have limited benefit in reducing the peak incidence (less than 10% reduction with 8-week school closure for regions in the early phase of the epidemic). When coupled with 25% adults teleworking, 8-week school closure would be enough to delay the peak by almost 2 months with an approximately 40% reduction of the case incidence at the peak. This is critical to reduce the burden on the healthcare system in the weeks of highest demand. Moderate overall reduction of the final attack rate (15%) would also be achieved. Results across regions are qualitatively similar, with differences

"It is now possible to trace the migratory paths of anatomically modern humans using genetic data. Early research pointed to a sub-Saharan African origin for modern humans by around 200,000-150,000 years ago1, and analyses of autosomal markers2 and Y DNA haplogroups3, 4 suggest the earliest structuring of the human population occurred approximately 140,000 years ago5,6,7,8. Initial efforts to characterize the movement of early humans in relation to ancestry grouped populations according to five geographical regions: Sub-Saharan Africa, Europe/the Middle East/Central Asia/South Asia, East Asia, Oceania, and the Americas9. Subsequent analyses allowed for refinement of the genetic history of global ancestries, revealing regional structure through the identification of 710, 1411, and 19 ancestries2."

Optimization is a key tool in machine learning, where the goal is to achieve the best possible objective function value in a minimum amount of time. Obtaining any form of global guarantees can usually be done with convex objective functions, or with special cases such as risk minimization with one-hidden over-parameterized layer neural networks (see the June post). In this post, I will consider low-dimensional problems (imagine 10 or 20), with no constraint on running time (thus get ready for some running-times that are exponential in dimension!).