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"In late spring 1940, Nazi Germany's domination of Europe looked unstoppable. With the British Isles in easy reach since the fall of France, Adolf Hitler was convinced that Great Britian would be defeated in the skies over the southern coast, confident his Messerchmitts and Heinkels would outclass anything the Royal Air Force threw at them. What Hitler hadn't planned for was the agility and resilience of a marvel of British engineering that would quickly pass into legend: the Spitfire. ... Here are edge-of-the-seat tales and heartstopping first-hand accounts of battling pilots, some forced to bail out over enemy territory ; of sacrifice and wartime love ; of aristocratic female flyers ; of the mechanics who braved the Nazi onslaught to keep the aircraft in battle-ready condition."--Book jacket

Heisenberg exchange coupling between neighboring electron spins in semiconductor quantum dots provides a powerful tool for quantum information processing and simulation. Although so far unrealized, extended Heisenberg spin chains can enable long-distance quantum information transfer and the generation of nonequilibrium quantum states. In this work, we implement simultaneous, coherent exchange coupling between all nearest-neighbor pairs of spins in a quadruple quantum dot. The main challenge in implementing simultaneous exchange couplings is the nonlinear and nonlocal dependence of the exchange couplings on gate voltages. Through a combination of electrostatic simulation and theoretical modeling, we show that this challenge arises primarily due to lateral shifts of the quantum dots during gate pulses. Building on this insight, we develop two models that can be used to predict the confinement gate voltages for a desired set of exchange couplings. Although the model parameters depend on the number of exchange couplings desired (suggesting that effects in addition to lateral wave-function shifts are important), the models are sufficient to enable simultaneous and independent control of all three exchange couplings in a quadruple quantum dot. We demonstrate two-, three-, and four-spin exchange oscillations, and our data agree with simulations. ; Defense Advanced Research Projects AgencyUnited States Department of DefenseDefense Advanced Research Projects Agency (DARPA) [D18AC00025]; Army Research Office [W911NF16-1-0260, W911NF-19-1-0167]; National Science FoundationNational Science Foundation (NSF) [DMR-1941673] ; This research was sponsored by the Defense Advanced Research Projects Agency under Grant No. D18AC00025, the Army Research Office under Grants No. W911NF16-1-0260 and No. W911NF-19-1-0167, and the National Science Foundation under Grant No. DMR-1941673. The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the official policies, either expressed or implied, of the Army Research Office or the U.S. Government. The U.S. Government is authorized to reproduce and distribute reprints for Government purposes notwithstanding any copyright notation herein.