  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 non-equilibrium 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, which 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 wavefunction 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.
