  Decoupling systems into independently evolving components has a long history
of simplifying seemingly complex systems. They enable a better understanding of
the underlying dynamics and causal structures while providing more efficient
means to simulate such processes on a computer. Here we outline a variational
decoupling algorithm for decoupling unitary quantum dynamics -- allowing us to
decompose a given $n$-qubit unitary gate into multiple independently evolving
sub-components. We apply this approach to quantum circuit synthesis - the task
of discovering quantum circuit implementations of target unitary dynamics. Our
numerical studies illustrate significant benefits, showing that variational
decoupling enables us to synthesize general $2$ and $4$-qubit gates to fidelity
that conventional variational circuits cannot reach.
