Variational Quantum Circuit Decoupling

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.