Fig. 2

Downfolding a 6-qubit circuit for n time-steps down to a constant-depth circuit. a The 6-qubit circuit for evolving the system by n time-steps with the time-evolution operator U(nΔt). A box highlights the last six columns of matchgates to which the matchgate mirroring identity will be applied. b The 6-qubit circuit after application of the \(\mathcal {H_{CD}}\) matchgate mirroring identity. Pairs of adjacent matchgates on the same qubit pairs which can be combined into one matchgate with new parameters are highlighted with an outline. c The final constant-depth circuit for a 6-qubit circuit, which has six columns of matchgates