  We introduce a scheme for efficiently describing pure states of strongly
correlated fermions in higher dimensions using unitary circuits featuring a
causal cone. A local way of computing local expectation values is presented. We
formulate a dynamical reordering scheme, corresponding to time-adaptive
Jordan-Wigner transformation, that avoids nonlocal string operators. Primitives
of such a reordering scheme are highlighted. Fermionic unitary circuits can be
contracted with the same complexity as in the spin case. The scheme gives rise
to a variational description of fermionic models not suffering from a sign
problem. We present numerical examples on $9\times 9$ and $6\times 6$ fermionic
lattice model to show the functioning of the approach.
