  Open quantum systems evolving according to discrete-time dynamics are
capable, unlike continuous-time counterparts, to converge to a stable
equilibrium in finite time with zero error. We consider dissipative quantum
circuits consisting of sequences of quantum channels subject to specified
quasi-locality constraints, and determine conditions under which stabilization
of a pure multipartite entangled state of interest may be exactly achieved in
finite time. Special emphasis is devoted to characterizing scenarios where
finite-time stabilization may be achieved robustly with respect to the order of
the applied quantum maps, as suitable for unsupervised control architectures.
We show that if a decomposition of the physical Hilbert space into virtual
subsystems is found, which is compatible with the locality constraint and
relative to which the target state factorizes, then robust stabilization may be
achieved by independently cooling each component. We further show that if the
same condition holds for a scalable class of pure states, a continuous-time
quasi-local Markov semigroup ensuring rapid mixing can be obtained. Somewhat
surprisingly, we find that the commutativity of the canonical parent
Hamiltonian one may associate to the target state does not directly relate to
its finite-time stabilizability properties, although in all cases where we can
guarantee robust stabilization, a (possibly non-canonical) commuting parent
Hamiltonian may be found. Beside graph states, quantum states amenable to
finite-time robust stabilization include a class of universal resource states
displaying two-dimensional symmetry-protected topological order, along with
tensor network states obtained by generalizing a construction due to Bravyi and
Vyalyi. Extensions to representative classes of mixed graph-product and thermal
states are also discussed.
