  A causal set C can describe a discrete spacetime, but this discrete spacetime
is not quantum, because C is endowed with Boolean logic, as it does not allow
cycles. In a quasi-ordered set Q, cycles are allowed. In this paper, we
consider a subset QC of a quasi-ordered set Q, whose elements are all the
cycles. In QC, which is endowed with quantum logic, each cycle of maximal
outdegree N in a node, is associated with N entangled qubits. Then QC describes
a quantum computing spacetime. This structure, which is non-local and
non-casual, can be understood as a proto-spacetime. Micro-causality and
locality can be restored in the subset U of Q whose elements are unentangled
qubits which we interpret as the states of quantum spacetime. The mapping of
quantum spacetime into proto-spacetime is given by the action of the XOR gate.
Moreover, a mapping is possible from the Boolean causal set into U by the
action of the Hadamard gate. In particular, the causal order defined on the
elements of U induces the causal evolution of spin networks.
