  A new quantum link microstructure was proposed for the lattice quantum
chromodynamics (QCD) Hamiltonian, replacing the Wilson gauge links with a
bilinear of fermionic qubits, later generalized to D-theory. This formalism
provides a general framework for building lattice field theory algorithms for
quantum computing. We focus mostly on the simplest case of a quantum rotor for
a single compact $U(1)$ field. We also make some progress for non-Abelian
setups, making it clear that the ideas developed in the $U(1)$ case extend to
other groups. These in turn are building blocks for $1 + 0$-dimensional ($1 +
0$-D) matrix models, $1 + 1$-D sigma models and non-Abelian gauge theories in
$2+1$ and $3+1$ dimensions. By introducing multiple flavors for the $U(1)$
field, where the flavor symmetry is gauged, we can efficiently approach the
infinite-dimensional Hilbert space of the quantum $O(2)$ rotor with increasing
flavors. The emphasis of the method is on preserving the symplectic algebra
exchanging fermionic qubits by sigma matrices (or hard bosons) and developing a
formal strategy capable of generalization to $SU(3)$ field for lattice QCD and
other non-Abelian $1 + 1$-D sigma models or $3 +3$-D gauge theories. For
$U(1)$, we discuss briefly the qubit algorithms for the study of the discrete
$1+1$-D Sine-Gordon equation.
