Symplectic Algebra for Quantum Computing Lattice Field Theory*

Lattice Field Theory  quatum computing  starts with a Hamiltonian discretized on

the base lattice manifold but also, due to current Quantum Hardware design, require

that  the field manifolds must be  drastically  reduced to very few Qubits per site.   The Quantum Link or D-theory framework

(Brower, Chandrasekharan and Wiese) is presented as a natural structure to accomplish while preserving  the Simplicial Algbra of the Hamiltonian

operator with very few  Fermionic Quibts per site. This  Fermionic structure can be converted into hard bosonic

(sigma) operators leading to a large class of Qubit Hamiltonians potentially

in the right Unversality class. This D-theory procedure is presented with particular

focus on the simplest compact  U(1) field manifold and  examples of 1 + 1 prototype Hamiltonians best suited

to earlly tests on  NISQ   era hardware are recommended.