LAUSR

We develop quantum simulation algorithms based on the light-front formulation of relativistic quantum field theories. We analyze a simple theory in $1+1D$ and show how to compute the analogues of parton distribution functions of composite particles in this theory. Upon quantizing the system in light-front coordinates, the Hamiltonian becomes block diagonal. Each block approximates the Fock space with a certain harmonic resolution $K$, where the light-front momentum is discretized in $K$ steps. The lower bound on the number of qubits required is $O(\sqrt{K})$, and we give a complete description of the algorithm in a mapping that requires $\widetilde{O}(\sqrt K)$ qubits. The cost of simulation of time evolution within a block of fixed $K$ is $\widetilde{O}(tK^4)$ gates. The cost of time-dependent simulation of adiabatic evolution for time $T$ along a Hamiltonian path with max norm bounded by final harmonic resolution $K$ is $\widetilde{O}(TK^4)$ gates. In higher dimensions, the qubit requirements scale as $\widetilde{O}(K)$. This is an advantage of the light-front formulation; in equal-time the qubit count will increase as the product of the momentum cutoffs over all dimensions. We provide qubit estimates for QCD in $3+1D$, and discuss measurements of form-factors and decay constants.