  Quantum simulation is a promising near term application for mesoscale quantum
information processors, with the potential to solve computationally intractable
problems at the scale of just a few dozen interacting quantum systems. Recent
experiments in a range of technical platforms have demonstrated the basic
functionality of quantum simulation applied to quantum magnetism, quantum phase
transitions, and relativistic quantum mechanics. In all cases, the underlying
hardware platforms restrict the achievable inter-particle interaction, forming
a serious constraint on the ability to realize a versatile, programmable
quantum simulator. In this work, we address this problem by developing novel
sequences of unitary operations that engineer desired effective Hamiltonians in
the time-domain. The result is a hybrid programmable analog simulator
permitting a broad class of interacting spin-lattice models to be generated
starting only with an arbitrary long-range native inter-particle interaction
and single-qubit addressing. Specifically, our approach permits the generation
of all symmetrically coupled translation-invariant two-body Hamiltonians with
homogeneous on-site terms, a class which includes all spin-1/2 XYZ chains, but
generalized to include long-range couplings. Building on previous work proving
that universal simulation is possible using both entangling gates and
single-qubit unitaries, we show that determining the "program" of unitary
pulses to implement an arbitrary spin Hamiltonian can be formulated as a linear
program that runs in polynomial time and scales efficiently in hardware
resources. Our analysis extends from circuit model quantum information to
adiabatic quantum evolutions, where our approach allows for the creation of
non-native ground state solutions to a computation.
