  We propose a method for general-purpose quantum computation and simulation
that is well suited for today's pre-threshold-fidelity superconducting qubits.
This approach makes use of the $n$-dimensional single-excitation subspace (SES)
of a system of $n$ tunably coupled qubits. It can be viewed as a nonscalable
special case of the standard gate-based quantum computing model, but allows
many operations in the unitary group SU($n$) to be implemented by a single
application of the Hamiltonian. Our approach bypasses the need to decompose the
evolution operator into elementary gates, making large, nontrivial computations
possible without error correction. The method is especially well suited for
universal quantum simulation, specifically simulation of the Schr\"odinger
equation with a real but otherwise arbitrary $n \times n$ Hamiltonian. We argue
that a 1000-qubit SES processor, which would require no known improvements in
superconducting device technology and which could be built today, should be
capable of achieving quantum speedup relative to a petaflop supercomputer. We
speculate on the utility and practicality of such a universal quantum
simulator.
