Can today's quantum hardware simulate physics it wasn't built for?

Cold-atom quantum simulators are normally stuck modeling whatever physics their hardware naturally implements. This framework uses variational algorithms to stretch existing fermionic platforms to simulate a much broader class of quantum many-body systems — including superconducting pairing and fractional quantum Hall physics — with simulation time growing only polynomially in the precision required. Numerical tests across three distinct models suggest this is a genuine exponential speedup over brute-force classical methods.