Fig. 2: Analogue and digital simulation.
From: Going beyond gadgets: the importance of scalability for analogue quantum simulators
A schematic description of our framework for analogue quantum simulation, in contrast with the digital approach. Both approaches aim to compute the observable expectation value \(\langle O\rangle (t)={{{\rm{tr}}}}[O{e}^{-itH}\rho {e}^{itH}]\), given an initial state ρ. The analogue simulator, which uses state encodings \({{{{\mathcal{E}}}}}_{{{{\rm{state}}}}}\) and \({{{{\mathcal{E}}}}}_{{{{\rm{obs}}}}}\) respectively, has accuracy ϵ if \(| {{{\rm{tr}}}}[O{e}^{-itH}\rho {e}^{itH}]-{{{\rm{tr}}}}[{{{{\mathcal{E}}}}}_{{{{\rm{obs}}}}}(O)({T}_{{t}^{\circ}} \, {{{{\mathcal{E}}}}}_{{{{\rm{state}}}}})(\rho )]| \le \epsilon\).
