Fig. 4: Dissipative gadget evolution.
From: Going beyond gadgets: the importance of scalability for analogue quantum simulators
Circuit representation of the non-unitary gadget procedure for a single timestep. The initial state \({\left\vert {\psi }_{0}(0)\right\rangle }_{{{{\mathcal{H}}}}}{\left\vert 0\right\rangle }_{{{{\mathcal{A}}}}}\) is evolved under a Hamiltonian \({H}^{{\prime} }\) for time δt, resulting in a superposition of states with the ancillary qubit in the \({\left\vert 0\right\rangle }_{{{{\mathcal{A}}}}}\) and \({\left\vert 1\right\rangle }_{{{{\mathcal{A}}}}}\) positions. After applying the dissipative channel to the \({{{\mathcal{A}}}}\) system, the system collapses to its \({\left\vert 0\right\rangle }_{{{{\mathcal{A}}}}}\) state with high probability due to the quantum Zeno effect. Meanwhile, the resulting state on the \({{{\mathcal{H}}}}\) system approximately corresponds to evolution under a different Hamiltonian, \({H}_{{{{\mathcal{H}}}}}\).
