Quantum Simulation of Generic Many-Body Open System Dynamics Using Classical Noise

We introduce a scheme for the quantum simulation of many-body decoherence based on the unitary evolution of a stochastic Hamiltonian. Modulating the strength of the interactions with stochastic processes, we show that the noise-averaged density matrix simulates an effectively open dynamics governed by $k$-body Lindblad operators. Markovian dynamics can be accessed with white-noise fluctuations; non-Markovian dynamics requires colored noise. The time scale governing the fidelity decay under many-body decoherence is shown to scale as $N^{-2k}$ with the system size $N$. Our proposal can be readily implemented in a variety of quantum platforms including optical lattices, superconducting circuits, and trapped ions.

Figure 1

Quantum simulation of many-body decoherence. The implementation in a quantum simulator of the unitary dynamics generated by a Hamiltonian with stochastic many-body terms is used to study the open dynamics induced by an environment $\mathcal{E}$ that monitors many-body operators of the system $\mathcal{S}$. The red traits illustrate the $k$-body interactions which are general in our simulation scheme—specifically long-range and 4-body interaction in this illustration.