Quantum experiments are performed in noisy platforms. In NISQ devices, realistic setups can be described by open systems or noisy Hamiltonians. Starting from a generic noisy Hamiltonian, I will first present a scheme to simulate long-range and many-body interactions in a quantum platform [1]. We then engineer a protocol for the fast thermalization of a harmonic oscillator [2], which can be adapted to generate squeezed thermal states [3] in arbitrary time. 

Then, going beyond the noise-averaged density matrix, I will introduce the concept of stochastic operator variance (SOV) of an observable. The SOV [4]  is an operator that characterizes the deviation of any operator from the noise-averaged operator in a stochastic evolution governed by the Hamiltonian. As such, it is relevant in the quantum simulation of open systems using NISQ devices, e.g., to engineer a given dissipative evolution. Surprisingly, we find that the evolution of the noise-averaged variance relates to an out-of-time-order correlator (OTOC), which connects fluctuations of the system with scrambling. This connection may allow computing the Lyapunov exponent and experimentally access OTOCs without the need to invert the sign of the Hamiltonian. I will illustrate the results in the stochastic LMG model, and show how noise changes the phase diagram of the system.

[1] A. Chenu, M. Beau, J. Cao, and A. del Campo, Quantum Simulation of Generic Many-Body Open System Dynamics Using Classical Noise. Phys. Rev. Lett. 118:140403 (2017).

[2] L. Dupays, I. L. Egusquiza, A. del Campo, and A. Chenu. Superadiabatic thermalization of a quantum oscillator by engineered dephasing, Phys. Rev. Res. 2:033178 (2020).

[3] L. Dupays and A. Chenu. Dynamical engineering of squeezed thermal state, Quantum 5:449 (2021).

[4] P. Martinez-Azcona, A.Kundu, A. del Campo, and A. Chenu, ArXiv:2302.12845 (2023).