A Note on Comprehensive Derivation of N-Qubit Lindblad Master Equations from Quantum Noise Channels

Pierre Rouchon

Hiba Chakir, Farid Abdi, F. M. Abbou

Characterizing the interactions between quantum systems and their environment is a major limitation to the development of robust quantum technologies. In this article, the dynamics of the qubit are analyzed under the influence of two quantum noise channels, the amplitude damping channel and the pure dephasing channel. We evaluate their respective and combined impact on the quantum state and the evolution of populations and coherence over time. we also present a comprehensive framework for performing Lindblad equation using Physics-Informed Neural Networks (PINNs). Our approach relies on learning the Lindblad equation to simulate the evolution of the quantum state under quantum noise channels. Our results demonstrate that PINN model can reproduce the dynamics of the quantum system, thus offering an efficient modeling of open quantum systems.

Evan Borras, Milad Marvian

We present a quantum algorithm for simulating a family of Markovian master equations that can be realized through a probabilistic application of unitary channels and state preparation. Our approach employs a second-order product formula for the Lindblad master equation, achieved by decomposing the dynamics into dissipative and Hamiltonian components and replacing the dissipative segments with randomly compiled, easily implementable elements. The sampling approach eliminates the need for ancillary qubits to simulate the dissipation process and reduces the gate complexity in terms of the number of jump operators. We provide a rigorous performance analysis of the algorithm. We also extend the algorithm to time-dependent Lindblad equations, generalize the family of Markovian master equations it can be applied to, and explore applications beyond the Markovian noise model. A new error bound, in terms of the diamond norm, for second-order product formulas for time-dependent Liouvillians is provided that might be of independent interest.

Rémi Robin, Pierre Rouchon, Lev-Arcady Sellem

We propose and analyze an experimentally accessible Lindblad master equation for a quantum harmonic oscillator, simplifying a previous proposal to alleviate implementation constraints. It approximately stabilizes periodic grid states introduced in 2001 by Gottesman, Kitaev and Preskill (GKP), with applications for quantum error correction and quantum metrology. We obtain explicit estimates for the energy of the solutions of the Lindblad master equation. We estimate the convergence rate to the codespace when stabilizing a GKP qubit, and numerically study the effect of noise. We then present simulations illustrating how a modification of parameters allows preparing states of metrological interest in steady-state.

Edgardo T. Garcia-Alvarez, Fabián H. Gaioli

K. Lendi