Simulating Open Quantum Systems Using Hamiltonian Simulations
Abstract
We present a novel method to simulate the Lindblad equation, drawing on the relationship between Lindblad dynamics, stochastic differential equations, and Hamiltonian simulations. We derive a sequence of unitary dynamics in an enlarged Hilbert space that can approximate the Lindblad dynamics up to an arbitrarily high order. This unitary representation can then be simulated using a quantum circuit that involves only Hamiltonian simulation and tracing out the ancilla qubits. There is no need for additional postselection in measurement outcomes, ensuring a success probability of one at each stage. Our method can be directly generalized to the time-dependent setting. We provide numerical examples that simulate both time-independent and time-dependent Lindbladian dynamics with accuracy up to the third order.
Cite
@article{arxiv.2311.15533,
title = {Simulating Open Quantum Systems Using Hamiltonian Simulations},
author = {Zhiyan Ding and Xiantao Li and Lin Lin},
journal= {arXiv preprint arXiv:2311.15533},
year = {2024}
}