Simulating Open Quantum Systems Using Hamiltonian Simulations

• Published in: PRX quantum Vol. 5; no. 2
• Main Authors: Ding, Zhiyan, Li, Xiantao, Lin, Lin
• Format: Journal Article
• Language: English
• Published: United States American Physical Society 10.05.2024
• ISSN: 2691-3399; 2691-3399
• DOI: 10.1103/PRXQuantum.5.020332

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. Published by the American Physical Society 2024