Wave Matrix Lindbladization I: Quantum Programs for Simulating Markovian Dynamics

07/27/2023

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by   Dhrumil Patel, et al.

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Density Matrix Exponentiation is a technique for simulating Hamiltonian dynamics when the Hamiltonian to be simulated is available as a quantum state. In this paper, we present a natural analogue to this technique, for simulating Markovian dynamics governed by the well known Lindblad master equation. For this purpose, we first propose an input model in which a Lindblad operator L is encoded into a quantum state ψ. Then, given access to n copies of the state ψ, the task is to simulate the corresponding Markovian dynamics for time t. We propose a quantum algorithm for this task, called Wave Matrix Lindbladization, and we also investigate its sample complexity. We show that our algorithm uses n = O(t^2/ε) samples of ψ to achieve the target dynamics, with an approximation error of O(ε).