Wave Matrix Lindbladization I: Quantum Programs for Simulating Markovian Dynamics

07/27/2023
by   Dhrumil Patel, et al.
0

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).

READ FULL TEXT

Please sign up or login with your details

Forgot password? Click here to reset

Sign in with Google

×

Use your Google Account to sign in to DeepAI

×

Consider DeepAI Pro