Wave Matrix Lindbladization I: Quantum Programs for Simulating Markovian Dynamics

• URL: http://arxiv.org/abs/2307.14932v1
• Date: Thu, 27 Jul 2023 15:22:04 GMT
• Title: Wave Matrix Lindbladization I: Quantum Programs for Simulating Markovian Dynamics
• Authors: Dhrumil Patel and Mark M. Wilde
• Abstract summary: Density Matrix Exponentiation is a technique for simulating Hamiltonian dynamics when the Hamiltonian to be simulated is available as a quantum state. We present a natural analogue to this technique, for simulating Markovian dynamics governed by the well known Lindblad master equation. We propose a quantum algorithm for this task, called Wave Matrix Lindbladization, and we also investigate its sample complexity.
• Score: 6.345523830122166
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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 $\psi$. Then, given access to $n$ copies of the state $\psi$, 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 $n = O(t^2/\varepsilon)$ samples of $\psi$ to achieve the target dynamics, with an approximation error of $O(\varepsilon)$.

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