%0 Generic %1 patel2023matrix %A Patel, Dhrumil %A Wilde, Mark M. %D 2023 %K markov quantum simulating %R 10.1142/S1230161223500105 %T Wave Matrix Lindbladization I: Quantum Programs for Simulating Markovian Dynamics %U http://arxiv.org/abs/2307.14932 %X 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 $O(\varepsilon)$.

@misc{patel2023matrix, 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 $O(\varepsilon)$.}, added-at = {2023-07-29T18:28:15.000+0200}, author = {Patel, Dhrumil and Wilde, Mark M.}, biburl = {https://www.bibsonomy.org/bibtex/26c8e088bebb6d67edc836d6bfc77b84e/gzhou}, description = {Wave Matrix Lindbladization I: Quantum Programs for Simulating Markovian Dynamics}, doi = {10.1142/S1230161223500105}, interhash = {ca9356fc452d6c627a9ff305e78c0f08}, intrahash = {6c8e088bebb6d67edc836d6bfc77b84e}, keywords = {markov quantum simulating}, note = {cite arxiv:2307.14932Comment: 29 pages, 7 figures, published in the journal special issue dedicated to the memory of G\"oran Lindblad}, timestamp = {2023-07-29T18:28:15.000+0200}, title = {Wave Matrix Lindbladization I: Quantum Programs for Simulating Markovian Dynamics}, url = {http://arxiv.org/abs/2307.14932}, year = 2023 }