Variational Quantum Algorithms for the Steady States of Open Quantum Systems
- 1 September 2021
- journal article
- research article
- Published by IOP Publishing in Chinese Physics Letters
Abstract
The solutions of the problems related to open quantum systems have attracted considerable interest. We propose a variational quantum algorithm to find the steady state of open quantum systems. In this algorithm, we employ parameterized quantum circuits to prepare the purification of the steady state and define the cost function based on the Lindblad master equation, which can be efficiently evaluated with quantum circuits. We then optimize the parameters of the quantum circuit to find the steady state. Numerical simulations are performed on the one-dimensional transverse field Ising model with dissipative channels. The result shows that the fidelity between the optimal mixed state and the true steady state is over 99%. This algorithm is derived from the natural idea of expressing mixed states with purification and it provides a reference for the study of open quantum systems.Keywords
This publication has 39 references indexed in Scilit:
- Nonequilibrium steady state in open quantum systems: Influence action, stochastic equation and power balanceAnnals of Physics, 2015
- Simulation of single-qubit open quantum systemsPhysical Review A, 2014
- A variational eigenvalue solver on a photonic quantum processorNature Communications, 2014
- QuTiP 2: A Python framework for the dynamics of open quantum systemsComputer Physics Communications, 2013
- Dissipative Quantum Church-Turing TheoremPhysical Review Letters, 2011
- An open-system quantum simulator with trapped ionsNature, 2011
- Stabilizing open quantum systems by Markovian reservoir engineeringPhysical Review A, 2010
- Nelder-Mead algorithmScholarpedia, 2009
- Quantum computation and quantum informationMathematical Structures in Computer Science, 2007
- On the generators of quantum dynamical semigroupsCommunications in Mathematical Physics, 1976