Hybrid quantum variational algorithm for simulating open quantum systems with near-term devices

Abstract

Hybrid quantum-classical (HQC) algorithms make it possible to use near-term quantum devices supported by classical computational resources by useful control schemes. In this paper, we develop an HQC algorithm using an efficient variational optimization approach to simulate open system dynamics under the Noisy-Intermediate Scale Quantum(NISQ) computer. Using the time-dependent variational principle (TDVP) method and extending it to McLachlan TDVP for density matrix which involves minimization of Frobenius norm of the error, we apply the unitary quantum circuit to obtain the time evolution of the open quantum system in the Lindblad formalism. Finally, we illustrate the use of our methods with detailed examples which are in good agreement with analytical calculations.

12 pages,6 figures

References in corpus (16)

• A variational eigenvalue solver on a quantum processor
• Hardware-efficient Variational Quantum Eigensolver for Small Molecules and Quantum Magnets
• The theory of variational hybrid quantum-classical algorithms
• A Quantum Approximate Optimization Algorithm
• Quantum Chemistry in the Age of Quantum Computing
• Quantum fingerprinting
• Time-dependent density-matrix renormalization-group using adaptive effective Hilbert spaces
• Nonequilibrium dynamical mean-field theory and its applications
• Efficient variational quantum simulator incorporating active error minimisation
• Simulating chemistry using quantum computers
• Localization and Glassy Dynamics Of Many-Body Quantum Systems
• Quantum Supremacy through the Quantum Approximate Optimization Algorithm
• Digital quantum simulation of molecular vibrations
• Non-linear quantum-classical scheme to simulate non-equilibrium strongly correlated fermionic many-body dynamics
• Problem-free time-dependent variational principle for open quantum systems
• The SWITCH test for discriminating quantum evolutions

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• Toward a quantum computing algorithm to quantify classical and quantum correlation of system states
• Hermitian-preserving ansatz and variational open quantum eigensolver
• Single entanglement connection architecture between multi-layer bipartite Hardware Efficient Ansatz
• Simulation of open quantum systems on universal quantum computers
• Digital Quantum Simulation of the Lindblad Master Equation and Its Nonlinear Extensions via Quantum Trajectory Averaging