Bootstrapping the stationary state of bosonic open quantum systems

2024/10/09 by Gustave Robichon, Antoine Tilloy, Robichon, Gustave +1 · 5 citations
Computer Science · Physics and Astronomy · #FOS: Physical sciences #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum Physics (quant-ph) #Spectroscopy and Quantum Chemical Studies

paper · pdf · doi:10.48550/arxiv.2410.07384

openalex publication_date 2024/10/09 · openalex created_date 2024/10/13 · openalex updated_date 2026/07/28

Abstract

We propose a method to compute expectation values of observables in the stationary state of a (Markovian) bosonic open quantum system. Using a hierarchy of semi-definite relaxations, we obtain finer and finer upper and lower bounds to any expectation value of interest. The bounds are rigorous, robust to stationary state degeneracies, and numerically improve as the occupation number increases on the examples we considered. This makes it adapted to the simulation of stationary states of bosonic qubits and in particular dissipatively stabilized cat qubits.

Cited by

• Quantum bootstrap for central potentials
• Bootstrapping supersymmetric (matrix) quantum mechanics
• Nonequilibrium Phase Transitions in Large N Matrix Quantum Mechanics
• Mapping phase diagrams of quantum spin systems through semidefinite-programming relaxations
• Bootstrapping periodic quantum systems

Related

• Universal Bounds on Quantum Mechanics through Energy Conservation and the Bootstrap Method
• Instantaneous Sobolev Regularization for Dissipative Bosonic Dynamics
• Hamiltonian Bootstrap
• Certifying steady-state properties of open quantum systems
• Pseudomode description of general open quantum system dynamics: non-perturbative master equation for the spin-boson model