Lecture Notes on the Theory of Open Quantum Systems

Abstract

This is a self-contained set of lecture notes covering various aspects of the theory of open quantum system, at a level appropriate for a one-semester graduate course. The main emphasis is on completely positive maps and master equations, both Markovian and non-Markovian.

131 pages. v2: A few corrections, and a simplified derivation of the solution of the post-Markovian master equations due to Haimeng Zhang (p.118)

Cited by in corpus (45)

• Quantum exceptional points of non-Hermitian Hamiltonians and Liouvillians: The effects of quantum jumps
• Hybrid-Liouvillian formalism connecting exceptional points of non-Hermitian Hamiltonians and Liouvillians via postselection of quantum trajectories
• Digital quantum simulation of open quantum systems using quantum imaginary time evolution
• Geometrical Bounds of the Irreversibility in Markovian Systems
• Completely positive master equation for arbitrary driving and small level spacing
• Open Quantum System Dynamics: recovering positivity of the Redfield equation via Partial-Secular Approximation
• Measurement-Induced Power-Law Negativity in an Open Monitored Quantum Circuit
• Bell-state generation for spin qubits via dissipative coupling
• Pulse-level noisy quantum circuits with QuTiP
• Quantum speed limits for information and coherence
• A universal approach to Krylov State and Operator complexities
• Predicting non-Markovian superconducting qubit dynamics from tomographic reconstruction
• Solving the Liouvillian Gap with Artificial Neural Networks
• Continuous Dissipative Phase Transitions without Symmetry Breaking
• Dynamics of Open Quantum Systems II, Markovian Approximation
• The Fermionic influence superoperator: a canonical derivation for the development of methods to simulate the influence of a Fermionic environment on a quantum system with arbitrary parity symmetry
• Entanglement negativity as a universal non-Markovianity witness
• Optimal Control for Closed and Open System Quantum Optimization
• Non-Markovian open quantum system approach to the early universe: I. Damping of gravitational waves by matter
• Room Temperature Terahertz Electroabsorption Modulation by Excitons in Monolayer Transition Metal Dichalcogenides
• Breakdown of the weak coupling limit in quantum annealing
• Arnoldi-Lindblad time evolution: Faster-than-the-clock algorithm for the spectrum of time-independent and Floquet open quantum systems
• Introduction to the theory of open quantum systems
• Effective qubit dephasing induced by spectator-qubit relaxation
• Discriminating the Phase of a Coherent Tone with a Flux-Switchable Superconducting Circuit
• Dissipative state transfer and Maxwell's demon in single quantum trajectories: Excitation transfer between two noninteracting qubits via unbalanced dissipation rates
• Quantum dynamics of Dissipative Kerr solitons
• Beyond unital noise in variational quantum algorithms: noise-induced barren plateaus and limit sets
• Searching for exceptional points and inspecting non-contractivity of trace distance in (anti-)$\mathcal{P}\mathcal{T}-$symmetric systems
• Memory effect on the bidirectional teleportation
• Necessary and sufficient condition for the reduced dynamics of an open quantum system interacting with an environment to be linear
• Universal equilibration dynamics of the Sachdev-Ye-Kitaev model
• Heat current and entropy production rate in local non-Markovian quantum dynamics of global Markovian evolution
• Quantify the Non-Markovian Process with Intervening Projections in a Superconducting Processor
• Landau-Zener without a Qubit: Unveiling Multiphoton Interference, Synthetic Floquet Dimensions, and Dissipative Quantum Chaos
• Generalized Gibbs ensembles in weakly interacting dissipative systems and digital quantum computers
• Quantum transport phenomena induced by time-dependent fields
• Availing non-Markovian dynamics in effective negative temperature-based transient quantum Otto engines
• Suppressing information storage in a structured thermal bath: Objectivity and non-Markovianity
• Improving quantum annealing by engineering the coupling to the environment
• High-frequency tails in spectral densities
• Requiring linearity leads to complete positivity
• A universal constraint for relaxation rates for quantum Markov generators: complete positivity and beyond
• Describing Trotterized Time Evolutions on Noisy Quantum Computers via Static Effective Lindbladians
• Coherent dynamical control of quantum processes