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Lindbladians with multiple steady states: theory and applications
TL;DR: In this article, the authors studied Lindbladian extensions of topics commonplace in degenerate Hamiltonian systems, providing examples and historical context along the way, and showed that such Lindbladians are dissipative analogues of Hamiltonians with multiple ground states.
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Abstract: Markovian master equations, often called Liouvillians or Lindbladians, are used to describe decay and decoherence of a quantum system induced by that system's environment. While a natural environment is detrimental to fragile quantum properties, an engineered environment can drive the system toward exotic phases of matter or toward subspaces protected from noise. These cases often require the Lindbladian to have more than one steady state, and such Lindbladians are dissipative analogues of Hamiltonians with multiple ground states. This thesis studies Lindbladian extensions of topics commonplace in degenerate Hamiltonian systems, providing examples and historical context along the way.
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Citations
Non-Hermitian Skin Effect and Chiral Damping in Open Quantum Systems.
Fei Song,Shunyu Yao,Zhong Wang +2 more
TL;DR: It is shown that the non-Hermitian skin effect dramatically shapes the long-time dynamics, such that the damping in a class of open quantum systems is algebraic under periodic boundary conditions but exponential under open boundary conditions.
Performance and structure of single-mode bosonic codes
Victor V. Albert,Victor V. Albert,Kyungjoo Noh,Kasper Duivenvoorden,Dylan Young,R. T. Brierley,Philip Reinhold,Christophe Vuillot,Linshu Li,Chao Shen,Steven Girvin,Barbara M. Terhal,Liang Jiang +12 more
TL;DR: An essential singularity is found in the entanglement fidelity of GKP codes in the limit of vanishing loss rate, and a generalization of spin-coherent states is introduced, extending the characterization to qudit binomial codes and yielding a multiqudit code.
Open quantum systems with local and collective incoherent processes: Efficient numerical simulations using permutational invariance
TL;DR: The Permutational-Invariant Quantum Solver (PIQS) as mentioned in this paper is an open-source library in python, which can be used to study several important physical phenomena in the presence of local incoherent processes, in which each degree of freedom couples to its own reservoir.
253
Hybrid-Liouvillian formalism connecting exceptional points of non-Hermitian Hamiltonians and Liouvillians via postselection of quantum trajectories
TL;DR: In this article, Naghiloo et al. generalized the notion of EPs to the spectra of Liouvillian superoperators governing open system dynamics described by Lindblad master equations.
116
Symmetry Breaking and Error Correction in Open Quantum Systems
Simon Lieu,Ron Belyansky,Jeremy T. Young,Rex Lundgren,Victor V. Albert,Victor V. Albert,Victor V. Albert,Alexey V. Gorshkov +7 more
TL;DR: This study forges a connection between driven-dissipative phase transitions and error correction, and shows how to dynamically recover the logical information after any gap-preserving strong-symmetric error; such recovery becomes perfect exponentially quickly in the number of photons.
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