Szegedy Walk Unitaries for Quantum Maps

Wocjan, Paweł; Temme, Kristan

doi:10.1007/s00220-023-04797-4

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Cited by 4 publications

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Quantum-centric supercomputing for materials science: A perspective on challenges and future directions

Alexeev,

Amsler,

Barroca

et al. 2024

Future Generation Computer Systems

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Quantum-centric supercomputing for materials science: A perspective on challenges and future directions

Alexeev,

Amsler,

Barroca

et al. 2024

Future Generation Computer Systems

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Area law for steady states of detailed-balance local Lindbladians

Firanko,

Goldstein,

Arad

2024

Journal of Mathematical Physics

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We study steady-states of quantum Markovian processes whose evolution is described by local Lindbladians. We assume that the Lindbladian is gapped and satisfies quantum detailed balance with respect to a unique full-rank steady state σ. We show that under mild assumptions on the Lindbladian terms, which can be checked efficiently, the Lindbladian can be mapped to a local Hamiltonian on a doubled Hilbert space that has the same spectrum and a ground state that is the vectorization of σ1/2. Consequently, we can use Hamiltonian complexity tools to study the steady states of such open systems. In particular, we show an area-law in the mutual information for the steady state of such 1D systems, together with a tensor-network representation that can be found efficiently.

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