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Abstract
While several numerical techniques are available for predicting the dynamics of nonMarkovian open quantum systems, most struggle with simulations for very long memory and propagation times, e.g., due to superlinear scaling with the number of time steps n. Here, we introduce a numerically exact algorithm to calculate process tensors—compact representations of environmental influences—which provides a scaling advantage over previous algorithms by leveraging selfsimilarity of the tensor networks that represent the environment. It is applicable to environments with Gaussian statistics, such as for spinbosontype open quantum systems. Based on a divideandconquer strategy, our approach requires only 𝒪(n log n) singular value decompositions for environments with infinite memory. Where the memory can be truncated after n_{c} time steps, a nominal scaling 𝒪(n_{c} log n_{c}) is found, which is independent of n. This improved scaling is enabled by identifying process tensors with repeatable blocks. To demonstrate the power and utility of our approach, we provide three examples. (1) We calculate the fluorescence spectra of a quantum dot under both strong driving and strong dotphonon couplings, a task requiring simulations over millions of time steps, which we are able to perform in minutes. (2) We efficiently find process tensors describing superradiance of multiple emitters. (3) We explore the limits of our algorithm by considering coherence decay with a very strongly coupled environment. The observed computation time is not necessarily proportional to the number of singular value decompositions because the matrix dimensions also depend on the number of time steps. Nevertheless, quasilinear and sublinear scaling of computation time is found in practice for a wide range of parameters. While there are instances where existing methods can achieve comparable nominal scaling by precalculating effective propagators for timeindependent or periodic system Hamiltonians, process tensors contain all the information needed to extract arbitrary multitime correlation functions of the system when driven by arbitrary timedependent system Hamiltonians. The algorithm we present here not only significantly extends the scope of numerically exact techniques to open quantum systems with long memory times, but it also has fundamental implications for the simulation complexity of tensor network approaches.
Original language  English 

Article number  011010 
Number of pages  25 
Journal  Physical Review X 
Volume  14 
Issue number  1 
Early online date  1 Feb 2024 
DOIs  
Publication status  Published  Mar 2024 
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Dive into the research topics of 'Sublinear scaling in nonMarkovian open quantum systems simulations'. Together they form a unique fingerprint.Projects
 1 Finished

Understanding and engineering: Understanding and engineering dissipation in nanoscale quantum devices
Lovett, B. W. (PI) & Keeling, J. M. J. (CoI)
1/04/20 → 31/03/23
Project: Standard
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Datafiles for "Sublinear scaling in nonMarkovian open quantum systems simulations"
Cygorek, M. (Creator), Keeling, J. (Contributor), Lovett, B. W. (Contributor) & Gauger, E. (Contributor), HeriotWatt University, 5 Jan 2024
DOI: 10.17861/6666a00a887c4d91887dc19bf3450180
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