Controlling quantum many-body systems using reduced-order modeling

Abstract

Quantum many-body control is among the most challenging problems in quantum science, due to computational complexity. We propose an efficient approach to a class of many-body quantum control problems, where time-dependent controls are applied to a sufficiently small subsystem. The method employs a tensor-network scheme to construct a reduced-order model of a subsystem's non-Markovian dynamics. The resulting reduced-order model serves as ``digital twin" of the original subsystem. Such twins allow significantly more efficient dynamics simulation, which enables the use of a gradient-based optimization toolbox in the control parameter space. This approach to building control protocols takes advantage of non-Markovian dynamics of subsystems by design. Our algorithm is able to find sequences that restore quantum information locally or transmit to another end of the chain. Physically, the identified sequences of local operations inject and re-absorb long-lived quasiparticles optimally. Further, we apply the optimization method to the many-body localized phase. We can find control protocols for local dynamics inversion that outperform existing spin-echo-type protocols for many-body localized systems. Thus, our approach enables automated discovery of optimal generalized spin-echo sequences in interacting systems. We expect that our results will find direct applications in the study of many-body systems, in probing non-trivial quasiparticle properties, as well as in development control tools for quantum computing devices.

Speaker

Maksim Gavreev
Russian Quantum Center
Russia

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