Exploring large-scale entanglement in quantum simulation

Manoj K. Joshi, Christian Kokail, Rick Bijnen, Florian Kranzl, Torsten V. Zache, Rainer Blatt, Christian F. Roos and Peter Zoller ()
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Manoj K. Joshi: Austrian Academy of Sciences
Christian Kokail: Austrian Academy of Sciences
Rick Bijnen: Austrian Academy of Sciences
Florian Kranzl: Austrian Academy of Sciences
Torsten V. Zache: Austrian Academy of Sciences
Rainer Blatt: Austrian Academy of Sciences
Christian F. Roos: Austrian Academy of Sciences
Peter Zoller: Austrian Academy of Sciences

Nature, 2023, vol. 624, issue 7992, 539-544

Abstract: Abstract Entanglement is a distinguishing feature of quantum many-body systems, and uncovering the entanglement structure for large particle numbers in quantum simulation experiments is a fundamental challenge in quantum information science1. Here we perform experimental investigations of entanglement on the basis of the entanglement Hamiltonian (EH)2 as an effective description of the reduced density operator for large subsystems. We prepare ground and excited states of a one-dimensional XXZ Heisenberg chain on a 51-ion programmable quantum simulator3 and perform sample-efficient ‘learning’ of the EH for subsystems of up to 20 lattice sites4. Our experiments provide compelling evidence for a local structure of the EH. To our knowledge, this observation marks the first instance of confirming the fundamental predictions of quantum field theory by Bisognano and Wichmann5,6, adapted to lattice models that represent correlated quantum matter. The reduced state takes the form of a Gibbs ensemble, with a spatially varying temperature profile as a signature of entanglement2. Our results also show the transition from area- to volume-law scaling7 of von Neumann entanglement entropies from ground to excited states. As we venture towards achieving quantum advantage, we anticipate that our findings and methods have wide-ranging applicability to revealing and understanding entanglement in many-body problems with local interactions including higher spatial dimensions.

Date: 2023
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DOI: 10.1038/s41586-023-06768-0

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