Quantum Circuits with Classically Simulable Operator Scrambling

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We introduce a new family of quantum circuits for which the scrambling of a subspace of nonlocal operators is classically simulable. We call these circuits "super-Clifford circuits"since the Heisenberg time evolution of these operators corresponds to Clifford evolution in operator space. Thus we are able to classically simulate the time evolution of certain single Pauli strings into operators with operator entanglement that grows linearly with the number of qubits. These circuits provide a new technique for studying scrambling in systems with a large number of qubits, and are an explicit counter example to the intuition that classical simulability implies the absence of scrambling.

Original languageEnglish
Article number030502
JournalPhysical Review Letters
Issue number3
Publication statusPublished - 15 Jul 2020

Bibliographical note

Funding Information:
We are grateful to Adam Nahum for valuable conversations. N. L. gratefully acknowledges support from the UK Engineering and Physical Sciences Research Council through Grants No. EP/R043957/1, No. EP/S005021/1, and No. EP/T001062/1.

Publisher Copyright:
© 2020 American Physical Society.


  • Quantum Information
  • Condensed Matter & Materials Physics
  • Particles & Fields
  • Statistical Physics


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