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Pseudochaotic many-body dynamics as a pseudorandom state generator.

Wonjun Lee1,2, Hyukjoon Kwon3, Gil Young Cho4,5,6

  • 1Department of Physics, Pohang University of Science and Technology, Pohang, South Korea. wonjun1998@postech.ac.kr.

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Researchers discovered pseudochaotic dynamics, a new quantum behavior computationally indistinguishable from quantum chaos. This offers efficient methods for creating pseudorandom quantum states essential for quantum information processing.

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Area of Science:

  • Quantum Information Science
  • Quantum Many-Body Dynamics
  • Quantum Chaos Theory

Background:

  • Quantum chaos is vital for understanding quantum dynamics and generating random quantum states for quantum information tasks.
  • Existing methods for detecting quantum chaos, like out-of-time-ordered correlators, cannot distinguish pseudochaotic dynamics from true chaos.
  • Haar-random states are a crucial resource in quantum information, but generating them efficiently remains a challenge.

Purpose of the Study:

  • Introduce a novel class of quantum many-body dynamics, termed pseudochaotic dynamics.
  • Demonstrate that pseudochaotic dynamics can generate pseudorandom states computationally indistinguishable from Haar-random states.
  • Establish efficient methods for creating pseudorandom states using pseudochaotic dynamics.

Main Methods:

  • Constructed pseudochaotic dynamics by embedding a smaller k-qubit subsystem within a larger n-qubit system.
  • Showed that a subsystem size of k = ω(log n) is sufficient to induce pseudochaotic behavior in the n-qubit system.
  • Designed a quantum circuit exhibiting pseudochaotic dynamics with polylog(n) depth.

Main Results:

  • Pseudochaotic dynamics were identified as a new class of quantum dynamics.
  • Out-of-time-ordered correlators were found unable to distinguish pseudochaotic dynamics from genuine quantum chaos.
  • The developed quantum circuit efficiently generates pseudorandom states.
  • A subsystem size of k = ω(log n) was shown to be sufficient for pseudochaotic behavior.

Conclusions:

  • Pseudochaotic dynamics offer a computationally indistinguishable alternative to genuine quantum chaos.
  • This discovery provides efficient routes for generating pseudorandom quantum states.
  • The findings advance the understanding of quantum dynamics and resource generation for quantum information processing.