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Entangling Power and Quantum Circuit Complexity.

J Eisert1

  • 1Dahlem Center for Complex Quantum Systems, Freie Universität Berlin, 14195 Berlin, Germany and Helmholtz-Zentrum Berlin für Materialien und Energie, 14109 Berlin, Germany.

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Summary
This summary is machine-generated.

This study reveals a direct link between quantum entanglement and circuit complexity for small values. As entanglement grows linearly over time, so does the cost of quantum computation, offering insights into quantum simulation.

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Area of Science:

  • Quantum Information Science
  • High Energy Physics
  • Quantum Computing

Background:

  • Circuit complexity and cost are crucial metrics in quantum computing and simulation for implementing unitaries.
  • These concepts are gaining traction in high energy physics, particularly in the study of holography.

Purpose of the Study:

  • To explore the relationship between quantum entanglement and the cost of quantum circuits.
  • To establish a bound connecting entanglement entropy growth to circuit cost.

Main Methods:

  • Developing a continuous-variable small incremental entangling bound.
  • Building upon the additive nature of entangling power in quantum gates.

Main Results:

  • A direct relationship is established between small values of entanglement and circuit cost.
  • The study shows that linear growth in entanglement entropy over time correlates with linear growth in circuit cost.
  • This provides insights into complexity growth in quantum systems at short times.

Conclusions:

  • The findings offer a new perspective on understanding complexity growth in quantum systems.
  • The established bound facilitates comparisons between digital and analog quantum simulators.
  • This work contributes a novel technical tool for analyzing quantum circuit complexity and entanglement.