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Area of Science:

  • Quantum physics
  • Quantum information science
  • Condensed matter theory

Background:

  • Random unitaries are crucial for quantum technologies and studying complex quantum many-body systems.
  • Current methods for generating random unitaries necessitate lengthy evolution times and intricate quantum circuits.
  • This limits their practical application and scalability in quantum computing.

Purpose of the Study:

  • To demonstrate that local quantum circuits can generate random unitaries with remarkably low circuit depth.
  • To show these shallow circuits are indistinguishable from exponentially complex random unitaries.
  • To explore the implications for quantum technologies and learning fundamental physical properties.

Main Methods:

  • Theoretical analysis of local quantum circuit constructions.
  • Investigation of correlation properties in shallow quantum circuits.
  • Comparison of generated unitaries with true random unitaries.

Main Results:

  • Local quantum circuits can form random unitaries in extremely low depth, irrespective of the underlying geometry.
  • These shallow circuits exhibit low complexity and generate only short-range correlations.
  • The generated unitaries are indistinguishable from those produced by exponentially complex circuits.
  • This contrasts with classical systems where randomness requires long evolution times.

Conclusions:

  • Shallow local quantum circuits provide an efficient method for generating random unitaries.
  • The findings have broad applications in quantum device benchmarking and demonstrating quantum advantages.
  • The study reveals inherent difficulties in learning fundamental physical properties like evolution time and causal structure from quantum systems.