Random unitaries in extremely low depth

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.