Experimental Equivalence Checking of Quantum Circuits by Nonlocality

Area of Science:

• Quantum Computing
• Quantum Information Science

Background:

• The quantum circuit model is foundational for quantum computing.
• Equivalence checking of unknown quantum circuits is a fundamental problem, yet QMA-hard.
• Efficient verification methods are vital for advancing quantum technologies.

Purpose of the Study:

• To experimentally implement and demonstrate a method for checking the equivalence of two unknown quantum circuits.
• To utilize quantum nonlocality as a resource for efficient circuit verification.
• To apply this protocol for validating quantum circuit optimizations.

Main Methods:

• Experimental implementation using a photonic system.
• Utilizing quantum nonlocality to measure an average-case distance between quantum circuits.
• Developing protocols for equivalence checking without circuit structure access.

Main Results:

• Successful experimental demonstration of equivalence checking for unknown quantum circuits.
• Efficient measurement of average-case distance between circuits via quantum nonlocality.
• Application of the protocol to verify quantum circuit optimizations.

Conclusions:

• This work provides a proof of concept for structural-independent quantum circuit equivalence checking.
• The developed method offers an efficient and practical approach for verification in quantum industries.
• Quantum nonlocality is a key resource for enabling efficient quantum circuit analysis.