Success-or-Draw: A Strategy Allowing Repeat-Until-Success in Quantum Computation

Area of Science:

• Quantum Information Science
• Quantum Computing
• Quantum Algorithms

Background:

• The repeat-until-success strategy is crucial for quantum algorithms, but quantum measurement disturbances complicate its application.
• Implementing this strategy requires overcoming challenges in maintaining quantum system integrity.

Purpose of the Study:

• To propose a new probabilistic higher-order transformation structure, termed "success-or-draw."
• To enable a robust repeat-until-success implementation in quantum systems.
• To provide a universal construction for this structure applicable to any probabilistic higher-order transformation on unitary operations.

Main Methods:

• Development of the "success-or-draw" probabilistic transformation structure.
• Universal construction for applying the success-or-draw structure to unitary operations.
• Utilization of a semidefinite programming approach to derive optimal protocols.

Main Results:

• Demonstrated a universal construction for the success-or-draw structure.
• Presented a semidefinite programming method for optimizing success-or-draw protocols.
• Detailed analysis of the problem of inverting general unitary operations using this framework.

Conclusions:

• The success-or-draw structure provides a viable method for repeat-until-success implementations in quantum computing.
• This approach enhances the reliability of quantum algorithms sensitive to measurement disturbances.
• The developed framework offers a pathway for optimizing complex quantum operations, including unitary inversion.