Efficient Benchmarking of Logical Magic State.

Area of Science:

• Quantum Information Science
• Quantum Computation
• Quantum Error Correction

Background:

• High-fidelity magic states are essential for fault-tolerant quantum computation, enabling crucial non-Clifford operations.
• Current benchmarking methods (state tomography) require impractically large sample sizes (proportional to 1/ε²) for high-fidelity states.
• Quantum error-correcting codes often restrict operations to fault-tolerant Clifford gates, complicating magic state benchmarking.

Purpose of the Study:

• To address the challenge of efficiently benchmarking high-fidelity magic states.
• To develop new protocols that overcome the quadratic sample complexity limitations of conventional methods.
• To achieve optimal O(1/ε) sample complexity for magic state benchmarking.

Main Methods:

• Analyzing the sample complexity of single-copy magic state benchmarking, proving a lower bound of Ω(1/ε²).
• Proposing two novel benchmarking schemes: Bell measurements on two twirled magic states and single-copy schemes with twirled multiqubit magic states.
• Utilizing measurements with stabilizer states orthogonal to the ideal magic state in the proposed schemes.

Main Results:

• Demonstrated that any single-copy benchmarking scheme requires Ω(1/ε²) samples for single-qubit magic states.
• Achieved an optimal O(1/ε) sample complexity using the proposed Bell measurement and multiqubit twirled state protocols.
• Proved the optimality of the O(1/ε) sample complexity for the developed benchmarking schemes.

Conclusions:

• The developed protocols offer a significant improvement in sample complexity for benchmarking magic states.
• These methods are robust under realistic noise models, as confirmed by numerical simulations.
• The findings pave the way for practical verification of resources needed for fault-tolerant quantum computation.