Fault-Tolerant Stabilizer Measurements in Surface Codes with Three-Qubit Gates

Area of Science:

• Quantum computing
• Quantum error correction
• Topological quantum codes

Background:

• Stabilizer quantum error correction (QEC) codes, especially topological surface codes, are crucial for practical quantum computing.
• Current fault-tolerant protocols predominantly rely on single- and two-qubit gates, despite native multi-qubit operations being available on several platforms.

Purpose of the Study:

• To demonstrate fault-tolerant stabilizer measurement circuits for unrotated surface codes utilizing three-qubit gates.
• To explore the potential benefits of incorporating multi-qubit gates into quantum error correction protocols.

Main Methods:

• Utilized single auxiliary qubits and three-qubit gates for stabilizer measurement circuits in unrotated surface codes.
• Analyzed circuit depth, fault locations, and QEC cycle times.
• Compared performance in an optimistic parameter regime with equivalent three- and two-qubit gate fidelities.

Main Results:

• Achieved fault tolerance for stabilizer measurements using three-qubit gates.
• Demonstrated potential for lower-depth circuits and reduced fault locations.
• Observed up to a tenfold reduction in logical error rate and a higher error threshold (≈0.83% vs. ≈0.63%) under optimistic fidelity assumptions.

Conclusions:

• Three-qubit gates offer a viable and advantageous alternative for fault-tolerant QEC in surface codes.
• These findings motivate further research into multi-qubit gates for substantial time and resource savings in quantum computing.
• Results are applicable across diverse quantum computing platforms supporting multi-qubit operations.