A fault-tolerant non-Clifford gate for the surface code in two dimensions

Area of Science:

• Quantum computing
• Quantum error correction
• Fault-tolerant quantum computation

Background:

• Fault-tolerant logic gates are resource-intensive in 2D quantum computing architectures.
• The surface code is a leading quantum error-correcting code currently under development.

Purpose of the Study:

• To demonstrate a fault-tolerant non-Clifford gate using the surface code.
• To reduce the resource overhead associated with universal gate sets in quantum computation.

Main Methods:

• Implementation of a fault-tolerant non-Clifford gate within a 2D surface code architecture.
• Utilization of local transversal gates and code deformations.
• Integration of a just-in-time decoder for efficient decoding.
• Employment of parity checks with a maximum weight of four.

Main Results:

• Successful performance of a fault-tolerant non-Clifford gate on a 2D quantum computing architecture.
• Elimination of the need for magic-state distillation or higher-dimensional components.
• Demonstration that the gate operation time scales with qubit array size.
• The gate is compatible with near-future technological capabilities.

Conclusions:

• The developed gate alleviates the need for resource-intensive distillation methods.
• This approach significantly reduces the resource overhead for surface-code quantum computation.
• The method enables the completion of a universal gate set on a 2D array.
• The gate's reliance on simple parity checks makes it amenable to near-term implementation.