Low-Overhead and High-Fidelity Preparation of Logical Non-Clifford States with Multilevel Transversal Injection

Area of Science:

• Quantum computing
• Quantum information science
• Fault-tolerant quantum computation

Background:

• Rotation gates are essential components in quantum algorithms.
• Current methods like state distillation and gate synthesis have high overhead, limiting scalability.
• Overhead increases with Clifford hierarchy levels and required gate fidelity.

Purpose of the Study:

• To propose a new method, multilevel transversal injection (MLTI), for preparing rotation states.
• To achieve high fidelity while significantly reducing the overhead associated with fault-tolerant rotation gates.
• To address the limitations of existing methods for large-scale quantum algorithm implementation.

Main Methods:

• Development of the multilevel transversal injection (MLTI) technique.
• Preparation of rotation states at arbitrary Clifford hierarchy levels.
• Introduction of a method to eliminate off-diagonal terms of rotation states without additional overhead.

Main Results:

• MLTI achieves high fidelity for rotation states.
• The overhead of MLTI decreases with Clifford hierarchy levels and plateaus, unlike linear scaling in state distillation.
• Space-time volume is reduced by several orders of magnitude.
• Unified infidelity and trace distance metrics by eliminating off-diagonal terms.

Conclusions:

• MLTI offers a significant reduction in overhead for high-precision rotation gates.
• The method overcomes prohibitive costs, enabling broader adoption of large-scale quantum algorithms.
• This advancement brings practical, large-scale quantum computation closer to reality.