Fault-Tolerant Non-Clifford State Preparation for Arbitrary Rotations
Quantum error correction is essential for practical quantum computing on noisy quantum hardware. However, logical operations on error-corrected qubits require a significant resource overhead, especially for high-precision and high-fidelity non-Clifford rotation gates. We propose a postselection-based protocol to resolve this issue. We efficiently prepare the resource states to be gate-teleported for small-angle rotations. The preparation of these non-Clifford states achieves fault tolerance, demonstrating the exponential suppression of logical error with code distances. The algorithm applies to any stabilizer codes including the codes with multiple logical qubits. We provide analytical derivations and numerical simulations of the fidelity and success probability of the state preparation. We benchmark the method on surface code and show a factor of 100 to 10,000 reduction in space-time overhead compared to existing methods. Our approach presents a promising path to reducing the resource requirement for quantum algorithms on error-corrected and noisy intermediate-scale quantum computers.
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