Probabilistic Interpolation of Quantum Rotation Angles.

Area of Science:

• Quantum Computing
• Quantum Information Science
• Quantum Algorithms

Background:

• Universal gate operations in quantum computing require precise control over rotation angles.
• Hardware limitations often restrict gate operations to discrete settings, leading to errors or increased circuit depth.
• Current methods for handling gate discretization in quantum algorithms are either error-prone or computationally expensive.

Purpose of the Study:

• To introduce and analyze Probabilistic Angle Interpolation (PAI) as a novel technique for implementing continuous quantum gate rotations.
• To demonstrate the optimality and efficiency of PAI for near-term quantum computing applications.
• To establish relaxed hardware requirements for first-generation quantum computers.

Main Methods:

• PAI implements arbitrary rotations by randomly selecting one of three discretized gate settings.
• Outputs from multiple circuit runs are postprocessed to achieve the desired continuous rotation.
• Theoretical analysis is used to prove the optimality and quantify the overhead of PAI.

Main Results:

• PAI optimally achieves desired rotations with the minimum possible overhead.
• The overhead associated with PAI is modest, even with thousands of gates and limited resolution (e.g., 7 bits).
• PAI is significantly more efficient than existing techniques, reducing engineering demands for quantum hardware.

Conclusions:

• PAI provides a practical and efficient solution for implementing precise quantum gates on near-term devices.
• The technique significantly lowers the hardware resolution requirements for building functional quantum computers.
• Even for advanced noisy intermediate-scale quantum (NISQ) era hardware, high bit resolution (beyond 9 bits) may not be necessary.