Reducing T-count and T-depth in approximate quantum Fourier transform circuits.

Area of Science:

• Quantum Computing
• Quantum Algorithms
• Fault-Tolerant Quantum Computation

Background:

• The quantum Fourier transform (QFT) is crucial for quantum algorithms like Shor's and HHL.
• Efficient QFT implementation is vital for large-scale, fault-tolerant quantum computers.
• The T gate is a resource bottleneck in Clifford+T gate synthesis for QFT.

Purpose of the Study:

• To develop novel approximate quantum Fourier transform (AQFT) circuits with reduced resource costs.
• To address the T-gate bottleneck in implementing QFT and related quantum algorithms.
• To optimize AQFT circuits for practical, large-scale quantum computing applications.

Main Methods:

• Introduction of two novel [Formula: see text]-qubit AQFT circuits with an approximation error of [Formula: see text].
• AQFT Circuit 1: Halves T-count using inverse phase gradient transformation (PGT) circuits implemented with quantum adders.
• AQFT Circuit 2: Reduces T-depth via parallelized inverse PGTs, adding minimal T gates, utilizing linear-depth quantum adders.

Main Results:

• AQFT Circuit 1 achieves a T-count of [Formula: see text].
• AQFT Circuit 2 achieves a T-depth of [Formula: see text].
• Both circuits employ state-of-the-art linear-depth quantum adders, outperforming logarithmic-depth adders for practical system sizes.

Conclusions:

• The proposed AQFT circuits offer significant reductions in T-count and T-depth compared to prior art.
• The use of linear-depth quantum adders is advantageous for optimizing AQFT resource costs.
• These advancements pave the way for more efficient and practical large-scale quantum algorithms reliant on QFT.