Efficient Synthesis of Multi-Controlled Toffoli Gates with Ternary Clifford +P 9 Gates

arXiv:2609.29884 · quant-ph · Submitted 2026-09-24 · Read on arXiv

quant-ph

Submitted: 2026-09-24

Updated: 2026-09-24

Terminology

• Core — 7× in this paper · explained in 2 episodes
• Benchmark — 6× in this paper · explained in 2 episodes
• Multi-controlled Toffoli — 6× in this paper
• Accuracy — 2× in this paper · explained in 1 episode
• Ancilla Qubits — 1× in this paper · explained in 1 episode
• Distillation — 1× in this paper · explained in 2 episodes

Sources

• Quantum circuit for multi-qubit Toffoli gate with optimal resource
• Rise of conditionally clean ancillae for efficient quantum circuit constructions
• On Exact Space-Depth Trade-Offs in Multi-Controlled Toffoli Decomposition
• Multi-qubit Toffoli with exponentially fewer T gates

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