A New Method For Manipulating Circuits, Application To Quantum Adders

arXiv:2609.26591 · quant-ph · Submitted 2026-09-22 · Read on arXiv

quant-ph

Submitted: 2026-09-22

Updated: 2026-10-04

Terminology

• Quantum Fourier Transform — 13× in this paper
• Quantum Circuits — 11× in this paper · explained in 2 episodes
• Transform Addition — 4× in this paper
• Ancilla Qubits — 3× in this paper · explained in 1 episode
• Ancillary Qubits — 1× in this paper · explained in 1 episode
• Consistency — 1× in this paper · explained in 3 episodes

Sources

• Addition on a Quantum Computer
• Quantum Networks for Elementary Arithmetic Operations
• A new quantum ripple-carry addition circuit
• Quantum Addition Circuits and Unbounded Fan-Out
• A logarithmic-depth quantum carry-lookahead adder
• Quantum adders: on the structural link between the ripple-carry and carry-lookahead techniques
• ZX-calculus for the working quantum computer scientist
• Circuit Extraction for ZX-diagrams can be #P-hard
• A Classical-Quantum Adder with Constant Workspace and Linear Gates
• Asymptotically Optimal Quantum Circuits for Comparators and Incrementers

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