A New Method For Manipulating Circuits, Application To Quantum Adders
quant-ph
Submitted: 2026-09-22
Updated: 2026-10-04
Comments: Typos and better exposition in section 3.1
License: http://creativecommons.org/licenses/by/4.0/
The gist: We use a new technique for manipulating controlled quantum circuits to convert between two distinct types of quantum adders, one based on the Quantum Fourier Transform and the other based on the
Terminology
Abstract
We use a new technique for manipulating controlled quantum circuits to convert between two distinct types of quantum adders, one based on the Quantum Fourier Transform and the other based on the Ripple-Carry technique from classical reversible logic. This conversion takes the form of an explicit gate-level transpilation. We also present a new quantum adder with a natural interpretation as a kind of Carry-Lookahead adder that uses no ancillas.
Sources
- Addition on a Quantum Computer
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- 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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