A Classical-Quantum Adder with Constant Workspace and Linear Gates
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866913967234875392 |
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| author | Gidney, Craig |
| author_facet | Gidney, Craig |
| contents | In 2004, Cuccaro et al found a quantum-quantum adder with $O(n)$ gate cost and $O(1)$ ancilla qubits. Since then, it's been an open question whether classical-quantum adders can achieve the same asymptotic complexity. These costs are particularly relevant to modular arithmetic circuits, which often offset by the classically known modulus.
In this paper, I construct an adder that uses 3 clean ancillae and $4n \pm O(1)$ Toffoli gates to add a classical offset into a quantum register. I also present an adder with a Toffoli cost of $3n \pm O(1)$ that uses 2 clean ancillae and $n-2$ dirty ancillae. I further show that applying the presented adders conditioned on a control qubit requires no additional workspace or Toffolis. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2507_23079 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Classical-Quantum Adder with Constant Workspace and Linear Gates Gidney, Craig Quantum Physics In 2004, Cuccaro et al found a quantum-quantum adder with $O(n)$ gate cost and $O(1)$ ancilla qubits. Since then, it's been an open question whether classical-quantum adders can achieve the same asymptotic complexity. These costs are particularly relevant to modular arithmetic circuits, which often offset by the classically known modulus. In this paper, I construct an adder that uses 3 clean ancillae and $4n \pm O(1)$ Toffoli gates to add a classical offset into a quantum register. I also present an adder with a Toffoli cost of $3n \pm O(1)$ that uses 2 clean ancillae and $n-2$ dirty ancillae. I further show that applying the presented adders conditioned on a control qubit requires no additional workspace or Toffolis. |
| title | A Classical-Quantum Adder with Constant Workspace and Linear Gates |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2507.23079 |