dorsal/arxiv
View SchemaImplementing fanout, parity, and Mod gates via spin exchange interactions
| Authors | Stephen A. Fenner, Yong Zhang |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0407125 |
| URL | https://arxiv.org/abs/quant-ph/0407125 |
Abstract
We show that, for any n > 0, the Heisenberg interaction among 2n qubits (as spin-1/2 particles) can be used to exactly implement an n-qubit parity gate, which is equivalent in constant depth to an n-qubit fanout gate. Either isotropic or nonisotropic versions of the interaction can be used. We generalize our basic results by showing that any Hamiltonian (acting on suitably encoded logical qubits), whose eigenvalues depend quadratically on the Hamming weight of the logical qubit values, can be used to implement generalized Mod_q gates for any q > 1. This paper is a sequel to quant-ph/0309163, and resolves a question left open in that paper.
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"abstract": "We show that, for any n \u003e 0, the Heisenberg interaction among 2n qubits (as\nspin-1/2 particles) can be used to exactly implement an n-qubit parity gate,\nwhich is equivalent in constant depth to an n-qubit fanout gate. Either\nisotropic or nonisotropic versions of the interaction can be used. We\ngeneralize our basic results by showing that any Hamiltonian (acting on\nsuitably encoded logical qubits), whose eigenvalues depend quadratically on the\nHamming weight of the logical qubit values, can be used to implement\ngeneralized Mod_q gates for any q \u003e 1.\n This paper is a sequel to quant-ph/0309163, and resolves a question left open\nin that paper.",
"arxiv_id": "quant-ph/0407125",
"authors": [
"Stephen A. Fenner",
"Yong Zhang"
],
"categories": [
"quant-ph"
],
"title": "Implementing fanout, parity, and Mod gates via spin exchange interactions",
"url": "https://arxiv.org/abs/quant-ph/0407125"
},
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"source": {
"execution_id": "239e57d4-df3b-492f-9d7c-6254fc32116e",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
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