dorsal/arxiv
View SchemaAn explicit family of unitaries with exponentially minimal length Pauli geodesics
| Authors | Wei Huang |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0701202 |
| URL | https://arxiv.org/abs/quant-ph/0701202 |
Abstract
Recently, Nielsen et al have proposed a geometric approach to quantum computation. They've shown that the size of the minimum quantum circuits implementing a unitary U, up to polynomial factors, equals to the length of minimal geodesic from identity I through U. They've investigated a large class of solutions to the geodesic equation, called Pauli geodesics. They've raised a natural question whether we can explicitly construct a family of unitaries U that have exponentially long minimal length Pauli geodesics? We give a positive answer to this question.
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"date_created": "2026-03-02T18:02:34.416000Z",
"date_modified": "2026-03-02T18:02:34.416000Z",
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"abstract": "Recently, Nielsen et al have proposed a geometric approach to quantum\ncomputation. They\u0027ve shown that the size of the minimum quantum circuits\nimplementing a unitary U, up to polynomial factors, equals to the length of\nminimal geodesic from identity I through U. They\u0027ve investigated a large class\nof solutions to the geodesic equation, called Pauli geodesics. They\u0027ve raised a\nnatural question whether we can explicitly construct a family of unitaries U\nthat have exponentially long minimal length Pauli geodesics? We give a positive\nanswer to this question.",
"arxiv_id": "quant-ph/0701202",
"authors": [
"Wei Huang"
],
"categories": [
"quant-ph"
],
"title": "An explicit family of unitaries with exponentially minimal length Pauli geodesics",
"url": "https://arxiv.org/abs/quant-ph/0701202"
},
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"variant": "snapshot-2026-03-01",
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