dorsal/arxiv
View SchemaUse of non-adiabatic geometric phase for quantum computing by nuclear magnetic resonance
| Authors | Ranabir Das, S. K. Karthick Kumar, Anil Kumar |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0503032 |
| URL | https://arxiv.org/abs/quant-ph/0503032 |
| DOI | 10.1016/j.jmr.2005.07.025 |
Abstract
Geometric phases have stimulated researchers for its potential applications in many areas of science. One of them is fault-tolerant quantum computation. A preliminary requisite of quantum computation is the implementation of controlled logic gates by controlled dynamics of qubits. In controlled dynamics, one qubit undergoes coherent evolution and acquires appropriate phase, depending on the state of other qubits. If the evolution is geometric, then the phase acquired depend only on the geometry of the path executed, and is robust against certain types of errors. This phenomenon leads to an inherently fault-tolerant quantum computation. Here we suggest a technique of using non-adiabatic geometric phase for quantum computation, using selective excitation. In a two-qubit system, we selectively evolve a suitable subsystem where the control qubit is in state |1>, through a closed circuit. By this evolution, the target qubit gains a phase controlled by the state of the control qubit. Using these geometric phase gates we demonstrate implementation of Deutsch-Jozsa algorithm and Grover's search algorithm in a two-qubit system.
{
"annotation_id": "f2147556-7b6f-4676-a283-bb1525f9548c",
"date_created": "2026-03-02T18:02:13.457000Z",
"date_modified": "2026-03-02T18:02:13.457000Z",
"file_hash": "0130dec6a88b7b76e810547eaa05f5e1500c3e8435cc410f940e566176fed529",
"private": false,
"record": {
"abstract": "Geometric phases have stimulated researchers for its potential applications\nin many areas of science. One of them is fault-tolerant quantum computation. A\npreliminary requisite of quantum computation is the implementation of\ncontrolled logic gates by controlled dynamics of qubits. In controlled\ndynamics, one qubit undergoes coherent evolution and acquires appropriate\nphase, depending on the state of other qubits. If the evolution is geometric,\nthen the phase acquired depend only on the geometry of the path executed, and\nis robust against certain types of errors. This phenomenon leads to an\ninherently fault-tolerant quantum computation.\n Here we suggest a technique of using non-adiabatic geometric phase for\nquantum computation, using selective excitation. In a two-qubit system, we\nselectively evolve a suitable subsystem where the control qubit is in state\n|1\u003e, through a closed circuit. By this evolution, the target qubit gains a\nphase controlled by the state of the control qubit. Using these geometric phase\ngates we demonstrate implementation of Deutsch-Jozsa algorithm and Grover\u0027s\nsearch algorithm in a two-qubit system.",
"arxiv_id": "quant-ph/0503032",
"authors": [
"Ranabir Das",
"S. K. Karthick Kumar",
"Anil Kumar"
],
"categories": [
"quant-ph"
],
"doi": "10.1016/j.jmr.2005.07.025",
"title": "Use of non-adiabatic geometric phase for quantum computing by nuclear magnetic resonance",
"url": "https://arxiv.org/abs/quant-ph/0503032"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "e59c978c-74a6-4a3d-baa8-796549f47b67",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}