dorsal/arxiv
View SchemaUniversal Quantum Computation with the Exchange Interaction
| Authors | D. P. DiVincenzo, D. Bacon, J. Kempe, G. Burkard, K. B. Whaley |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0005116 |
| URL | https://arxiv.org/abs/quant-ph/0005116 |
| DOI | 10.1038/35042541 |
| Journal | NATURE, Vol. 408, p. 339-342 (2000) |
Abstract
Experimental implementations of quantum computer architectures are now being investigated in many different physical settings. The full set of requirements that must be met to make quantum computing a reality in the laboratory [1] is daunting, involving capabilities well beyond the present state of the art. In this report we develop a significant simplification of these requirements that can be applied in many recent solid-state approaches, using quantum dots [2], and using donor-atom nuclear spins [3] or electron spins [4]. In these approaches, the basic two-qubit quantum gate is generated by a tunable Heisenberg interaction (the Hamiltonian is $H_{ij}=J(t){\vec S}_i\cdot{\vec S}_j$ between spins $i$ and $j$), while the one-qubit gates require the control of a local Zeeman field. Compared to the Heisenberg operation, the one-qubit operations are significantly slower and require substantially greater materials and device complexity, which may also contribute to increasing the decoherence rate. Here we introduce an explicit scheme in which the Heisenberg interaction alone suffices to exactly implement any quantum computer circuit, at a price of a factor of three in additional qubits and about a factor of ten in additional two-qubit operations. Even at this cost, the ability to eliminate the complexity of one-qubit operations should accelerate progress towards these solid-state implementations of quantum computation.
{
"annotation_id": "2f58e45e-2954-4c6d-9e4c-42ab26f6bd93",
"date_created": "2026-03-02T18:01:39.214000Z",
"date_modified": "2026-03-02T18:01:39.214000Z",
"file_hash": "178af068bbd140fdcea3e560bbe8dca90226221f9ef5d87028d26adefe3c58ed",
"private": false,
"record": {
"abstract": "Experimental implementations of quantum computer architectures are now being\ninvestigated in many different physical settings. The full set of requirements\nthat must be met to make quantum computing a reality in the laboratory [1] is\ndaunting, involving capabilities well beyond the present state of the art. In\nthis report we develop a significant simplification of these requirements that\ncan be applied in many recent solid-state approaches, using quantum dots [2],\nand using donor-atom nuclear spins [3] or electron spins [4]. In these\napproaches, the basic two-qubit quantum gate is generated by a tunable\nHeisenberg interaction (the Hamiltonian is $H_{ij}=J(t){\\vec S}_i\\cdot{\\vec\nS}_j$ between spins $i$ and $j$), while the one-qubit gates require the control\nof a local Zeeman field. Compared to the Heisenberg operation, the one-qubit\noperations are significantly slower and require substantially greater materials\nand device complexity, which may also contribute to increasing the decoherence\nrate. Here we introduce an explicit scheme in which the Heisenberg interaction\nalone suffices to exactly implement any quantum computer circuit, at a price of\na factor of three in additional qubits and about a factor of ten in additional\ntwo-qubit operations. Even at this cost, the ability to eliminate the\ncomplexity of one-qubit operations should accelerate progress towards these\nsolid-state implementations of quantum computation.",
"arxiv_id": "quant-ph/0005116",
"authors": [
"D. P. DiVincenzo",
"D. Bacon",
"J. Kempe",
"G. Burkard",
"K. B. Whaley"
],
"categories": [
"quant-ph"
],
"doi": "10.1038/35042541",
"journal_ref": "NATURE, Vol. 408, p. 339-342 (2000)",
"title": "Universal Quantum Computation with the Exchange Interaction",
"url": "https://arxiv.org/abs/quant-ph/0005116"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "54182e28-d4e1-47b7-9972-3e253693bf35",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}