dorsal/arxiv
View SchemaImproved magic states distillation for quantum universality
| Authors | Ben W. Reichardt |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0411036 |
| URL | https://arxiv.org/abs/quant-ph/0411036 |
| DOI | 10.1007/s11128-005-7654-8 |
| Journal | Quant. Inf. Proc. 4:251-264 (2005) |
Abstract
Given stabilizer operations and the ability to repeatedly prepare a single-qubit mixed state rho, can we do universal quantum computation? As motivation for this question, "magic state" distillation procedures can reduce the general fault-tolerance problem to that of performing fault-tolerant stabilizer circuits. We improve the procedures of Bravyi and Kitaev in the Hadamard "magic" direction of the Bloch sphere to achieve a sharp threshold between those rho allowing universal quantum computation, and those for which any calculation can be efficiently classically simulated. As a corollary, the ability to repeatedly prepare any pure state which is not a stabilizer state (e.g., any single-qubit pure state which is not a Pauli eigenstate), together with stabilizer operations, gives quantum universality. It remains open whether there is also a tight separation in the so-called T direction.
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"abstract": "Given stabilizer operations and the ability to repeatedly prepare a\nsingle-qubit mixed state rho, can we do universal quantum computation? As\nmotivation for this question, \"magic state\" distillation procedures can reduce\nthe general fault-tolerance problem to that of performing fault-tolerant\nstabilizer circuits.\n We improve the procedures of Bravyi and Kitaev in the Hadamard \"magic\"\ndirection of the Bloch sphere to achieve a sharp threshold between those rho\nallowing universal quantum computation, and those for which any calculation can\nbe efficiently classically simulated. As a corollary, the ability to repeatedly\nprepare any pure state which is not a stabilizer state (e.g., any single-qubit\npure state which is not a Pauli eigenstate), together with stabilizer\noperations, gives quantum universality. It remains open whether there is also a\ntight separation in the so-called T direction.",
"arxiv_id": "quant-ph/0411036",
"authors": [
"Ben W. Reichardt"
],
"categories": [
"quant-ph"
],
"doi": "10.1007/s11128-005-7654-8",
"journal_ref": "Quant. Inf. Proc. 4:251-264 (2005)",
"title": "Improved magic states distillation for quantum universality",
"url": "https://arxiv.org/abs/quant-ph/0411036"
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