dorsal/arxiv
View SchemaGeneralised Clifford groups and simulation of associated quantum circuits
| Authors | Sean Clark, Richard Jozsa, Noah Linden |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0701103 |
| URL | https://arxiv.org/abs/quant-ph/0701103 |
Abstract
Quantum computations that involve only Clifford operations are classically simulable despite the fact that they generate highly entangled states; this is the content of the Gottesman-Knill theorem. Here we isolate the ingredients of the theorem and provide generalisations of some of them with the aim of identifying new classes of simulable quantum computations. In the usual construction, Clifford operations arise as projective normalisers of the first and second tensor powers of the Pauli group. We consider replacing the Pauli group by an arbitrary finite subgroup G of U(d). In particular we seek G such that G tensor G has an entangling normaliser. Via a generalisation of the Gottesman-Knill theorem the resulting normalisers lead to classes of quantum circuits that can be classically efficiently simulated. For the qubit case d=2 we exhaustively treat all finite subgroups of U(2) and find that the only ones (up to unitary equivalence and trivial phase extensions) with entangling normalisers are the groups G_n generated by X and the n^th root of Z.
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"abstract": "Quantum computations that involve only Clifford operations are classically\nsimulable despite the fact that they generate highly entangled states; this is\nthe content of the Gottesman-Knill theorem. Here we isolate the ingredients of\nthe theorem and provide generalisations of some of them with the aim of\nidentifying new classes of simulable quantum computations. In the usual\nconstruction, Clifford operations arise as projective normalisers of the first\nand second tensor powers of the Pauli group. We consider replacing the Pauli\ngroup by an arbitrary finite subgroup G of U(d). In particular we seek G such\nthat G tensor G has an entangling normaliser. Via a generalisation of the\nGottesman-Knill theorem the resulting normalisers lead to classes of quantum\ncircuits that can be classically efficiently simulated. For the qubit case d=2\nwe exhaustively treat all finite subgroups of U(2) and find that the only ones\n(up to unitary equivalence and trivial phase extensions) with entangling\nnormalisers are the groups G_n generated by X and the n^th root of Z.",
"arxiv_id": "quant-ph/0701103",
"authors": [
"Sean Clark",
"Richard Jozsa",
"Noah Linden"
],
"categories": [
"quant-ph"
],
"title": "Generalised Clifford groups and simulation of associated quantum circuits",
"url": "https://arxiv.org/abs/quant-ph/0701103"
},
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