dorsal/arxiv
View SchemaGeometric Approach to Digital Quantum Information
| Authors | Chad Rigetti, Remy Mosseri, Michel Devoret |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0312196 |
| URL | https://arxiv.org/abs/quant-ph/0312196 |
Abstract
We present geometric methods for uniformly discretizing the continuous N-qubit Hilbert space. When considered as the vertices of a geometrical figure, the resulting states form the equivalent of a Platonic solid. The discretization technique inherently describes a class of pi/2 rotations that connect neighboring states in the set, i.e. that leave the geometrical figures invariant. These rotations are shown to generate the Clifford group, a general group of discrete transformations on N qubits. Discretizing the N-qubit Hilbert space allows us to define its digital quantum information content, and we show that this information content grows as N^2. While we believe the discrete sets are interesting because they allow extra-classical behavior--such as quantum entanglement and quantum parallelism--to be explored while circumventing the continuity of Hilbert space, we also show how they may be a useful tool for problems in traditional quantum computation. We describe in detail the discrete sets for one and two qubits.
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"abstract": "We present geometric methods for uniformly discretizing the continuous\nN-qubit Hilbert space. When considered as the vertices of a geometrical figure,\nthe resulting states form the equivalent of a Platonic solid. The\ndiscretization technique inherently describes a class of pi/2 rotations that\nconnect neighboring states in the set, i.e. that leave the geometrical figures\ninvariant. These rotations are shown to generate the Clifford group, a general\ngroup of discrete transformations on N qubits. Discretizing the N-qubit Hilbert\nspace allows us to define its digital quantum information content, and we show\nthat this information content grows as N^2. While we believe the discrete sets\nare interesting because they allow extra-classical behavior--such as quantum\nentanglement and quantum parallelism--to be explored while circumventing the\ncontinuity of Hilbert space, we also show how they may be a useful tool for\nproblems in traditional quantum computation. We describe in detail the discrete\nsets for one and two qubits.",
"arxiv_id": "quant-ph/0312196",
"authors": [
"Chad Rigetti",
"Remy Mosseri",
"Michel Devoret"
],
"categories": [
"quant-ph"
],
"title": "Geometric Approach to Digital Quantum Information",
"url": "https://arxiv.org/abs/quant-ph/0312196"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "b0dc7424-6f56-4189-9af4-c8186d36d6ff",
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