dorsal/arxiv
View SchemaImplementing high dimensional unitary representations of SU(2) on a Quantum Computer
| Authors | Christof Zalka |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0407140 |
| URL | https://arxiv.org/abs/quant-ph/0407140 |
Abstract
In this note we consider a system with a large angular momentum l whose state we can store using some log_2(l) qubits. The problem then is how to carry out spatial rotations of the system in this representation. In other words we are looking at a unitary representation of SU(2) with dimension 2l+1 and want to implement these transformations with resources polynomial in log(l). We only give a sketch of our solution which involves ``storing'' discretised spherical harmonic functions Y_{l,m}(Theta,phi) in a quantum register. Also there are some technical gaps in the construction, but they are based on plausible assumptions. Our approach is rather cumbersome and we hope somebody will find a nicer solution. For a nice, elementary explanation of what we are trying to do (not involving physics or representation theory) see section 4.6.2.
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"abstract": "In this note we consider a system with a large angular momentum l whose state\nwe can store using some log_2(l) qubits. The problem then is how to carry out\nspatial rotations of the system in this representation. In other words we are\nlooking at a unitary representation of SU(2) with dimension 2l+1 and want to\nimplement these transformations with resources polynomial in log(l). We only\ngive a sketch of our solution which involves ``storing\u0027\u0027 discretised spherical\nharmonic functions Y_{l,m}(Theta,phi) in a quantum register. Also there are\nsome technical gaps in the construction, but they are based on plausible\nassumptions. Our approach is rather cumbersome and we hope somebody will find a\nnicer solution. For a nice, elementary explanation of what we are trying to do\n(not involving physics or representation theory) see section 4.6.2.",
"arxiv_id": "quant-ph/0407140",
"authors": [
"Christof Zalka"
],
"categories": [
"quant-ph"
],
"title": "Implementing high dimensional unitary representations of SU(2) on a Quantum Computer",
"url": "https://arxiv.org/abs/quant-ph/0407140"
},
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