dorsal/arxiv
View SchemaSynthesis of multi-qudit Hybrid and d-valued Quantum Logic Circuits by Decomposition
| Authors | Faisal Shah Khan, Marek Perkowski |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0511019 |
| URL | https://arxiv.org/abs/quant-ph/0511019 |
| DOI | 10.1016/j.tcs.2006.09.006 |
| Journal | Theoretical Computer Science, Volume 367, Issue 3, 1 December 2006, Pages 336-346 |
Abstract
Recent research in generalizing quantum computation from 2-valued qudits to d-valued qudits has shown practical advantages for scaling up a quantum computer. A further generalization leads to quantum computing with hybrid qudits where two or more qudits have different finite dimensions. Advantages of hybrid and d-valued gates (circuits) and their physical realizations have been studied in detail by Muthukrishnan and Stroud (Physical Review A, 052309, 2000), Daboul et al. (J. Phys. A: Math. Gen. 36 2525-2536, 2003), and Bartlett et al (Physical Review A, Vol.65, 052316, 2002). In both cases, a quantum computation is performed when a unitary evolution operator, acting as a quantum logic gate, transforms the state of qudits in a quantum system. Unitary operators can be represented by square unitary matrices. If the system consists of a single qudit, then Tilma et al (J.Phys. A: Math. Gen. 35 (2002) 10467-10501) have shown that the unitary evolution matrix (gate) can be synthesized in terms of its Euler angle parameterization. However, if the quantum system consists of multiple qudits, then a gate may be synthesized by matrix decomposition techniques such as QR factorization and the Cosine-sine Decomposition (CSD). In this article, we present a CSD based synthesis method for n qudit hybrid quantum gates, and as a consequence, derive a CSD based synthesis method for n qudit gates where all the qudits have the same dimension.
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"abstract": "Recent research in generalizing quantum computation from 2-valued qudits to\nd-valued qudits has shown practical advantages for scaling up a quantum\ncomputer. A further generalization leads to quantum computing with hybrid\nqudits where two or more qudits have different finite dimensions. Advantages of\nhybrid and d-valued gates (circuits) and their physical realizations have been\nstudied in detail by Muthukrishnan and Stroud (Physical Review A, 052309,\n2000), Daboul et al. (J. Phys. A: Math. Gen. 36 2525-2536, 2003), and Bartlett\net al (Physical Review A, Vol.65, 052316, 2002). In both cases, a quantum\ncomputation is performed when a unitary evolution operator, acting as a quantum\nlogic gate, transforms the state of qudits in a quantum system. Unitary\noperators can be represented by square unitary matrices. If the system consists\nof a single qudit, then Tilma et al (J.Phys. A: Math. Gen. 35 (2002)\n10467-10501) have shown that the unitary evolution matrix (gate) can be\nsynthesized in terms of its Euler angle parameterization. However, if the\nquantum system consists of multiple qudits, then a gate may be synthesized by\nmatrix decomposition techniques such as QR factorization and the Cosine-sine\nDecomposition (CSD). In this article, we present a CSD based synthesis method\nfor n qudit hybrid quantum gates, and as a consequence, derive a CSD based\nsynthesis method for n qudit gates where all the qudits have the same\ndimension.",
"arxiv_id": "quant-ph/0511019",
"authors": [
"Faisal Shah Khan",
"Marek Perkowski"
],
"categories": [
"quant-ph"
],
"doi": "10.1016/j.tcs.2006.09.006",
"journal_ref": "Theoretical Computer Science, Volume 367, Issue 3, 1 December\n 2006, Pages 336-346",
"title": "Synthesis of multi-qudit Hybrid and d-valued Quantum Logic Circuits by Decomposition",
"url": "https://arxiv.org/abs/quant-ph/0511019"
},
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