dorsal/arxiv
View SchemaQuantum Optimization Problems
| Authors | Tomoyuki Yamakami |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0204010 |
| URL | https://arxiv.org/abs/quant-ph/0204010 |
Abstract
Krentel [J. Comput. System. Sci., 36, pp.490--509] presented a framework for an NP optimization problem that searches an optimal value among exponentially-many outcomes of polynomial-time computations. This paper expands his framework to a quantum optimization problem using polynomial-time quantum computations and introduces the notion of an ``universal'' quantum optimization problem similar to a classical ``complete'' optimization problem. We exhibit a canonical quantum optimization problem that is universal for the class of polynomial-time quantum optimization problems. We show in a certain relativized world that all quantum optimization problems cannot be approximated closely by quantum polynomial-time computations. We also study the complexity of quantum optimization problems in connection to well-known complexity classes.
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"abstract": "Krentel [J. Comput. System. Sci., 36, pp.490--509] presented a framework for\nan NP optimization problem that searches an optimal value among\nexponentially-many outcomes of polynomial-time computations. This paper expands\nhis framework to a quantum optimization problem using polynomial-time quantum\ncomputations and introduces the notion of an ``universal\u0027\u0027 quantum optimization\nproblem similar to a classical ``complete\u0027\u0027 optimization problem. We exhibit a\ncanonical quantum optimization problem that is universal for the class of\npolynomial-time quantum optimization problems. We show in a certain relativized\nworld that all quantum optimization problems cannot be approximated closely by\nquantum polynomial-time computations. We also study the complexity of quantum\noptimization problems in connection to well-known complexity classes.",
"arxiv_id": "quant-ph/0204010",
"authors": [
"Tomoyuki Yamakami"
],
"categories": [
"quant-ph",
"cs.CC"
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"title": "Quantum Optimization Problems",
"url": "https://arxiv.org/abs/quant-ph/0204010"
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