Total functions in QMA
Abstract The complexity class $${\textsc {QMA}}$$ is the quantum analog of the classical complexity class $${\textsc {NP}}$$. The functional analogs of $${\textsc {NP}}$$ and $${\textsc {QMA}}$$, called functional $${\textsc {NP}}$$ ($${\textsc {FNP}}$$) and functional $${\textsc {QMA}}$$ ($${\texts...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Massar, Serge [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2021 |
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| Schlagwörter: |
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| Anmerkung: |
© The Author(s), under exclusive licence to Springer Science+Business Media, LLC part of Springer Nature 2021 |
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| Übergeordnetes Werk: |
Enthalten in: Quantum information processing - Springer US, 2002, 20(2021), 1 vom: Jan. |
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| Übergeordnetes Werk: |
volume:20 ; year:2021 ; number:1 ; month:01 |
| Links: |
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| DOI / URN: |
10.1007/s11128-020-02959-0 |
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OLC2122641037 |
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| 520 | |a Abstract The complexity class $${\textsc {QMA}}$$ is the quantum analog of the classical complexity class $${\textsc {NP}}$$. The functional analogs of $${\textsc {NP}}$$ and $${\textsc {QMA}}$$, called functional $${\textsc {NP}}$$ ($${\textsc {FNP}}$$) and functional $${\textsc {QMA}}$$ ($${\textsc {FQMA}}$$), consist in either outputting a (classical or quantum) witness or outputting NO if there does not exist a witness. The classical complexity class total functional $${\textsc {NP}}$$ ($${\textsc {TFNP}}$$) is the subset of $${\textsc {FNP}}$$ for which it can be shown that the NO outcome never occurs. $${\textsc {TFNP}}$$ includes many natural and important problems. Here we introduce the complexity class total functional $${\textsc {QMA}}$$ ($${\textsc {TFQMA}}$$), the quantum analog of $${\textsc {TFNP}}$$. We show that $${\textsc {FQMA}}$$ and $${\textsc {TFQMA}}$$ can be defined in such a way that they do not depend on the values of the completeness and soundness probabilities. We provide examples of problems that lie in $${\textsc {TFQMA}}$$, coming from areas such as the complexity of k-local Hamiltonians and public key quantum money. In the context of black-box groups, we note that group non-membership, which was known to belong to $${\textsc {QMA}}$$, in fact belongs to $${\textsc {TFQMA}}$$. We also provide a simple oracle with respect to which we have a separation between $${\textsc {FBQP}}$$ and $${\textsc {TFQMA}}$$. | ||
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10.1007/s11128-020-02959-0 doi (DE-627)OLC2122641037 (DE-He213)s11128-020-02959-0-p DE-627 ger DE-627 rakwb eng 004 VZ 33.23$jQuantenphysik bkl 54.10$jTheoretische Informatik bkl Massar, Serge verfasserin (orcid)0000-0002-4381-2485 aut Total functions in QMA 2021 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s), under exclusive licence to Springer Science+Business Media, LLC part of Springer Nature 2021 Abstract The complexity class $${\textsc {QMA}}$$ is the quantum analog of the classical complexity class $${\textsc {NP}}$$. The functional analogs of $${\textsc {NP}}$$ and $${\textsc {QMA}}$$, called functional $${\textsc {NP}}$$ ($${\textsc {FNP}}$$) and functional $${\textsc {QMA}}$$ ($${\textsc {FQMA}}$$), consist in either outputting a (classical or quantum) witness or outputting NO if there does not exist a witness. The classical complexity class total functional $${\textsc {NP}}$$ ($${\textsc {TFNP}}$$) is the subset of $${\textsc {FNP}}$$ for which it can be shown that the NO outcome never occurs. $${\textsc {TFNP}}$$ includes many natural and important problems. Here we introduce the complexity class total functional $${\textsc {QMA}}$$ ($${\textsc {TFQMA}}$$), the quantum analog of $${\textsc {TFNP}}$$. We show that $${\textsc {FQMA}}$$ and $${\textsc {TFQMA}}$$ can be defined in such a way that they do not depend on the values of the completeness and soundness probabilities. We provide examples of problems that lie in $${\textsc {TFQMA}}$$, coming from areas such as the complexity of k-local Hamiltonians and public key quantum money. In the context of black-box groups, we note that group non-membership, which was known to belong to $${\textsc {QMA}}$$, in fact belongs to $${\textsc {TFQMA}}$$. We also provide a simple oracle with respect to which we have a separation between $${\textsc {FBQP}}$$ and $${\textsc {TFQMA}}$$. Quantum Complexity Quantum algorithms Quantum Merlin Arthur Games Functional QMA Total Functional QMA Santha, Miklos aut Enthalten in Quantum information processing Springer US, 2002 20(2021), 1 vom: Jan. (DE-627)489255752 (DE-600)2191523-4 (DE-576)9489255750 1570-0755 nnns volume:20 year:2021 number:1 month:01 https://doi.org/10.1007/s11128-020-02959-0 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT 33.23$jQuantenphysik VZ 106407910 (DE-625)106407910 54.10$jTheoretische Informatik VZ 106418815 (DE-625)106418815 AR 20 2021 1 01 |
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10.1007/s11128-020-02959-0 doi (DE-627)OLC2122641037 (DE-He213)s11128-020-02959-0-p DE-627 ger DE-627 rakwb eng 004 VZ 33.23$jQuantenphysik bkl 54.10$jTheoretische Informatik bkl Massar, Serge verfasserin (orcid)0000-0002-4381-2485 aut Total functions in QMA 2021 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s), under exclusive licence to Springer Science+Business Media, LLC part of Springer Nature 2021 Abstract The complexity class $${\textsc {QMA}}$$ is the quantum analog of the classical complexity class $${\textsc {NP}}$$. The functional analogs of $${\textsc {NP}}$$ and $${\textsc {QMA}}$$, called functional $${\textsc {NP}}$$ ($${\textsc {FNP}}$$) and functional $${\textsc {QMA}}$$ ($${\textsc {FQMA}}$$), consist in either outputting a (classical or quantum) witness or outputting NO if there does not exist a witness. The classical complexity class total functional $${\textsc {NP}}$$ ($${\textsc {TFNP}}$$) is the subset of $${\textsc {FNP}}$$ for which it can be shown that the NO outcome never occurs. $${\textsc {TFNP}}$$ includes many natural and important problems. Here we introduce the complexity class total functional $${\textsc {QMA}}$$ ($${\textsc {TFQMA}}$$), the quantum analog of $${\textsc {TFNP}}$$. We show that $${\textsc {FQMA}}$$ and $${\textsc {TFQMA}}$$ can be defined in such a way that they do not depend on the values of the completeness and soundness probabilities. We provide examples of problems that lie in $${\textsc {TFQMA}}$$, coming from areas such as the complexity of k-local Hamiltonians and public key quantum money. In the context of black-box groups, we note that group non-membership, which was known to belong to $${\textsc {QMA}}$$, in fact belongs to $${\textsc {TFQMA}}$$. We also provide a simple oracle with respect to which we have a separation between $${\textsc {FBQP}}$$ and $${\textsc {TFQMA}}$$. Quantum Complexity Quantum algorithms Quantum Merlin Arthur Games Functional QMA Total Functional QMA Santha, Miklos aut Enthalten in Quantum information processing Springer US, 2002 20(2021), 1 vom: Jan. (DE-627)489255752 (DE-600)2191523-4 (DE-576)9489255750 1570-0755 nnns volume:20 year:2021 number:1 month:01 https://doi.org/10.1007/s11128-020-02959-0 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT 33.23$jQuantenphysik VZ 106407910 (DE-625)106407910 54.10$jTheoretische Informatik VZ 106418815 (DE-625)106418815 AR 20 2021 1 01 |
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10.1007/s11128-020-02959-0 doi (DE-627)OLC2122641037 (DE-He213)s11128-020-02959-0-p DE-627 ger DE-627 rakwb eng 004 VZ 33.23$jQuantenphysik bkl 54.10$jTheoretische Informatik bkl Massar, Serge verfasserin (orcid)0000-0002-4381-2485 aut Total functions in QMA 2021 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s), under exclusive licence to Springer Science+Business Media, LLC part of Springer Nature 2021 Abstract The complexity class $${\textsc {QMA}}$$ is the quantum analog of the classical complexity class $${\textsc {NP}}$$. The functional analogs of $${\textsc {NP}}$$ and $${\textsc {QMA}}$$, called functional $${\textsc {NP}}$$ ($${\textsc {FNP}}$$) and functional $${\textsc {QMA}}$$ ($${\textsc {FQMA}}$$), consist in either outputting a (classical or quantum) witness or outputting NO if there does not exist a witness. The classical complexity class total functional $${\textsc {NP}}$$ ($${\textsc {TFNP}}$$) is the subset of $${\textsc {FNP}}$$ for which it can be shown that the NO outcome never occurs. $${\textsc {TFNP}}$$ includes many natural and important problems. Here we introduce the complexity class total functional $${\textsc {QMA}}$$ ($${\textsc {TFQMA}}$$), the quantum analog of $${\textsc {TFNP}}$$. We show that $${\textsc {FQMA}}$$ and $${\textsc {TFQMA}}$$ can be defined in such a way that they do not depend on the values of the completeness and soundness probabilities. We provide examples of problems that lie in $${\textsc {TFQMA}}$$, coming from areas such as the complexity of k-local Hamiltonians and public key quantum money. In the context of black-box groups, we note that group non-membership, which was known to belong to $${\textsc {QMA}}$$, in fact belongs to $${\textsc {TFQMA}}$$. We also provide a simple oracle with respect to which we have a separation between $${\textsc {FBQP}}$$ and $${\textsc {TFQMA}}$$. Quantum Complexity Quantum algorithms Quantum Merlin Arthur Games Functional QMA Total Functional QMA Santha, Miklos aut Enthalten in Quantum information processing Springer US, 2002 20(2021), 1 vom: Jan. (DE-627)489255752 (DE-600)2191523-4 (DE-576)9489255750 1570-0755 nnns volume:20 year:2021 number:1 month:01 https://doi.org/10.1007/s11128-020-02959-0 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT 33.23$jQuantenphysik VZ 106407910 (DE-625)106407910 54.10$jTheoretische Informatik VZ 106418815 (DE-625)106418815 AR 20 2021 1 01 |
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10.1007/s11128-020-02959-0 doi (DE-627)OLC2122641037 (DE-He213)s11128-020-02959-0-p DE-627 ger DE-627 rakwb eng 004 VZ 33.23$jQuantenphysik bkl 54.10$jTheoretische Informatik bkl Massar, Serge verfasserin (orcid)0000-0002-4381-2485 aut Total functions in QMA 2021 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s), under exclusive licence to Springer Science+Business Media, LLC part of Springer Nature 2021 Abstract The complexity class $${\textsc {QMA}}$$ is the quantum analog of the classical complexity class $${\textsc {NP}}$$. The functional analogs of $${\textsc {NP}}$$ and $${\textsc {QMA}}$$, called functional $${\textsc {NP}}$$ ($${\textsc {FNP}}$$) and functional $${\textsc {QMA}}$$ ($${\textsc {FQMA}}$$), consist in either outputting a (classical or quantum) witness or outputting NO if there does not exist a witness. The classical complexity class total functional $${\textsc {NP}}$$ ($${\textsc {TFNP}}$$) is the subset of $${\textsc {FNP}}$$ for which it can be shown that the NO outcome never occurs. $${\textsc {TFNP}}$$ includes many natural and important problems. Here we introduce the complexity class total functional $${\textsc {QMA}}$$ ($${\textsc {TFQMA}}$$), the quantum analog of $${\textsc {TFNP}}$$. We show that $${\textsc {FQMA}}$$ and $${\textsc {TFQMA}}$$ can be defined in such a way that they do not depend on the values of the completeness and soundness probabilities. We provide examples of problems that lie in $${\textsc {TFQMA}}$$, coming from areas such as the complexity of k-local Hamiltonians and public key quantum money. In the context of black-box groups, we note that group non-membership, which was known to belong to $${\textsc {QMA}}$$, in fact belongs to $${\textsc {TFQMA}}$$. We also provide a simple oracle with respect to which we have a separation between $${\textsc {FBQP}}$$ and $${\textsc {TFQMA}}$$. Quantum Complexity Quantum algorithms Quantum Merlin Arthur Games Functional QMA Total Functional QMA Santha, Miklos aut Enthalten in Quantum information processing Springer US, 2002 20(2021), 1 vom: Jan. (DE-627)489255752 (DE-600)2191523-4 (DE-576)9489255750 1570-0755 nnns volume:20 year:2021 number:1 month:01 https://doi.org/10.1007/s11128-020-02959-0 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT 33.23$jQuantenphysik VZ 106407910 (DE-625)106407910 54.10$jTheoretische Informatik VZ 106418815 (DE-625)106418815 AR 20 2021 1 01 |
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Total functions in QMA |
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total functions in qma |
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Abstract The complexity class $${\textsc {QMA}}$$ is the quantum analog of the classical complexity class $${\textsc {NP}}$$. The functional analogs of $${\textsc {NP}}$$ and $${\textsc {QMA}}$$, called functional $${\textsc {NP}}$$ ($${\textsc {FNP}}$$) and functional $${\textsc {QMA}}$$ ($${\textsc {FQMA}}$$), consist in either outputting a (classical or quantum) witness or outputting NO if there does not exist a witness. The classical complexity class total functional $${\textsc {NP}}$$ ($${\textsc {TFNP}}$$) is the subset of $${\textsc {FNP}}$$ for which it can be shown that the NO outcome never occurs. $${\textsc {TFNP}}$$ includes many natural and important problems. Here we introduce the complexity class total functional $${\textsc {QMA}}$$ ($${\textsc {TFQMA}}$$), the quantum analog of $${\textsc {TFNP}}$$. We show that $${\textsc {FQMA}}$$ and $${\textsc {TFQMA}}$$ can be defined in such a way that they do not depend on the values of the completeness and soundness probabilities. We provide examples of problems that lie in $${\textsc {TFQMA}}$$, coming from areas such as the complexity of k-local Hamiltonians and public key quantum money. In the context of black-box groups, we note that group non-membership, which was known to belong to $${\textsc {QMA}}$$, in fact belongs to $${\textsc {TFQMA}}$$. We also provide a simple oracle with respect to which we have a separation between $${\textsc {FBQP}}$$ and $${\textsc {TFQMA}}$$. © The Author(s), under exclusive licence to Springer Science+Business Media, LLC part of Springer Nature 2021 |
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Abstract The complexity class $${\textsc {QMA}}$$ is the quantum analog of the classical complexity class $${\textsc {NP}}$$. The functional analogs of $${\textsc {NP}}$$ and $${\textsc {QMA}}$$, called functional $${\textsc {NP}}$$ ($${\textsc {FNP}}$$) and functional $${\textsc {QMA}}$$ ($${\textsc {FQMA}}$$), consist in either outputting a (classical or quantum) witness or outputting NO if there does not exist a witness. The classical complexity class total functional $${\textsc {NP}}$$ ($${\textsc {TFNP}}$$) is the subset of $${\textsc {FNP}}$$ for which it can be shown that the NO outcome never occurs. $${\textsc {TFNP}}$$ includes many natural and important problems. Here we introduce the complexity class total functional $${\textsc {QMA}}$$ ($${\textsc {TFQMA}}$$), the quantum analog of $${\textsc {TFNP}}$$. We show that $${\textsc {FQMA}}$$ and $${\textsc {TFQMA}}$$ can be defined in such a way that they do not depend on the values of the completeness and soundness probabilities. We provide examples of problems that lie in $${\textsc {TFQMA}}$$, coming from areas such as the complexity of k-local Hamiltonians and public key quantum money. In the context of black-box groups, we note that group non-membership, which was known to belong to $${\textsc {QMA}}$$, in fact belongs to $${\textsc {TFQMA}}$$. We also provide a simple oracle with respect to which we have a separation between $${\textsc {FBQP}}$$ and $${\textsc {TFQMA}}$$. © The Author(s), under exclusive licence to Springer Science+Business Media, LLC part of Springer Nature 2021 |
| abstract_unstemmed |
Abstract The complexity class $${\textsc {QMA}}$$ is the quantum analog of the classical complexity class $${\textsc {NP}}$$. The functional analogs of $${\textsc {NP}}$$ and $${\textsc {QMA}}$$, called functional $${\textsc {NP}}$$ ($${\textsc {FNP}}$$) and functional $${\textsc {QMA}}$$ ($${\textsc {FQMA}}$$), consist in either outputting a (classical or quantum) witness or outputting NO if there does not exist a witness. The classical complexity class total functional $${\textsc {NP}}$$ ($${\textsc {TFNP}}$$) is the subset of $${\textsc {FNP}}$$ for which it can be shown that the NO outcome never occurs. $${\textsc {TFNP}}$$ includes many natural and important problems. Here we introduce the complexity class total functional $${\textsc {QMA}}$$ ($${\textsc {TFQMA}}$$), the quantum analog of $${\textsc {TFNP}}$$. We show that $${\textsc {FQMA}}$$ and $${\textsc {TFQMA}}$$ can be defined in such a way that they do not depend on the values of the completeness and soundness probabilities. We provide examples of problems that lie in $${\textsc {TFQMA}}$$, coming from areas such as the complexity of k-local Hamiltonians and public key quantum money. In the context of black-box groups, we note that group non-membership, which was known to belong to $${\textsc {QMA}}$$, in fact belongs to $${\textsc {TFQMA}}$$. We also provide a simple oracle with respect to which we have a separation between $${\textsc {FBQP}}$$ and $${\textsc {TFQMA}}$$. © The Author(s), under exclusive licence to Springer Science+Business Media, LLC part of Springer Nature 2021 |
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