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 %${\textsc {QMA}}%$ (%${\texts...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Massar, Serge [verfasserIn] Santha, Miklos [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2021 |
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| Schlagwörter: |
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| Übergeordnetes Werk: |
Enthalten in: Quantum information processing - Dordrecht : Springer Science + Business Media B.V., 2002, 20(2021), 1 vom: Jan. |
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| Übergeordnetes Werk: |
volume:20 ; year:2021 ; number:1 ; month:01 |
| Links: |
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| DOI / URN: |
10.1007/s11128-020-02959-0 |
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| Katalog-ID: |
SPR042683203 |
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| 520 | |a Abstract The complexity class %${\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 %${\textsc {TFQMA}}%$. | ||
| 650 | 4 | |a Quantum Complexity |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Quantum algorithms |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Quantum Merlin Arthur Games |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Functional QMA |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Total Functional QMA |7 (dpeaa)DE-He213 | |
| 700 | 1 | |a Santha, Miklos |e verfasserin |4 aut | |
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| 773 | 1 | 8 | |g volume:20 |g year:2021 |g number:1 |g month:01 |
| 856 | 4 | 0 | |u https://dx.doi.org/10.1007/s11128-020-02959-0 |z lizenzpflichtig |3 Volltext |
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10.1007/s11128-020-02959-0 doi (DE-627)SPR042683203 (DE-599)SPRs11128-020-02959-0-e (SPR)s11128-020-02959-0-e DE-627 ger DE-627 rakwb eng 004 ASE 54.00 bkl 33.23 bkl Massar, Serge verfasserin aut Total functions in QMA 2021 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier 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 (dpeaa)DE-He213 Quantum algorithms (dpeaa)DE-He213 Quantum Merlin Arthur Games (dpeaa)DE-He213 Functional QMA (dpeaa)DE-He213 Total Functional QMA (dpeaa)DE-He213 Santha, Miklos verfasserin aut Enthalten in Quantum information processing Dordrecht : Springer Science + Business Media B.V., 2002 20(2021), 1 vom: Jan. (DE-627)354193031 (DE-600)2088114-9 1573-1332 nnns volume:20 year:2021 number:1 month:01 https://dx.doi.org/10.1007/s11128-020-02959-0 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 54.00 ASE 33.23 ASE AR 20 2021 1 01 |
| spelling |
10.1007/s11128-020-02959-0 doi (DE-627)SPR042683203 (DE-599)SPRs11128-020-02959-0-e (SPR)s11128-020-02959-0-e DE-627 ger DE-627 rakwb eng 004 ASE 54.00 bkl 33.23 bkl Massar, Serge verfasserin aut Total functions in QMA 2021 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier 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 (dpeaa)DE-He213 Quantum algorithms (dpeaa)DE-He213 Quantum Merlin Arthur Games (dpeaa)DE-He213 Functional QMA (dpeaa)DE-He213 Total Functional QMA (dpeaa)DE-He213 Santha, Miklos verfasserin aut Enthalten in Quantum information processing Dordrecht : Springer Science + Business Media B.V., 2002 20(2021), 1 vom: Jan. (DE-627)354193031 (DE-600)2088114-9 1573-1332 nnns volume:20 year:2021 number:1 month:01 https://dx.doi.org/10.1007/s11128-020-02959-0 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 54.00 ASE 33.23 ASE AR 20 2021 1 01 |
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10.1007/s11128-020-02959-0 doi (DE-627)SPR042683203 (DE-599)SPRs11128-020-02959-0-e (SPR)s11128-020-02959-0-e DE-627 ger DE-627 rakwb eng 004 ASE 54.00 bkl 33.23 bkl Massar, Serge verfasserin aut Total functions in QMA 2021 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier 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 (dpeaa)DE-He213 Quantum algorithms (dpeaa)DE-He213 Quantum Merlin Arthur Games (dpeaa)DE-He213 Functional QMA (dpeaa)DE-He213 Total Functional QMA (dpeaa)DE-He213 Santha, Miklos verfasserin aut Enthalten in Quantum information processing Dordrecht : Springer Science + Business Media B.V., 2002 20(2021), 1 vom: Jan. (DE-627)354193031 (DE-600)2088114-9 1573-1332 nnns volume:20 year:2021 number:1 month:01 https://dx.doi.org/10.1007/s11128-020-02959-0 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 54.00 ASE 33.23 ASE AR 20 2021 1 01 |
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10.1007/s11128-020-02959-0 doi (DE-627)SPR042683203 (DE-599)SPRs11128-020-02959-0-e (SPR)s11128-020-02959-0-e DE-627 ger DE-627 rakwb eng 004 ASE 54.00 bkl 33.23 bkl Massar, Serge verfasserin aut Total functions in QMA 2021 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier 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 (dpeaa)DE-He213 Quantum algorithms (dpeaa)DE-He213 Quantum Merlin Arthur Games (dpeaa)DE-He213 Functional QMA (dpeaa)DE-He213 Total Functional QMA (dpeaa)DE-He213 Santha, Miklos verfasserin aut Enthalten in Quantum information processing Dordrecht : Springer Science + Business Media B.V., 2002 20(2021), 1 vom: Jan. (DE-627)354193031 (DE-600)2088114-9 1573-1332 nnns volume:20 year:2021 number:1 month:01 https://dx.doi.org/10.1007/s11128-020-02959-0 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 54.00 ASE 33.23 ASE AR 20 2021 1 01 |
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10.1007/s11128-020-02959-0 doi (DE-627)SPR042683203 (DE-599)SPRs11128-020-02959-0-e (SPR)s11128-020-02959-0-e DE-627 ger DE-627 rakwb eng 004 ASE 54.00 bkl 33.23 bkl Massar, Serge verfasserin aut Total functions in QMA 2021 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier 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 (dpeaa)DE-He213 Quantum algorithms (dpeaa)DE-He213 Quantum Merlin Arthur Games (dpeaa)DE-He213 Functional QMA (dpeaa)DE-He213 Total Functional QMA (dpeaa)DE-He213 Santha, Miklos verfasserin aut Enthalten in Quantum information processing Dordrecht : Springer Science + Business Media B.V., 2002 20(2021), 1 vom: Jan. (DE-627)354193031 (DE-600)2088114-9 1573-1332 nnns volume:20 year:2021 number:1 month:01 https://dx.doi.org/10.1007/s11128-020-02959-0 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 54.00 ASE 33.23 ASE AR 20 2021 1 01 |
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Enthalten in Quantum information processing 20(2021), 1 vom: Jan. volume:20 year:2021 number:1 month:01 |
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Massar, Serge @@aut@@ Santha, Miklos @@aut@@ |
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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 %${\textsc {TFQMA}}%$. 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Massar, Serge |
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Massar, Serge ddc 004 bkl 54.00 bkl 33.23 misc Quantum Complexity misc Quantum algorithms misc Quantum Merlin Arthur Games misc Functional QMA misc Total Functional QMA Total functions in QMA |
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004 ASE 54.00 bkl 33.23 bkl Total functions in QMA Quantum Complexity (dpeaa)DE-He213 Quantum algorithms (dpeaa)DE-He213 Quantum Merlin Arthur Games (dpeaa)DE-He213 Functional QMA (dpeaa)DE-He213 Total Functional QMA (dpeaa)DE-He213 |
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ddc 004 bkl 54.00 bkl 33.23 misc Quantum Complexity misc Quantum algorithms misc Quantum Merlin Arthur Games misc Functional QMA misc Total Functional QMA |
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Total functions in QMA |
| abstract |
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 %${\textsc {TFQMA}}%$. |
| abstractGer |
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 %${\textsc {TFQMA}}%$. |
| 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 %${\textsc {TFQMA}}%$. |
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| container_issue |
1 |
| title_short |
Total functions in QMA |
| url |
https://dx.doi.org/10.1007/s11128-020-02959-0 |
| remote_bool |
true |
| author2 |
Santha, Miklos |
| author2Str |
Santha, Miklos |
| ppnlink |
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| mediatype_str_mv |
c |
| isOA_txt |
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| hochschulschrift_bool |
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| doi_str |
10.1007/s11128-020-02959-0 |
| up_date |
2024-07-03T14:14:34.383Z |
| _version_ |
1803567575219568640 |
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| score |
7.400339 |