What Can Quantum Optics Say about Computational Complexity Theory?
Considering the problem of sampling from the output photon-counting probability distribution of a linear-optical network for input Gaussian states, we obtain results that are of interest from both quantum theory and the computational complexity theory point of view. We derive a general formula for c...
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| Vydáno v: | Physical review letters Ročník 114; číslo 6; s. 060501 |
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| Hlavní autoři: | , , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
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United States
13.02.2015
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| ISSN: | 0031-9007, 1079-7114, 1079-7114 |
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| Abstract | Considering the problem of sampling from the output photon-counting probability distribution of a linear-optical network for input Gaussian states, we obtain results that are of interest from both quantum theory and the computational complexity theory point of view. We derive a general formula for calculating the output probabilities, and by considering input thermal states, we show that the output probabilities are proportional to permanents of positive-semidefinite Hermitian matrices. It is believed that approximating permanents of complex matrices in general is a #P-hard problem. However, we show that these permanents can be approximated with an algorithm in the BPP^{NP} complexity class, as there exists an efficient classical algorithm for sampling from the output probability distribution. We further consider input squeezed-vacuum states and discuss the complexity of sampling from the probability distribution at the output. |
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| AbstractList | Considering the problem of sampling from the output photon-counting probability distribution of a linear-optical network for input Gaussian states, we obtain results that are of interest from both quantum theory and the computational complexity theory point of view. We derive a general formula for calculating the output probabilities, and by considering input thermal states, we show that the output probabilities are proportional to permanents of positive-semidefinite Hermitian matrices. It is believed that approximating permanents of complex matrices in general is a #P-hard problem. However, we show that these permanents can be approximated with an algorithm in the BPP^{NP} complexity class, as there exists an efficient classical algorithm for sampling from the output probability distribution. We further consider input squeezed-vacuum states and discuss the complexity of sampling from the probability distribution at the output.Considering the problem of sampling from the output photon-counting probability distribution of a linear-optical network for input Gaussian states, we obtain results that are of interest from both quantum theory and the computational complexity theory point of view. We derive a general formula for calculating the output probabilities, and by considering input thermal states, we show that the output probabilities are proportional to permanents of positive-semidefinite Hermitian matrices. It is believed that approximating permanents of complex matrices in general is a #P-hard problem. However, we show that these permanents can be approximated with an algorithm in the BPP^{NP} complexity class, as there exists an efficient classical algorithm for sampling from the output probability distribution. We further consider input squeezed-vacuum states and discuss the complexity of sampling from the probability distribution at the output. Considering the problem of sampling from the output photon-counting probability distribution of a linear-optical network for input Gaussian states, we obtain results that are of interest from both quantum theory and the computational complexity theory point of view. We derive a general formula for calculating the output probabilities, and by considering input thermal states, we show that the output probabilities are proportional to permanents of positive-semidefinite Hermitian matrices. It is believed that approximating permanents of complex matrices in general is a #P-hard problem. However, we show that these permanents can be approximated with an algorithm in the BPPNP complexity class, as there exists an efficient classical algorithm for sampling from the output probability distribution. We further consider input squeezed-vacuum states and discuss the complexity of sampling from the probability distribution at the output. Considering the problem of sampling from the output photon-counting probability distribution of a linear-optical network for input Gaussian states, we obtain results that are of interest from both quantum theory and the computational complexity theory point of view. We derive a general formula for calculating the output probabilities, and by considering input thermal states, we show that the output probabilities are proportional to permanents of positive-semidefinite Hermitian matrices. It is believed that approximating permanents of complex matrices in general is a #P-hard problem. However, we show that these permanents can be approximated with an algorithm in the BPP^{NP} complexity class, as there exists an efficient classical algorithm for sampling from the output probability distribution. We further consider input squeezed-vacuum states and discuss the complexity of sampling from the probability distribution at the output. |
| ArticleNumber | 060501 |
| Author | Lund, Austin P. Ralph, Timothy C. Rahimi-Keshari, Saleh |
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| BackLink | https://www.ncbi.nlm.nih.gov/pubmed/25723196$$D View this record in MEDLINE/PubMed |
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| CitedBy_id | crossref_primary_10_1103_PhysRevA_111_042412 crossref_primary_10_1103_PhysRevLett_134_140601 crossref_primary_10_1007_s40766_023_00040_x crossref_primary_10_3390_e25121584 crossref_primary_10_1038_s41598_018_24302_5 crossref_primary_10_1103_PhysRevApplied_20_054043 crossref_primary_10_1103_PhysRevA_111_012418 crossref_primary_10_1038_s41598_017_07770_z crossref_primary_10_1103_PRXQuantum_5_040312 crossref_primary_10_1007_s00453_023_01169_1 crossref_primary_10_1103_PhysRevResearch_6_013004 crossref_primary_10_1103_PhysRevX_6_021039 crossref_primary_10_1038_s41534_023_00791_9 crossref_primary_10_1080_09500340_2015_1088096 crossref_primary_10_1088_1742_6596_1071_1_012009 crossref_primary_10_1103_PhysRevApplied_8_064008 crossref_primary_10_1117_1_APN_4_1_016011 crossref_primary_10_1126_science_abe8770 crossref_primary_10_1103_PhysRevResearch_3_043116 crossref_primary_10_1016_j_scib_2019_04_007 crossref_primary_10_1073_pnas_1815884116 crossref_primary_10_1007_s11128_019_2525_x crossref_primary_10_1007_s12200_024_00133_3 crossref_primary_10_1103_PhysRevA_111_032622 crossref_primary_10_1088_2040_8986_aae74a crossref_primary_10_1088_2058_9565_acf06c crossref_primary_10_1088_1367_2630_ab0610 crossref_primary_10_1038_s41598_018_22086_2 crossref_primary_10_1088_1742_5468_2015_05_P05018 crossref_primary_10_1063_5_0129638 crossref_primary_10_1088_1751_8121_ab1cc7 crossref_primary_10_1088_1674_1056_ac01e3 crossref_primary_10_1088_1742_6596_2894_1_012002 crossref_primary_10_1038_s41598_017_15596_y crossref_primary_10_1038_s41598_017_17506_8 crossref_primary_10_1088_1742_6596_2894_1_012003 crossref_primary_10_1088_1361_6455_aaf031 crossref_primary_10_1103_PhysRevResearch_5_013177 crossref_primary_10_1103_PRXQuantum_5_020337 crossref_primary_10_1088_1742_6596_1612_1_012015 |
| Cites_doi | 10.1098/rspa.2011.0232 10.4086/toc.2013.v009a004 10.1126/science.1231692 10.1145/1008731.1008738 10.1137/0220053 10.1016/0304-3975(79)90044-6 10.1038/nphoton.2013.102 10.1137/0214060 10.1103/PhysRevA.88.044301 10.1038/nphoton.2014.135 10.1017/CBO9781139644105 10.1103/PhysRevLett.10.84 10.1126/science.1231440 10.1038/nphoton.2013.112 10.1103/PhysRevLett.10.277 10.1103/PhysRevA.88.063822 10.1364/OE.21.013450 10.1103/PhysRevLett.113.020502 10.1103/PhysRevLett.113.100502 |
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| Title | What Can Quantum Optics Say about Computational Complexity Theory? |
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