Predicting many properties of a quantum system from very few measurements
Predicting the properties of complex, large-scale quantum systems is essential for developing quantum technologies. We present an efficient method for constructing an approximate classical description of a quantum state using very few measurements of the state. This description, called a ‘classical...
Saved in:
| Published in | Nature physics Vol. 16; no. 10; pp. 1050 - 1057 |
|---|---|
| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
London
Nature Publishing Group UK
01.10.2020
Nature Publishing Group |
| Subjects | |
| Online Access | Get full text |
Cover
Loading…
| Abstract | Predicting the properties of complex, large-scale quantum systems is essential for developing quantum technologies. We present an efficient method for constructing an approximate classical description of a quantum state using very few measurements of the state. This description, called a ‘classical shadow’, can be used to predict many different properties; order
log
(
M
)
measurements suffice to accurately predict
M
different functions of the state with high success probability. The number of measurements is independent of the system size and saturates information-theoretic lower bounds. Moreover, target properties to predict can be selected after the measurements are completed. We support our theoretical findings with extensive numerical experiments. We apply classical shadows to predict quantum fidelities, entanglement entropies, two-point correlation functions, expectation values of local observables and the energy variance of many-body local Hamiltonians. The numerical results highlight the advantages of classical shadows relative to previously known methods.
An efficient method has been proposed through which the properties of a complex, large-scale quantum system can be predicted without fully characterizing the quantum state. |
|---|---|
| AbstractList | Predicting the properties of complex, large-scale quantum systems is essential for developing quantum technologies. We present an efficient method for constructing an approximate classical description of a quantum state using very few measurements of the state. This description, called a ‘classical shadow’, can be used to predict many different properties; order
log
(
M
)
measurements suffice to accurately predict
M
different functions of the state with high success probability. The number of measurements is independent of the system size and saturates information-theoretic lower bounds. Moreover, target properties to predict can be selected after the measurements are completed. We support our theoretical findings with extensive numerical experiments. We apply classical shadows to predict quantum fidelities, entanglement entropies, two-point correlation functions, expectation values of local observables and the energy variance of many-body local Hamiltonians. The numerical results highlight the advantages of classical shadows relative to previously known methods.
An efficient method has been proposed through which the properties of a complex, large-scale quantum system can be predicted without fully characterizing the quantum state. Predicting the properties of complex, large-scale quantum systems is essential for developing quantum technologies. We present an efficient method for constructing an approximate classical description of a quantum state using very few measurements of the state. This description, called a ‘classical shadow’, can be used to predict many different properties; order log(M) measurements suffice to accurately predict M different functions of the state with high success probability. The number of measurements is independent of the system size and saturates information-theoretic lower bounds. Moreover, target properties to predict can be selected after the measurements are completed. We support our theoretical findings with extensive numerical experiments. We apply classical shadows to predict quantum fidelities, entanglement entropies, two-point correlation functions, expectation values of local observables and the energy variance of many-body local Hamiltonians. The numerical results highlight the advantages of classical shadows relative to previously known methods.An efficient method has been proposed through which the properties of a complex, large-scale quantum system can be predicted without fully characterizing the quantum state. |
| Author | Kueng, Richard Preskill, John Huang, Hsin-Yuan |
| Author_xml | – sequence: 1 givenname: Hsin-Yuan orcidid: 0000-0001-5317-2613 surname: Huang fullname: Huang, Hsin-Yuan email: hsinyuan@caltech.edu organization: Institute for Quantum Information and Matter, California Institute of Technology, Department of Computing and Mathematical Sciences, California Institute of Technology – sequence: 2 givenname: Richard surname: Kueng fullname: Kueng, Richard organization: Institute for Quantum Information and Matter, California Institute of Technology, Department of Computing and Mathematical Sciences, California Institute of Technology, Institute for Integrated Circuits, Johannes Kepler University Linz – sequence: 3 givenname: John surname: Preskill fullname: Preskill, John organization: Institute for Quantum Information and Matter, California Institute of Technology, Department of Computing and Mathematical Sciences, California Institute of Technology, Walter Burke Institute for Theoretical Physics, California Institute of Technology |
| BookMark | eNp9kEtLxDAUhYOM4MzoD3AXcF3Nq026lMEXDOhC1yFNb4YO03QmSZX-eztUFARd3bs43z3nngWa-c4DQpeUXFPC1U0UNC9kRhjJSMlZJk_QnEqRZ0woOvveJT9Dixi3hAhWUD5HTy8B6samxm9wa_yA96HbQ0gNRNw5bPChNz71LY5DTNBiF7oWv0MYsIMP3IKJfYAWfIrn6NSZXYSLr7lEb_d3r6vHbP388LS6XWeWK5ayMq8tU9zYShQkr6UoLTAqWQWkrJ1RhFe1ygvlKidsYRzjBbc1UOcU5WL8bYmuprtj0kMPMelt1wc_WmomRClyITgdVXRS2dDFGMDpfWhaEwZNiT42pqfG9NiYPjam5cjIX4xtkklN51Mwze5fkk1kHF38BsJPpr-hT6r2gk0 |
| CitedBy_id | crossref_primary_10_1103_PhysRevLett_133_060802 crossref_primary_10_1103_PRXQuantum_4_010303 crossref_primary_10_1103_RevModPhys_94_015004 crossref_primary_10_1140_epjqt_s40507_023_00166_1 crossref_primary_10_1103_PhysRevLett_129_220502 crossref_primary_10_1103_PhysRevResearch_6_043284 crossref_primary_10_1103_PhysRevA_109_052423 crossref_primary_10_1103_PRXQuantum_5_030311 crossref_primary_10_1038_s41534_024_00927_5 crossref_primary_10_1103_PhysRevA_108_032417 crossref_primary_10_1103_PRXQuantum_4_010305 crossref_primary_10_1007_s10773_023_05527_1 crossref_primary_10_1021_acs_jctc_3c01113 crossref_primary_10_1103_PhysRevLett_127_260401 crossref_primary_10_1103_PhysRevLett_132_130602 crossref_primary_10_1103_PRXQuantum_5_040352 crossref_primary_10_1103_PhysRevResearch_6_033111 crossref_primary_10_1103_PhysRevX_14_011013 crossref_primary_10_1109_JSTQE_2023_3266662 crossref_primary_10_1007_JHEP09_2021_034 crossref_primary_10_35848_1347_4065_adb438 crossref_primary_10_1038_s41534_021_00455_6 crossref_primary_10_1007_s11128_022_03630_6 crossref_primary_10_1038_s41467_023_39382_9 crossref_primary_10_1038_s41467_024_47983_1 crossref_primary_10_22331_q_2024_01_10_1220 crossref_primary_10_1016_j_scib_2023_04_003 crossref_primary_10_1103_PhysRevResearch_5_033193 crossref_primary_10_1088_2058_9565_ad92a4 crossref_primary_10_1116_5_0192456 crossref_primary_10_1021_acs_jctc_3c00012 crossref_primary_10_1103_PhysRevResearch_5_023027 crossref_primary_10_1103_RevModPhys_95_035001 crossref_primary_10_1088_2058_9565_acfc62 crossref_primary_10_1103_PhysRevResearch_6_033248 crossref_primary_10_1103_PhysRevLett_132_070202 crossref_primary_10_1016_j_optcom_2025_131604 crossref_primary_10_1103_PhysRevA_110_012409 crossref_primary_10_1016_j_physleta_2023_129279 crossref_primary_10_1103_PhysRevResearch_4_013054 crossref_primary_10_1103_PhysRevResearch_6_043041 crossref_primary_10_1103_PRXQuantum_5_040349 crossref_primary_10_22331_q_2024_05_08_1340 crossref_primary_10_1103_PhysRevApplied_21_014037 crossref_primary_10_1103_PhysRevResearch_6_043267 crossref_primary_10_1103_PhysRevLett_134_010603 crossref_primary_10_1145_3718349 crossref_primary_10_22331_q_2025_01_15_1594 crossref_primary_10_1038_s41534_024_00881_2 crossref_primary_10_1088_2058_9565_acc4e3 crossref_primary_10_1007_s11433_022_2057_y crossref_primary_10_22331_q_2025_01_15_1597 crossref_primary_10_1126_science_abk3333 crossref_primary_10_1145_3639528_3639535 crossref_primary_10_1038_s41567_022_01742_5 crossref_primary_10_1007_JHEP02_2025_128 crossref_primary_10_1038_s42254_022_00535_2 crossref_primary_10_1103_PhysRevLett_127_100502 crossref_primary_10_22331_q_2024_08_16_1442 crossref_primary_10_1088_2058_9565_acc4e2 crossref_primary_10_1103_PRXQuantum_4_020325 crossref_primary_10_1038_s41586_021_04351_z crossref_primary_10_1109_JETCAS_2022_3201730 crossref_primary_10_1103_PhysRevResearch_6_033217 crossref_primary_10_1103_PhysRevApplied_21_014053 crossref_primary_10_1088_2058_9565_ad17d8 crossref_primary_10_1038_s42005_024_01811_6 crossref_primary_10_1103_PhysRevA_110_012431 crossref_primary_10_1103_PhysRevX_12_041022 crossref_primary_10_1021_acs_jpclett_4c02368 crossref_primary_10_3390_electronics12051096 crossref_primary_10_1088_1751_8121_ad0ac7 crossref_primary_10_1103_PhysRevLett_131_110601 crossref_primary_10_1140_epjp_s13360_024_05832_6 crossref_primary_10_1103_PhysRevA_108_022409 crossref_primary_10_1103_PRXQuantum_5_040325 crossref_primary_10_1038_s41467_023_37902_1 crossref_primary_10_1103_PhysRevA_108_022408 crossref_primary_10_1016_j_future_2024_06_012 crossref_primary_10_1038_s41467_024_48213_4 crossref_primary_10_22331_q_2024_04_30_1319 crossref_primary_10_1116_5_0136828 crossref_primary_10_1038_s41586_023_06481_y crossref_primary_10_1002_qute_202100118 crossref_primary_10_1103_PRXQuantum_1_020308 crossref_primary_10_22331_q_2024_03_21_1293 crossref_primary_10_1038_s41534_024_00949_z crossref_primary_10_1103_PhysRevResearch_6_023118 crossref_primary_10_1063_5_0183022 crossref_primary_10_3390_electronics12020347 crossref_primary_10_1088_1402_4896_ad41a1 crossref_primary_10_1103_PhysRevResearch_5_043087 crossref_primary_10_1103_PhysRevA_105_062424 crossref_primary_10_1103_PhysRevA_111_012620 crossref_primary_10_1140_epjqt_s40507_024_00262_w crossref_primary_10_3390_info15110727 crossref_primary_10_1103_PhysRevResearch_6_033280 crossref_primary_10_1103_PhysRevLett_126_150501 crossref_primary_10_1103_PhysRevLett_129_230503 crossref_primary_10_1103_PhysRevLett_133_130803 crossref_primary_10_1038_s41586_022_05442_1 crossref_primary_10_1103_PhysRevLett_129_230501 crossref_primary_10_1103_PhysRevResearch_6_033035 crossref_primary_10_1021_acs_jctc_3c00071 crossref_primary_10_22331_q_2024_08_29_1455 crossref_primary_10_22331_q_2024_08_29_1456 crossref_primary_10_1088_2058_9565_ace6cd crossref_primary_10_22331_q_2023_10_09_1129 crossref_primary_10_1103_PhysRevResearch_5_013026 crossref_primary_10_1038_s41467_023_43957_x crossref_primary_10_1038_s41567_021_01232_0 crossref_primary_10_1103_PhysRevLett_127_030503 crossref_primary_10_1103_PhysRevLett_130_250403 crossref_primary_10_22331_q_2024_03_27_1300 crossref_primary_10_1103_PhysRevA_110_012454 crossref_primary_10_1103_PRXQuantum_2_040320 crossref_primary_10_1038_s41534_022_00649_6 crossref_primary_10_1103_PhysRevA_110_012458 crossref_primary_10_22331_q_2023_04_13_978 crossref_primary_10_1103_PhysRevResearch_6_023250 crossref_primary_10_1021_acs_jctc_2c00709 crossref_primary_10_1038_s41534_022_00592_6 crossref_primary_10_1103_PRXQuantum_5_040301 crossref_primary_10_1103_PhysRevResearch_6_043082 crossref_primary_10_1007_s11128_024_04428_4 crossref_primary_10_1103_PRXQuantum_5_040306 crossref_primary_10_1103_PRXQuantum_5_040308 crossref_primary_10_1145_3717450 crossref_primary_10_1021_acs_jpca_2c06453 crossref_primary_10_22331_q_2024_09_11_1467 crossref_primary_10_1021_acs_jpca_2c08993 crossref_primary_10_1103_PhysRevB_107_075147 crossref_primary_10_1088_2632_2153_aca06b crossref_primary_10_1103_PhysRevLett_132_190801 crossref_primary_10_1038_s42254_023_00599_8 crossref_primary_10_1038_s41524_021_00540_6 crossref_primary_10_1088_2058_9565_acdcb4 crossref_primary_10_1103_PhysRevResearch_6_013205 crossref_primary_10_1038_s41534_024_00901_1 crossref_primary_10_1038_s42005_024_01813_4 crossref_primary_10_1103_PhysRevLett_133_250402 crossref_primary_10_1088_2058_9565_ad04e7 crossref_primary_10_1016_j_optmat_2023_114510 crossref_primary_10_1103_PhysRevA_110_012231 crossref_primary_10_22331_q_2023_01_26_906 crossref_primary_10_1007_s11704_024_40414_w crossref_primary_10_22331_q_2023_04_20_984 crossref_primary_10_1038_s41467_024_54859_x crossref_primary_10_1007_s00220_022_04343_8 crossref_primary_10_22331_q_2021_06_01_464 crossref_primary_10_1103_PhysRevLett_133_240604 crossref_primary_10_1039_D3CP03523A crossref_primary_10_1109_TIT_2021_3128110 crossref_primary_10_1038_s42254_023_00662_4 crossref_primary_10_1103_PhysRevResearch_6_043063 crossref_primary_10_1103_PRXQuantum_5_037001 crossref_primary_10_1103_PhysRevLett_130_200403 crossref_primary_10_1038_s41467_024_51439_x crossref_primary_10_1103_PhysRevA_108_022208 crossref_primary_10_1109_TIT_2023_3250100 crossref_primary_10_1103_PhysRevResearch_5_043284 crossref_primary_10_1038_s41534_021_00487_y crossref_primary_10_1063_5_0137167 crossref_primary_10_22331_q_2023_09_11_1106 crossref_primary_10_1103_PhysRevA_106_052422 crossref_primary_10_1038_s41567_023_02240_y crossref_primary_10_1103_PhysRevA_102_042604 crossref_primary_10_1088_2058_9565_ac3c53 crossref_primary_10_1038_s41467_023_39024_0 crossref_primary_10_1038_s41534_023_00797_3 crossref_primary_10_22331_q_2023_10_03_1126 crossref_primary_10_1038_s41534_024_00851_8 crossref_primary_10_1145_3700885 crossref_primary_10_1038_s41467_022_31639_z crossref_primary_10_1103_PhysRevLett_125_200501 crossref_primary_10_22331_q_2021_11_16_580 crossref_primary_10_1103_PhysRevLett_127_200503 crossref_primary_10_1103_PhysRevLett_127_200501 crossref_primary_10_22331_q_2024_11_11_1520 crossref_primary_10_22331_q_2021_09_09_539 crossref_primary_10_1103_Physics_17_120 crossref_primary_10_1126_science_abn7293 crossref_primary_10_1103_PhysRevLett_133_020402 crossref_primary_10_1088_1751_8121_ad4c2b crossref_primary_10_1038_s41567_021_01260_w crossref_primary_10_22331_q_2022_10_20_844 crossref_primary_10_1103_PhysRevLett_133_010603 crossref_primary_10_1103_PhysRevX_14_041051 crossref_primary_10_1103_PhysRevLett_130_100801 crossref_primary_10_1103_PRXQuantum_4_027001 crossref_primary_10_1103_PhysRevA_106_062441 crossref_primary_10_1021_acs_jctc_2c00910 crossref_primary_10_1021_acs_jctc_4c00295 crossref_primary_10_1103_RevModPhys_95_045005 crossref_primary_10_1103_PhysRevLett_134_090801 crossref_primary_10_1103_PhysRevLett_128_180505 crossref_primary_10_1103_PhysRevLett_129_240501 crossref_primary_10_1088_1367_2630_ad2f67 crossref_primary_10_1103_PhysRevLett_133_080601 crossref_primary_10_1038_s41598_021_95973_w crossref_primary_10_1038_s42005_024_01815_2 crossref_primary_10_1021_acs_jctc_4c01280 crossref_primary_10_1021_acs_jctc_4c00070 crossref_primary_10_1103_PhysRevLett_130_221003 crossref_primary_10_1103_PRXQuantum_2_040342 crossref_primary_10_1103_PhysRevA_110_032415 crossref_primary_10_1103_PRXQuantum_2_030318 crossref_primary_10_1063_5_0173591 crossref_primary_10_1103_PhysRevApplied_17_054018 crossref_primary_10_1103_PhysRevX_14_031035 crossref_primary_10_1021_acs_jctc_4c00069 crossref_primary_10_1002_qute_202300311 crossref_primary_10_1103_PhysRevA_107_062425 crossref_primary_10_1103_PhysRevLett_131_060601 crossref_primary_10_1103_PhysRevResearch_5_043002 crossref_primary_10_1103_PRXQuantum_3_040315 crossref_primary_10_1007_s11467_024_1397_4 crossref_primary_10_1088_1361_6633_ac58a4 crossref_primary_10_1103_PhysRevA_107_062424 crossref_primary_10_22331_q_2025_01_23_1606 crossref_primary_10_1103_PRXQuantum_3_040310 crossref_primary_10_22331_q_2025_01_23_1607 crossref_primary_10_1103_PRXQuantum_6_010344 crossref_primary_10_22331_q_2023_03_02_934 crossref_primary_10_1103_PRXQuantum_6_010348 crossref_primary_10_1080_23746149_2020_1797528 crossref_primary_10_1103_PRXQuantum_2_030348 crossref_primary_10_22331_q_2024_07_30_1426 crossref_primary_10_1103_PhysRevResearch_5_033154 crossref_primary_10_1103_PhysRevResearch_6_033310 crossref_primary_10_3389_fphy_2022_873810 crossref_primary_10_1038_s41567_024_02738_z crossref_primary_10_1103_PRXQuantum_6_010352 crossref_primary_10_22331_q_2022_02_02_638 crossref_primary_10_1103_PhysRevApplied_19_014068 crossref_primary_10_22331_q_2022_04_13_688 crossref_primary_10_1109_TQE_2022_3175267 crossref_primary_10_1103_PhysRevX_14_021029 crossref_primary_10_1103_PhysRevA_105_022417 crossref_primary_10_22331_q_2022_10_06_828 crossref_primary_10_1103_PhysRevA_106_042424 crossref_primary_10_21468_SciPostPhys_15_6_251 crossref_primary_10_1103_PhysRevA_104_L050401 crossref_primary_10_1088_1742_5468_ad138f crossref_primary_10_1038_s42254_022_00552_1 crossref_primary_10_1103_PRXQuantum_6_010334 crossref_primary_10_1038_s41467_024_53765_6 crossref_primary_10_1103_PRXQuantum_6_010335 crossref_primary_10_22331_q_2024_09_09_1463 crossref_primary_10_1103_PRXQuantum_6_010336 crossref_primary_10_3390_photonics10020116 crossref_primary_10_1103_PhysRevResearch_6_043118 crossref_primary_10_1088_1742_5468_ad17b4 crossref_primary_10_1103_PhysRevA_109_022247 crossref_primary_10_1103_PhysRevLett_126_070504 crossref_primary_10_1103_PhysRevX_13_011049 crossref_primary_10_1103_PhysRevResearch_6_033201 crossref_primary_10_1007_s11433_023_2337_2 crossref_primary_10_1103_PhysRevA_105_022407 crossref_primary_10_22331_q_2024_12_03_1546 crossref_primary_10_22331_q_2025_01_08_1586 crossref_primary_10_1103_PhysRevA_107_062403 crossref_primary_10_1103_PhysRevResearch_4_023136 crossref_primary_10_1103_PhysRevResearch_6_043221 crossref_primary_10_1103_PRXQuantum_3_040333 crossref_primary_10_1103_PhysRevA_109_012422 crossref_primary_10_1088_1751_8121_ad8607 crossref_primary_10_1103_PhysRevLett_127_090503 crossref_primary_10_1007_s42484_021_00056_8 crossref_primary_10_1103_PhysRevResearch_4_033173 crossref_primary_10_1103_PhysRevA_111_L030402 crossref_primary_10_1103_PhysRevLett_133_010402 crossref_primary_10_1007_s42484_024_00182_z crossref_primary_10_1103_PhysRevResearch_5_043035 crossref_primary_10_1103_PhysRevA_107_062417 crossref_primary_10_3389_fphy_2021_731007 crossref_primary_10_1103_PhysRevResearch_5_023200 crossref_primary_10_1021_acs_jpca_1c05884 crossref_primary_10_1103_PhysRevLett_130_040601 crossref_primary_10_1038_s41467_023_41217_6 crossref_primary_10_1088_1367_2630_ad2c3b crossref_primary_10_22331_q_2023_07_25_1067 crossref_primary_10_1103_PhysRevLett_134_040201 crossref_primary_10_1103_PhysRevResearch_6_033301 crossref_primary_10_1007_s42484_022_00088_8 crossref_primary_10_22331_q_2022_09_19_806 crossref_primary_10_1103_PhysRevD_109_046005 crossref_primary_10_1038_s41534_022_00559_7 crossref_primary_10_1016_j_future_2024_04_060 crossref_primary_10_1007_s11128_025_04653_5 crossref_primary_10_1088_1361_6633_ad7f69 crossref_primary_10_22331_q_2025_03_20_1665 crossref_primary_10_1103_PhysRevA_106_L010402 crossref_primary_10_1103_PhysRevA_107_062409 crossref_primary_10_1038_s41598_023_30983_4 crossref_primary_10_1088_1361_6633_acf8d7 crossref_primary_10_1103_PRXQuantum_3_030312 crossref_primary_10_1038_s41598_022_13627_x crossref_primary_10_1103_PhysRevLett_127_060504 crossref_primary_10_1039_D2CS00203E crossref_primary_10_3390_e26090722 crossref_primary_10_1088_0256_307X_40_11_110303 crossref_primary_10_1103_PhysRevX_12_011018 crossref_primary_10_1103_PRXQuantum_2_010307 crossref_primary_10_1038_s42005_024_01698_3 crossref_primary_10_1088_2632_2153_ad3330 crossref_primary_10_1021_acs_jpca_2c04726 crossref_primary_10_1103_PhysRevResearch_7_013105 crossref_primary_10_1103_PhysRevA_110_042623 crossref_primary_10_1103_PhysRevLett_127_140502 crossref_primary_10_22331_q_2024_12_11_1559 crossref_primary_10_1038_s42005_024_01542_8 crossref_primary_10_1140_epjqt_s40507_022_00151_0 crossref_primary_10_22331_q_2022_05_30_726 crossref_primary_10_1088_2632_2153_ac362b crossref_primary_10_1103_PRXQuantum_3_030306 crossref_primary_10_22331_qv_2020_11_19_47 crossref_primary_10_1126_sciadv_ado1069 crossref_primary_10_1103_PhysRevLett_132_240802 crossref_primary_10_1103_PhysRevA_103_052435 crossref_primary_10_1103_PhysRevApplied_20_034044 crossref_primary_10_1109_TIT_2024_3367787 crossref_primary_10_1140_epjp_s13360_023_04364_9 crossref_primary_10_1103_PhysRevA_110_052430 crossref_primary_10_1103_PhysRevD_110_103027 crossref_primary_10_1103_PhysRevResearch_6_013299 crossref_primary_10_1088_2058_9565_ac47f0 crossref_primary_10_1103_PhysRevLett_126_190505 crossref_primary_10_1103_PhysRevApplied_23_014021 crossref_primary_10_1103_PhysRevA_106_042435 crossref_primary_10_1103_PRXQuantum_2_010201 crossref_primary_10_1103_PRXQuantum_2_010322 crossref_primary_10_1109_TPAMI_2023_3272029 crossref_primary_10_22331_q_2022_12_29_886 crossref_primary_10_1016_j_cosrev_2025_100747 crossref_primary_10_1103_PRXQuantum_6_010320 crossref_primary_10_1088_1751_8121_ad40e3 crossref_primary_10_1103_PhysRevA_106_042431 crossref_primary_10_1038_s42005_024_01763_x crossref_primary_10_1140_epja_s10050_024_01385_5 crossref_primary_10_1103_PhysRevLett_129_260501 crossref_primary_10_1063_5_0178897 crossref_primary_10_1088_2632_2153_acb0b4 crossref_primary_10_1109_TIT_2021_3081415 crossref_primary_10_1103_PhysRevLett_134_096503 crossref_primary_10_1038_s42254_021_00348_9 crossref_primary_10_1103_PhysRevLett_131_090201 crossref_primary_10_1002_andp_202100597 crossref_primary_10_1103_PhysRevA_102_023706 crossref_primary_10_1103_PhysRevA_105_022438 crossref_primary_10_1103_PRXQuantum_6_010318 crossref_primary_10_1038_s41534_024_00854_5 crossref_primary_10_1109_TIT_2024_3357972 crossref_primary_10_1038_s41534_022_00621_4 crossref_primary_10_1103_PhysRevA_103_062214 crossref_primary_10_1103_PhysRevD_111_043038 crossref_primary_10_1103_PhysRevA_110_052407 crossref_primary_10_1103_PhysRevA_106_032408 crossref_primary_10_1103_PRXQuantum_6_010316 crossref_primary_10_1103_PhysRevLett_132_160802 crossref_primary_10_22331_q_2024_05_27_1361 crossref_primary_10_1098_rsif_2022_0541 crossref_primary_10_1103_PhysRevB_107_L161101 crossref_primary_10_1103_PhysRevResearch_4_033027 crossref_primary_10_1038_s42254_024_00799_w crossref_primary_10_1177_15485129231154929 crossref_primary_10_1063_5_0219143 crossref_primary_10_1103_PhysRevX_13_021021 crossref_primary_10_1103_PRXQuantum_5_010346 crossref_primary_10_1038_s41467_025_55955_2 crossref_primary_10_1103_PhysRevLett_131_140601 crossref_primary_10_1145_3670418 crossref_primary_10_1088_2632_2153_ac9036 crossref_primary_10_1103_PhysRevB_111_054443 crossref_primary_10_1103_PhysRevLett_126_050501 crossref_primary_10_1103_PRXQuantum_2_010102 crossref_primary_10_1007_s11128_024_04442_6 crossref_primary_10_1103_PhysRevA_108_062423 crossref_primary_10_1088_2058_9565_ac79c9 crossref_primary_10_1103_PhysRevResearch_3_033155 crossref_primary_10_1002_andp_202200064 crossref_primary_10_1038_s41467_024_55342_3 crossref_primary_10_1021_acs_jctc_4c00037 crossref_primary_10_1007_s00453_023_01169_1 crossref_primary_10_1103_PRXQuantum_4_040311 crossref_primary_10_1103_PhysRevLett_134_050405 crossref_primary_10_1103_PRXQuantum_5_010350 crossref_primary_10_1002_qute_202300031 crossref_primary_10_1088_2058_9565_ad7168 crossref_primary_10_1103_PhysRevResearch_7_013045 crossref_primary_10_1103_PhysRevApplied_23_014075 crossref_primary_10_1103_PhysRevC_110_064320 crossref_primary_10_1103_PRXQuantum_5_010352 crossref_primary_10_1021_acs_jctc_3c00851 crossref_primary_10_1038_s41467_023_37747_8 crossref_primary_10_1103_PhysRevLett_133_040203 crossref_primary_10_1039_D4FD00039K crossref_primary_10_1103_PhysRevLett_133_040202 crossref_primary_10_1021_acs_jctc_2c01119 crossref_primary_10_1103_PhysRevLett_133_020601 crossref_primary_10_1103_PhysRevLett_133_020602 crossref_primary_10_1038_s41534_025_00970_w crossref_primary_10_22331_q_2023_06_07_1036 crossref_primary_10_1002_qute_202300042 crossref_primary_10_1007_s11128_023_04008_y crossref_primary_10_1007_s10773_024_05811_8 crossref_primary_10_1038_s41467_022_34279_5 crossref_primary_10_1103_PRXQuantum_4_040328 crossref_primary_10_1103_PhysRevB_111_054306 crossref_primary_10_1103_PhysRevA_102_020401 crossref_primary_10_1103_PhysRevLett_132_010602 crossref_primary_10_1103_PRXQuantum_5_010324 crossref_primary_10_22331_q_2023_11_28_1189 crossref_primary_10_1088_1367_2630_ac706c crossref_primary_10_1109_TIT_2024_3360951 crossref_primary_10_22331_q_2025_02_18_1635 crossref_primary_10_22331_q_2025_02_19_1639 crossref_primary_10_1088_1367_2630_ad5df1 crossref_primary_10_1088_2058_9565_ad9d74 crossref_primary_10_1103_PRXQuantum_5_020367 crossref_primary_10_1016_j_jss_2024_112223 crossref_primary_10_1021_acs_jctc_4c01221 crossref_primary_10_1063_5_0209201 crossref_primary_10_1021_acs_jctc_4c01468 crossref_primary_10_1103_PhysRevB_106_L041110 crossref_primary_10_1103_PRXQuantum_3_020323 crossref_primary_10_1103_PRXQuantum_4_040331 crossref_primary_10_1103_PhysRevLett_129_270501 crossref_primary_10_21468_SciPostPhys_12_3_106 crossref_primary_10_1021_acs_jpclett_2c03617 crossref_primary_10_1103_PhysRevA_107_042403 crossref_primary_10_1103_PRXQuantum_4_040337 crossref_primary_10_1103_PRXQuantum_4_040338 crossref_primary_10_1103_PhysRevA_107_042406 crossref_primary_10_22331_q_2021_01_20_385 crossref_primary_10_1103_PhysRevA_108_012414 crossref_primary_10_1103_PRXQuantum_5_010336 crossref_primary_10_1038_s41534_021_00513_z crossref_primary_10_1103_PhysRevLett_133_120804 crossref_primary_10_1103_PhysRevLett_134_030801 crossref_primary_10_1103_PRXQuantum_5_010334 crossref_primary_10_1103_PhysRevResearch_3_043199 crossref_primary_10_1103_PhysRevA_103_062411 crossref_primary_10_22331_q_2023_01_03_889 crossref_primary_10_1002_qua_26853 crossref_primary_10_1103_PhysRevLett_130_206501 crossref_primary_10_1103_PhysRevResearch_4_043011 crossref_primary_10_1088_2058_9565_ada08e crossref_primary_10_22331_q_2024_05_23_1358 crossref_primary_10_1002_qute_202400150 crossref_primary_10_1088_2058_9565_adc14f crossref_primary_10_1039_D4SC05839A crossref_primary_10_1002_qute_202300060 crossref_primary_10_1007_s41745_023_00406_4 crossref_primary_10_1016_j_physrep_2022_08_003 crossref_primary_10_1038_s41467_023_44012_5 crossref_primary_10_1088_2058_9565_ac051a crossref_primary_10_1103_PhysRevA_104_052418 crossref_primary_10_1103_PRXQuantum_4_030313 crossref_primary_10_1103_PhysRevA_107_032414 crossref_primary_10_1103_PhysRevLett_130_150602 crossref_primary_10_1103_PhysRevResearch_6_033083 crossref_primary_10_1103_PRXQuantum_4_030319 crossref_primary_10_1103_PhysRevA_111_012424 crossref_primary_10_22331_q_2023_06_01_1026 crossref_primary_10_1103_PRXQuantum_5_020347 crossref_primary_10_1103_PRXQuantum_3_020344 crossref_primary_10_1103_PhysRevLett_133_130601 crossref_primary_10_1103_PhysRevA_107_022616 crossref_primary_10_1007_s42484_022_00091_z crossref_primary_10_1103_PhysRevLett_132_220802 crossref_primary_10_1088_1402_4896_adb7a1 crossref_primary_10_1103_PhysRevLett_132_050201 crossref_primary_10_1088_2632_2153_ac28dd crossref_primary_10_1088_2058_9565_ac969c crossref_primary_10_1088_2058_9565_ada2b7 crossref_primary_10_1103_PhysRevResearch_6_013106 crossref_primary_10_1088_2516_1075_ad3592 crossref_primary_10_1103_PhysRevResearch_5_013082 crossref_primary_10_1007_s00220_023_04844_0 crossref_primary_10_1038_s41467_023_37511_y crossref_primary_10_1103_PRXQuantum_4_030322 crossref_primary_10_1103_PhysRevLett_132_120402 crossref_primary_10_1103_PRXQuantum_4_030323 crossref_primary_10_1039_D1RA07451B crossref_primary_10_1103_PhysRevApplied_21_064017 crossref_primary_10_22331_q_2021_10_05_557 crossref_primary_10_7498_aps_70_20210985 crossref_primary_10_1103_PhysRevA_108_052419 crossref_primary_10_1103_PhysRevResearch_6_023050 crossref_primary_10_1103_PhysRevA_108_052414 crossref_primary_10_1103_PRXQuantum_5_020351 crossref_primary_10_1088_1751_8121_acf747 crossref_primary_10_1103_PhysRevC_108_024313 crossref_primary_10_1038_s41534_024_00836_7 crossref_primary_10_1103_PhysRevResearch_6_013211 crossref_primary_10_1103_PRXQuantum_3_020357 crossref_primary_10_1038_s41534_022_00599_z crossref_primary_10_1103_PhysRevA_107_022608 crossref_primary_10_1109_TQE_2023_3325167 crossref_primary_10_1038_s41467_024_51932_3 crossref_primary_10_1039_D2CP04493E crossref_primary_10_1038_s41467_021_22539_9 crossref_primary_10_1039_D4DD00321G crossref_primary_10_1103_PhysRevA_109_062406 crossref_primary_10_1103_PhysRevResearch_3_043145 crossref_primary_10_1103_PhysRevResearch_6_013010 crossref_primary_10_1103_PhysRevResearch_4_043221 crossref_primary_10_1103_PhysRevApplied_21_064001 crossref_primary_10_1038_s41534_021_00447_6 crossref_primary_10_1038_s41534_023_00801_w crossref_primary_10_22331_q_2024_10_22_1503 crossref_primary_10_1007_s12046_024_02660_3 crossref_primary_10_1103_PhysRevB_104_235109 crossref_primary_10_1103_PhysRevLett_133_260401 crossref_primary_10_1007_s43673_022_00058_z crossref_primary_10_1002_andp_202200289 crossref_primary_10_1103_PRXQuantum_3_020365 crossref_primary_10_1145_3715106 crossref_primary_10_22331_q_2023_05_04_995 crossref_primary_10_1103_PhysRevResearch_6_013244 crossref_primary_10_1016_j_comcom_2022_10_006 crossref_primary_10_1088_1367_2630_ad985b crossref_primary_10_1126_sciadv_adj4249 crossref_primary_10_1103_PRXQuantum_5_020328 crossref_primary_10_1103_PhysRevA_104_042403 crossref_primary_10_22331_q_2023_08_03_1072 crossref_primary_10_1103_PhysRevA_109_062417 crossref_primary_10_1103_PhysRevA_105_062414 crossref_primary_10_1103_PhysRevA_109_062415 crossref_primary_10_22331_qv_2023_06_29_74 crossref_primary_10_1103_PhysRevResearch_4_043210 crossref_primary_10_1103_PhysRevA_109_062412 crossref_primary_10_22331_q_2023_01_13_896 crossref_primary_10_1103_PhysRevLett_126_170502 crossref_primary_10_1038_s41467_024_49877_8 crossref_primary_10_1103_PhysRevA_109_052616 crossref_primary_10_1007_s11128_023_03966_7 crossref_primary_10_1038_s41467_022_33928_z crossref_primary_10_1103_PhysRevLett_131_240602 crossref_primary_10_1038_s41467_021_27922_0 crossref_primary_10_1088_1367_2630_acfcd3 crossref_primary_10_1109_TQE_2024_3421294 crossref_primary_10_1103_PhysRevLett_130_210401 crossref_primary_10_21468_SciPostPhys_15_3_089 crossref_primary_10_3390_e23111519 crossref_primary_10_1063_5_0099469 crossref_primary_10_22331_q_2023_04_17_981 crossref_primary_10_1016_j_cma_2024_117428 crossref_primary_10_1016_j_jcp_2024_113213 crossref_primary_10_1103_PhysRevB_109_094209 crossref_primary_10_1103_PhysRevA_109_032612 crossref_primary_10_1038_s41534_024_00846_5 crossref_primary_10_1103_PhysRevLett_130_230403 crossref_primary_10_1103_PhysRevA_106_012441 crossref_primary_10_1103_PRXQuantum_3_010342 crossref_primary_10_22331_q_2024_11_20_1531 crossref_primary_10_1007_s11768_024_00215_9 crossref_primary_10_1007_s42484_023_00132_1 crossref_primary_10_1103_PhysRevLett_133_060203 crossref_primary_10_22331_q_2021_03_16_413 crossref_primary_10_1103_PhysRevA_109_052624 crossref_primary_10_22331_q_2022_10_24_845 crossref_primary_10_1103_PhysRevB_109_174207 crossref_primary_10_1103_PhysRevA_108_042420 crossref_primary_10_1103_PhysRevApplied_23_034014 crossref_primary_10_21468_SciPostPhys_14_5_094 crossref_primary_10_1073_pnas_2217031120 crossref_primary_10_1103_PhysRevResearch_6_013029 crossref_primary_10_1103_PRXQuantum_5_020304 crossref_primary_10_1103_PhysRevA_108_022814 crossref_primary_10_1103_PhysRevLett_126_030601 crossref_primary_10_1038_s41534_024_00857_2 crossref_primary_10_1103_PhysRevA_104_062411 crossref_primary_10_22331_q_2024_06_17_1373 crossref_primary_10_1021_acs_jctc_3c00218 crossref_primary_10_1103_PhysRevLett_132_250402 crossref_primary_10_22331_q_2024_08_08_1433 crossref_primary_10_1088_2058_9565_ad133e crossref_primary_10_22331_q_2022_08_16_776 crossref_primary_10_1103_PhysRevA_108_L040201 crossref_primary_10_1038_s41467_023_39381_w crossref_primary_10_1016_j_ascom_2024_100803 crossref_primary_10_1103_PhysRevLett_134_110802 crossref_primary_10_1103_PhysRevA_110_062421 crossref_primary_10_1103_PhysRevLett_131_160601 crossref_primary_10_1103_PhysRevLett_133_030801 crossref_primary_10_1126_sciadv_add7131 crossref_primary_10_1145_3665335 crossref_primary_10_1103_PRXQuantum_4_010325 crossref_primary_10_1038_s41467_024_53101_y crossref_primary_10_1088_2632_2153_acb4df crossref_primary_10_1103_PhysRevResearch_5_013095 crossref_primary_10_22331_q_2023_06_29_1044 crossref_primary_10_22331_q_2023_05_22_1010 crossref_primary_10_1126_science_abi8378 crossref_primary_10_1103_PRXQuantum_5_030338 crossref_primary_10_1007_s42484_025_00261_9 crossref_primary_10_1103_PhysRevLett_127_260501 crossref_primary_10_22331_q_2024_12_04_1549 crossref_primary_10_1103_PhysRevLett_128_060601 crossref_primary_10_1103_PhysRevX_12_031044 crossref_primary_10_22331_q_2021_07_01_492 crossref_primary_10_1103_PhysRevLett_133_260603 crossref_primary_10_1007_s42484_024_00189_6 crossref_primary_10_1088_1751_8121_acc369 crossref_primary_10_1038_s41467_024_45014_7 crossref_primary_10_1103_PhysRevB_108_235141 crossref_primary_10_1103_PhysRevResearch_7_013201 crossref_primary_10_1103_PRXQuantum_4_010311 crossref_primary_10_1007_s42484_024_00167_y crossref_primary_10_1103_PhysRevLett_127_110504 crossref_primary_10_1109_TPWRS_2022_3196608 crossref_primary_10_1016_j_ffa_2024_102388 crossref_primary_10_1103_PhysRevA_102_022410 crossref_primary_10_1103_PRXQuantum_4_010318 crossref_primary_10_1016_j_physrep_2024_09_009 crossref_primary_10_1140_epja_s10050_024_01314_6 crossref_primary_10_1103_PhysRevX_13_041008 crossref_primary_10_1038_s41586_021_03582_4 crossref_primary_10_1063_5_0204167 crossref_primary_10_1103_PhysRevA_107_022429 crossref_primary_10_1038_s41567_021_01201_7 crossref_primary_10_1038_s41467_024_45882_z crossref_primary_10_1116_5_0202971 crossref_primary_10_1103_PhysRevA_110_062403 crossref_primary_10_1103_PhysRevLett_130_160401 crossref_primary_10_1016_j_aop_2023_169400 |
| Cites_doi | 10.1016/j.physrep.2009.02.004 10.1063/1.1499754 10.1063/1.1737053 10.1016/0304-3975(86)90174-X 10.1088/1751-8121/ab8111 10.1103/PhysRevLett.43.1434 10.1038/ncomms1147 10.1038/s41586-019-1177-4 10.1126/science.aau4963 10.1038/nphys4035 10.1146/annurev-conmatphys-031214-014726 10.1038/s42256-019-0028-1 10.1038/s41567-018-0048-5 10.1016/0022-0000(88)90003-7 10.1103/PhysRevB.22.1305 10.1103/PhysRevLett.106.230501 10.1126/science.aag2302 10.1038/nature23879 10.22331/q-2018-08-06-79 10.1103/PhysRevLett.124.200502 10.1103/PhysRevX.10.031064 10.1119/1.1937609 10.1145/3313276.3316378 10.1007/978-1-4612-0919-5_20 10.1007/978-94-017-0849-4_10 10.1145/3188745.3188802 |
| ContentType | Journal Article |
| Copyright | The Author(s), under exclusive licence to Springer Nature Limited 2020 The Author(s), under exclusive licence to Springer Nature Limited 2020. |
| Copyright_xml | – notice: The Author(s), under exclusive licence to Springer Nature Limited 2020 – notice: The Author(s), under exclusive licence to Springer Nature Limited 2020. |
| DBID | AAYXX CITATION 3V. 7U5 7XB 88I 8FD 8FE 8FG 8FK ABUWG AEUYN AFKRA ARAPS AZQEC BENPR BGLVJ BHPHI BKSAR CCPQU DWQXO GNUQQ HCIFZ L7M M2P P5Z P62 PCBAR PHGZM PHGZT PKEHL PQEST PQGLB PQQKQ PQUKI Q9U |
| DOI | 10.1038/s41567-020-0932-7 |
| DatabaseName | CrossRef ProQuest Central (Corporate) Solid State and Superconductivity Abstracts ProQuest Central (purchase pre-March 2016) Science Database (Alumni Edition) Technology Research Database ProQuest SciTech Collection ProQuest Technology Collection ProQuest Central (Alumni) (purchase pre-March 2016) ProQuest Central (Alumni Edition) ProQuest One Sustainability ProQuest Central UK/Ireland Advanced Technologies & Aerospace Collection ProQuest Central Essentials ProQuest Central Technology Collection Natural Science Collection Earth, Atmospheric & Aquatic Science Collection ProQuest One Community College ProQuest Central Korea ProQuest Central Student SciTech Premium Collection Advanced Technologies Database with Aerospace Science Database Advanced Technologies & Aerospace Database ProQuest Advanced Technologies & Aerospace Collection Earth, Atmospheric & Aquatic Science Database ProQuest Central Premium ProQuest One Academic (New) ProQuest One Academic Middle East (New) ProQuest One Academic Eastern Edition (DO NOT USE) ProQuest One Applied & Life Sciences ProQuest One Academic ProQuest One Academic UKI Edition ProQuest Central Basic |
| DatabaseTitle | CrossRef ProQuest Central Student Technology Collection Technology Research Database ProQuest One Academic Middle East (New) ProQuest Advanced Technologies & Aerospace Collection ProQuest Central Essentials ProQuest Central (Alumni Edition) SciTech Premium Collection ProQuest One Community College ProQuest Central Earth, Atmospheric & Aquatic Science Collection ProQuest One Applied & Life Sciences ProQuest One Sustainability Natural Science Collection ProQuest Central Korea ProQuest Central (New) Advanced Technologies Database with Aerospace Advanced Technologies & Aerospace Collection ProQuest Science Journals (Alumni Edition) ProQuest Central Basic ProQuest Science Journals ProQuest One Academic Eastern Edition Earth, Atmospheric & Aquatic Science Database ProQuest Technology Collection ProQuest SciTech Collection Advanced Technologies & Aerospace Database ProQuest One Academic UKI Edition Solid State and Superconductivity Abstracts ProQuest One Academic ProQuest Central (Alumni) ProQuest One Academic (New) |
| DatabaseTitleList | ProQuest Central Student |
| Database_xml | – sequence: 1 dbid: 8FG name: ProQuest Technology Collection url: https://search.proquest.com/technologycollection1 sourceTypes: Aggregation Database |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Physics |
| EISSN | 1745-2481 |
| EndPage | 1057 |
| ExternalDocumentID | 10_1038_s41567_020_0932_7 |
| GrantInformation_xml | – fundername: DOE | NNSA | Office of Naval Reactors (NNSA’s Naval Reactors Office) grantid: N00014-17-1-2146 funderid: https://doi.org/10.13039/100006146 – fundername: National Science Foundation (NSF) grantid: PHY-1733907 funderid: https://doi.org/10.13039/100000001 – fundername: United States Department of Defense | United States Army | U.S. Army Research, Development and Engineering Command | Army Research Office (ARO) grantid: W911NF121054 funderid: https://doi.org/10.13039/100000183 |
| GroupedDBID | 0R~ 123 29M 39C 3V. 4.4 5BI 5M7 6OB 70F 88I 8FE 8FG 8FH 8R4 8R5 AAEEF AARCD AAYZH AAZLF ABAWZ ABDBF ABJNI ABLJU ABUWG ABZEH ACBWK ACGFO ACGFS ACGOD ACMJI ACUHS ADBBV ADFRT AENEX AEUYN AFBBN AFKRA AFSHS AFWHJ AGAYW AGHTU AHBCP AHOSX AHSBF AIBTJ ALFFA ALMA_UNASSIGNED_HOLDINGS AMTXH ARAPS ARMCB ASPBG AVWKF AXYYD AZFZN AZQEC BENPR BGLVJ BHPHI BKKNO BKSAR BPHCQ CCPQU DB5 DU5 DWQXO EBS EE. EJD ESX EXGXG F5P FEDTE FQGFK FSGXE GNUQQ HCIFZ HVGLF HZ~ I-F LGEZI LK5 LOTEE M2P M7R N9A NADUK NNMJJ NXXTH O9- ODYON P2P P62 PCBAR PQQKQ PROAC Q2X RNS RNT RNTTT SHXYY SIXXV SJN SNYQT SOJ TAOOD TBHMF TDRGL TSG TUS ~8M AAYXX ABFSG ACMFV ACSTC AEZWR AFANA AFHIU AHWEU AIXLP ALPWD ATHPR CITATION PHGZM PHGZT 7U5 7XB 8FD 8FK L7M PKEHL PQEST PQGLB PQUKI Q9U |
| ID | FETCH-LOGICAL-c382t-95dc283acb4605d749ce2172be09dfa803bd8568fbf4c6af2363cde1ff8134093 |
| IEDL.DBID | BENPR |
| ISSN | 1745-2473 |
| IngestDate | Sat Aug 23 13:05:43 EDT 2025 Tue Jul 01 00:25:40 EDT 2025 Thu Apr 24 23:02:03 EDT 2025 Fri Feb 21 02:37:13 EST 2025 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 10 |
| Language | English |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c382t-95dc283acb4605d749ce2172be09dfa803bd8568fbf4c6af2363cde1ff8134093 |
| Notes | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 |
| ORCID | 0000-0001-5317-2613 |
| PQID | 2449454431 |
| PQPubID | 27545 |
| PageCount | 8 |
| ParticipantIDs | proquest_journals_2449454431 crossref_primary_10_1038_s41567_020_0932_7 crossref_citationtrail_10_1038_s41567_020_0932_7 springer_journals_10_1038_s41567_020_0932_7 |
| ProviderPackageCode | CITATION AAYXX |
| PublicationCentury | 2000 |
| PublicationDate | 2020-10-01 |
| PublicationDateYYYYMMDD | 2020-10-01 |
| PublicationDate_xml | – month: 10 year: 2020 text: 2020-10-01 day: 01 |
| PublicationDecade | 2020 |
| PublicationPlace | London |
| PublicationPlace_xml | – name: London |
| PublicationTitle | Nature physics |
| PublicationTitleAbbrev | Nat. Phys |
| PublicationYear | 2020 |
| Publisher | Nature Publishing Group UK Nature Publishing Group |
| Publisher_xml | – name: Nature Publishing Group UK – name: Nature Publishing Group |
| References | Ma, Dasgupta, Hu (CR24) 1979; 43 CR19 CR12 CR11 Kokail (CR18) 2019; 569 Nandkishore, Huse (CR22) 2015; 6 CR30 Carrasquilla, Torlai, Melko, Aolita (CR3) 2019; 1 Flammia, Liu (CR14) 2011; 106 Carrasquilla, Melko (CR29) 2017; 13 Torlai (CR4) 2018; 14 Brydges (CR20) 2019; 364 Weilenmann, Dive, Trillo, Aguilar, Navascués (CR16) 2020; 124 Kandala (CR17) 2017; 549 Cramer (CR2) 2010; 1 CR6 CR5 Guta, Kahn, Kueng, Tropp (CR7) 2020; 53 CR8 CR9 CR27 Jerrum, Valiant, Vazirani (CR10) 1986; 43 Gühne, Tóth (CR15) 2009; 474 CR25 Dasgupta, Ma (CR23) 1980; 22 Raghavan (CR26) 1988; 37 Preskill (CR1) 2018; 2 Renes, Blume-Kohout, Scott, Caves (CR21) 2004; 45 Dennis, Kitaev, Landahl, Preskill (CR13) 2002; 43 Carleo, Troyer (CR28) 2017; 355 ST Flammia (932_CR14) 2011; 106 C Kokail (932_CR18) 2019; 569 M Weilenmann (932_CR16) 2020; 124 J Carrasquilla (932_CR3) 2019; 1 G Carleo (932_CR28) 2017; 355 932_CR5 M Cramer (932_CR2) 2010; 1 932_CR25 932_CR27 R Nandkishore (932_CR22) 2015; 6 J Carrasquilla (932_CR29) 2017; 13 T Brydges (932_CR20) 2019; 364 J Preskill (932_CR1) 2018; 2 O Gühne (932_CR15) 2009; 474 JM Renes (932_CR21) 2004; 45 G Torlai (932_CR4) 2018; 14 S-k Ma (932_CR24) 1979; 43 A Kandala (932_CR17) 2017; 549 P Raghavan (932_CR26) 1988; 37 E Dennis (932_CR13) 2002; 43 932_CR19 932_CR9 932_CR8 932_CR6 M Guta (932_CR7) 2020; 53 932_CR12 932_CR11 C Dasgupta (932_CR23) 1980; 22 932_CR30 MR Jerrum (932_CR10) 1986; 43 |
| References_xml | – volume: 474 start-page: 1 year: 2009 end-page: 75 ident: CR15 article-title: Entanglement detection publication-title: Phys. Rep. doi: 10.1016/j.physrep.2009.02.004 – volume: 43 start-page: 4452 year: 2002 end-page: 4505 ident: CR13 article-title: Topological quantum memory. publication-title: J. Math. Phys. doi: 10.1063/1.1499754 – volume: 45 start-page: 2171 year: 2004 end-page: 2180 ident: CR21 article-title: Symmetric informationally complete quantum measurements publication-title: J. Math. Phys. doi: 10.1063/1.1737053 – volume: 43 start-page: 169 year: 1986 end-page: 188 ident: CR10 article-title: Random generation of combinatorial structures from a uniform distribution publication-title: Theoret. Comput. Sci. doi: 10.1016/0304-3975(86)90174-X – ident: CR12 – ident: CR30 – volume: 53 start-page: 204001 year: 2020 ident: CR7 article-title: Fast state tomography with optimal error bounds publication-title: J. Phys. A doi: 10.1088/1751-8121/ab8111 – ident: CR6 – ident: CR8 – volume: 43 start-page: 1434 year: 1979 ident: CR24 article-title: Random antiferromagnetic chain publication-title: Phys. Rev. Lett. doi: 10.1103/PhysRevLett.43.1434 – volume: 1 year: 2010 ident: CR2 article-title: Efficient quantum state tomography publication-title: Nat. Commun. doi: 10.1038/ncomms1147 – ident: CR25 – ident: CR27 – volume: 569 start-page: 355 year: 2019 end-page: 360 ident: CR18 article-title: Self-verifying variational quantum simulation of lattice models publication-title: Nature doi: 10.1038/s41586-019-1177-4 – volume: 364 start-page: 260 year: 2019 end-page: 263 ident: CR20 article-title: Probing Rényi entanglement entropy via randomized measurements publication-title: Science doi: 10.1126/science.aau4963 – volume: 13 start-page: 431 year: 2017 end-page: 434 ident: CR29 article-title: Machine learning phases of matter publication-title: Nat. Phys doi: 10.1038/nphys4035 – ident: CR19 – volume: 6 start-page: 15 year: 2015 end-page: 38 ident: CR22 article-title: Many-body localization and thermalization in quantum statistical mechanics publication-title: Annu. Rev. Condens. Matter Phys. doi: 10.1146/annurev-conmatphys-031214-014726 – volume: 1 start-page: 155 year: 2019 end-page: 161 ident: CR3 article-title: Reconstructing quantum states with generative models publication-title: Nat. Mach. Intell. doi: 10.1038/s42256-019-0028-1 – volume: 14 start-page: 447 year: 2018 end-page: 450 ident: CR4 article-title: Neural-network quantum state tomography publication-title: Nat. Phys. doi: 10.1038/s41567-018-0048-5 – volume: 37 start-page: 130 year: 1988 end-page: 143 ident: CR26 article-title: Probabilistic construction of deterministic algorithms: approximating packing integer programs. publication-title: J. Comput. Syst. Sci. doi: 10.1016/0022-0000(88)90003-7 – volume: 22 start-page: 1305 year: 1980 ident: CR23 article-title: Low-temperature properties of the random Heisenberg antiferromagnetic chain publication-title: Phys. Rev. B doi: 10.1103/PhysRevB.22.1305 – volume: 106 start-page: 230501 year: 2011 ident: CR14 article-title: Direct fidelity estimation from few Pauli measurements publication-title: Phys. Rev. Lett. doi: 10.1103/PhysRevLett.106.230501 – ident: CR11 – ident: CR9 – ident: CR5 – volume: 355 start-page: 602 year: 2017 end-page: 606 ident: CR28 article-title: Solving the quantum many-body problem with artificial neural networks publication-title: Science doi: 10.1126/science.aag2302 – volume: 549 start-page: 242 year: 2017 end-page: 246 ident: CR17 article-title: Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets publication-title: Nature doi: 10.1038/nature23879 – volume: 2 start-page: 79 year: 2018 ident: CR1 article-title: Quantum computing in the NISQ era and beyond publication-title: Quantum doi: 10.22331/q-2018-08-06-79 – volume: 124 start-page: 200502 year: 2020 ident: CR16 article-title: Entanglement detection beyond measuring fidelities publication-title: Phys. Rev. Lett. doi: 10.1103/PhysRevLett.124.200502 – ident: 932_CR25 doi: 10.1103/PhysRevX.10.031064 – volume: 45 start-page: 2171 year: 2004 ident: 932_CR21 publication-title: J. Math. Phys. doi: 10.1063/1.1737053 – volume: 22 start-page: 1305 year: 1980 ident: 932_CR23 publication-title: Phys. Rev. B doi: 10.1103/PhysRevB.22.1305 – volume: 355 start-page: 602 year: 2017 ident: 932_CR28 publication-title: Science doi: 10.1126/science.aag2302 – volume: 1 start-page: 155 year: 2019 ident: 932_CR3 publication-title: Nat. Mach. Intell. doi: 10.1038/s42256-019-0028-1 – volume: 14 start-page: 447 year: 2018 ident: 932_CR4 publication-title: Nat. Phys. doi: 10.1038/s41567-018-0048-5 – ident: 932_CR8 – volume: 43 start-page: 4452 year: 2002 ident: 932_CR13 publication-title: J. Math. Phys. doi: 10.1063/1.1499754 – volume: 13 start-page: 431 year: 2017 ident: 932_CR29 publication-title: Nat. Phys doi: 10.1038/nphys4035 – ident: 932_CR9 doi: 10.1119/1.1937609 – volume: 6 start-page: 15 year: 2015 ident: 932_CR22 publication-title: Annu. Rev. Condens. Matter Phys. doi: 10.1146/annurev-conmatphys-031214-014726 – ident: 932_CR6 doi: 10.1145/3313276.3316378 – volume: 43 start-page: 1434 year: 1979 ident: 932_CR24 publication-title: Phys. Rev. Lett. doi: 10.1103/PhysRevLett.43.1434 – volume: 2 start-page: 79 year: 2018 ident: 932_CR1 publication-title: Quantum doi: 10.22331/q-2018-08-06-79 – ident: 932_CR27 – volume: 474 start-page: 1 year: 2009 ident: 932_CR15 publication-title: Phys. Rep. doi: 10.1016/j.physrep.2009.02.004 – ident: 932_CR19 doi: 10.1007/978-1-4612-0919-5_20 – ident: 932_CR12 doi: 10.1007/978-94-017-0849-4_10 – ident: 932_CR30 – volume: 364 start-page: 260 year: 2019 ident: 932_CR20 publication-title: Science doi: 10.1126/science.aau4963 – volume: 37 start-page: 130 year: 1988 ident: 932_CR26 publication-title: J. Comput. Syst. Sci. doi: 10.1016/0022-0000(88)90003-7 – volume: 1 year: 2010 ident: 932_CR2 publication-title: Nat. Commun. doi: 10.1038/ncomms1147 – volume: 124 start-page: 200502 year: 2020 ident: 932_CR16 publication-title: Phys. Rev. Lett. doi: 10.1103/PhysRevLett.124.200502 – ident: 932_CR11 – ident: 932_CR5 doi: 10.1145/3188745.3188802 – volume: 53 start-page: 204001 year: 2020 ident: 932_CR7 publication-title: J. Phys. A doi: 10.1088/1751-8121/ab8111 – volume: 43 start-page: 169 year: 1986 ident: 932_CR10 publication-title: Theoret. Comput. Sci. doi: 10.1016/0304-3975(86)90174-X – volume: 569 start-page: 355 year: 2019 ident: 932_CR18 publication-title: Nature doi: 10.1038/s41586-019-1177-4 – volume: 106 start-page: 230501 year: 2011 ident: 932_CR14 publication-title: Phys. Rev. Lett. doi: 10.1103/PhysRevLett.106.230501 – volume: 549 start-page: 242 year: 2017 ident: 932_CR17 publication-title: Nature doi: 10.1038/nature23879 |
| SSID | ssj0042613 |
| Score | 2.7299693 |
| Snippet | Predicting the properties of complex, large-scale quantum systems is essential for developing quantum technologies. We present an efficient method for... |
| SourceID | proquest crossref springer |
| SourceType | Aggregation Database Enrichment Source Index Database Publisher |
| StartPage | 1050 |
| SubjectTerms | 639/705 639/766/259 639/766/483 639/766/483/481 639/766/483/640 Approximation Atomic Circuits Classical and Continuum Physics Complex Systems Condensed Matter Physics Entropy Hamiltonian functions Information theory Lower bounds Mathematical and Computational Physics Molecular Optical and Plasma Physics Physics Physics and Astronomy Properties (attributes) Quantum entanglement Quantum theory Shadows Theoretical Tomography |
| Title | Predicting many properties of a quantum system from very few measurements |
| URI | https://link.springer.com/article/10.1038/s41567-020-0932-7 https://www.proquest.com/docview/2449454431 |
| Volume | 16 |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| link | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwfV1LSwMxEB60RfAiPrFaSw6elNBus5vNnqSV1ipYiljobWleJ_vcFvHfm9mHi4I9bzaHb5KZ-WYmMwC3YRDq0DJ3eBlX1I8Up4JZj3p-YFRgnYmUSBRfh3ww9l8mwSQPuCV5WWWhE1NFrRcKY-RNZ4YiH5u1eQ_LFcWpUZhdzUdo7EPVqWDhyFe12xuO3gpdjPyAZU8iA9r2Q1bkNZloJkhdQor0ybF652b-tkylu_knQ5oanv4xHOUeI-lkIj6BPTM_hYO0clMlZ_A8WmOuBauXyczdbLLE8Poa-6SShSVTsto68LYzkvVsJviehLjz-0Ws-SSzMkSYnMO433t_HNB8PgJVTLQ3NAq0ct7BVElMburQIW1w3pQ0rUjbqWgxqUXAhZXWV3xq24wzpY1nrfCY43XsAirzxdxcAvE1F1JwrWWksF2MEMrZbhn5UiojPF6DVoFNrPLm4TjD4iNOk9hMxBmcsYMzRjjjsAZ3P78ss84ZuxbXC8Dj_BIlcSnyGtwXQig__7vZ1e7NruGwjVJPK_LqUNmst-bGeRYb2YB90X9qQLXT73aHjfwwfQMiAsvA |
| linkProvider | ProQuest |
| linkToHtml | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtV3JTsMwEB0hEIILYhVl9QEuIIsmdhzngBACSssmDiBxM_V2ogtNK8RP8Y14koYKJLhxTmJF4-dZPDNvAPbSJLWpZwG8TBjKMyOoZD6iEU-cSXwwkRoDxds70XzkV0_J0xR8VL0wWFZZ6cRCUduewTvyo2CGMo5kbdFJ_5Xi1CjMrlYjNEpYXLv3txCy5cet87C_-3HcuHg4a9LxVAFqmIyHNEusCTa1bTSmBG0a_s_hlCbt6pn1bVln2spESK89N6LtYyaYsS7yXkaMF-RLQeXPcMYyPFGycVlpfoxGWNmAmdCYp6zKojJ5lGOglFIM1sISwan9bgcnzu2PfGxh5hqLsDD2T8lpCaglmHLdZZgt6kRNvgKt-wFmdrBWmnSCHiF9vMwfICsr6XnSJq-jsFWjDikZogl2r5BwWt6Jd2-kM7mQzFfh8V_ktgbT3V7XrQPhVkgthbU6M0hOI6UJnoLOuNbGyUjUoF7JRpkxVTlOzHhRRcqcSVWKUwVxKhSnSmtw8PVJv-Tp-OvlrUrganxkczUBWA0Oq02YPP51sY2_F9uFuebD7Y26ad1db8J8jAgoagG3YHo4GLnt4NMM9U4BJALP_43cT56sBYM |
| linkToPdf | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtV1LbxMxEB5VqYq4ICggAoX6ABeQleza6_UeKgRto4aWKEJU6s3ErxN5NJuo6l_j13VmH42o1N563l1rNf48D8_MNwAf8yz3eRQIXqEcl4VTXIuY8ERmwWURTaSlQPHnSJ2cyx8X2cUW_Gt7YaisstWJlaL2c0d35D00Q4UksrakF5uyiPHR4OviktMEKcq0tuM0aoichusrDN_Kg-ER7vWnNB0c_z484c2EAe6ETle8yLxD-zpxltKDPsd_DTSxyYZ-4eNE94X1OlM62iidmsRUKOF8SGLUiZAVEROq_-0co6J-B7a_H4_Gv1o7QLGJqNsxM57KXLQ5VaF7JYVNOafQDRdBF_d_q7hxde9kZyujN3gOzxpvlX2r4fUCtsJsF3aqqlFXvoTheEl5HqqcZlPUKmxBV_tL4mhl88gm7HKNG7eespovmlEvC8Ozc81iuGLTzfVk-QrOH0Vyr6Ezm8_CG2DSK2218t4WjqhqtHboN9hCWuuCTlQX-q1sjGuIy2l-xl9TJdCFNrU4DYrTkDhN3oXPt58sataOh17eawVumgNcmg3cuvCl3YTN43sXe_vwYvvwBFFrzoaj03fwNCUAVIWBe9BZLdfhPTo4K_uhQRKDP48N3hsz0gsV |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Predicting+many+properties+of+a+quantum+system+from+very+few+measurements&rft.jtitle=Nature+physics&rft.au=Hsin-Yuan%2C+Huang&rft.au=Kueng%2C+Richard&rft.au=Preskill%2C+John&rft.date=2020-10-01&rft.pub=Nature+Publishing+Group&rft.issn=1745-2473&rft.eissn=1745-2481&rft.volume=16&rft.issue=10&rft.spage=1050&rft.epage=1057&rft_id=info:doi/10.1038%2Fs41567-020-0932-7&rft.externalDBID=HAS_PDF_LINK |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=1745-2473&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=1745-2473&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=1745-2473&client=summon |