Department of Physics and Center for Theory of Quantum Matter, University of Colorado, Boulder CO 80309, USA
Find this paper interesting or want to discuss? Scite or leave a comment on SciRate.
Abstract
We show that it is possible to perform Heisenberg-limited metrology on GHZ-like states, in the presence of generic spatially local, possibly strong interactions during the measurement process. An explicit protocol, which relies on single-qubit measurements and feedback based on polynomial-time classical computation, achieves the Heisenberg limit. In one dimension, matrix product state methods can be used to perform this classical calculation, while in higher dimensions the cluster expansion underlies the efficient calculations. The latter approach is based on an efficient classical sampling algorithm for short-time quantum dynamics, which may be of independent interest.
Featured image: robust and efficient protocol for GHZ metrology
Presentation “Heisenberg limited metrology with perturbing interactions and efficient sampling” by Chao Yin and Andrew Lucas at QIP 2024
► BibTeX data
► References
[1] Géza Tóth and Iagoba Apellaniz. “Quantum metrology from a quantum information science perspective”. Journal of Physics A: Mathematical and Theoretical 47, 424006 (2014).
https://doi.org/10.1088/1751-8113/47/42/424006
[2] Vittorio Giovannetti, Seth Lloyd, and Lorenzo Maccone. “Advances in quantum metrology”. Nature photonics 5, 222–229 (2011).
https://doi.org/10.1038/nphoton.2011.35
[3] C. L. Degen, F. Reinhard, and P. Cappellaro. “Quantum sensing”. Rev. Mod. Phys. 89, 035002 (2017).
https://doi.org/10.1103/RevModPhys.89.035002
[4] A. De Pasquale, D. Rossini, P. Facchi, and V. Giovannetti. “Quantum parameter estimation affected by unitary disturbance”. Phys. Rev. A 88, 052117 (2013).
https://doi.org/10.1103/PhysRevA.88.052117
[5] Shengshi Pang and Todd A. Brun. “Quantum metrology for a general hamiltonian parameter”. Phys. Rev. A 90, 022117 (2014).
https://doi.org/10.1103/PhysRevA.90.022117
[6] Michael Skotiniotis, Pavel Sekatski, and Wolfgang Dür. “Quantum metrology for the ising hamiltonian with transverse magnetic field”. New Journal of Physics 17, 073032 (2015).
https://doi.org/10.1088/1367-2630/17/7/073032
[7] Soonwon Choi, Norman Y Yao, and Mikhail D Lukin. “Quantum metrology based on strongly correlated matter” (2018). arXiv:1801.00042.
arXiv:1801.00042
[8] Meghana Raghunandan, Jörg Wrachtrup, and Hendrik Weimer. “High-density quantum sensing with dissipative first order transitions”. Phys. Rev. Lett. 120, 150501 (2018).
https://doi.org/10.1103/PhysRevLett.120.150501
[9] Shane Dooley, Michael Hanks, Shojun Nakayama, William J Munro, and Kae Nemoto. “Robust quantum sensing with strongly interacting probe systems”. npj Quantum Information 4, 24 (2018).
https://doi.org/10.1038/s41534-018-0073-3
[10] Atsuki Yoshinaga, Mamiko Tatsuta, and Yuichiro Matsuzaki. “Entanglement-enhanced sensing using a chain of qubits with always-on nearest-neighbor interactions”. Phys. Rev. A 103, 062602 (2021).
https://doi.org/10.1103/PhysRevA.103.062602
[11] Takuya Hatomura, Atsuki Yoshinaga, Yuichiro Matsuzaki, and Mamiko Tatsuta. “Quantum metrology based on symmetry-protected adiabatic transformation: imperfection, finite time duration, and dephasing”. New Journal of Physics 24, 033005 (2022).
https://doi.org/10.1088/1367-2630/ac5375
[12] Shane Dooley. “Robust quantum sensing in strongly interacting systems with many-body scars”. PRX Quantum 2, 020330 (2021).
https://doi.org/10.1103/PRXQuantum.2.020330
[13] Atsuki Yoshinaga, Yuichiro Matsuzaki, and Ryusuke Hamazaki. “Quantum Metrology Protected by Hilbert Space Fragmentation” (2022). arXiv:2211.09567.
arXiv:2211.09567
[14] Jing Yang, Shengshi Pang, Adolfo del Campo, and Andrew N. Jordan. “Super-heisenberg scaling in hamiltonian parameter estimation in the long-range kitaev chain”. Phys. Rev. Res. 4, 013133 (2022).
https://doi.org/10.1103/PhysRevResearch.4.013133
[15] B L Higgins, D W Berry, S D Bartlett, M W Mitchell, H M Wiseman, and G J Pryde. “Demonstrating heisenberg-limited unambiguous phase estimation without adaptive measurements”. New Journal of Physics 11, 073023 (2009).
https://doi.org/10.1088/1367-2630/11/7/073023
[16] Shelby Kimmel, Guang Hao Low, and Theodore J. Yoder. “Robust calibration of a universal single-qubit gate set via robust phase estimation”. Phys. Rev. A 92, 062315 (2015).
https://doi.org/10.1103/PhysRevA.92.062315
[17] Federico Belliardo and Vittorio Giovannetti. “Achieving heisenberg scaling with maximally entangled states: An analytic upper bound for the attainable root-mean-square error”. Phys. Rev. A 102, 042613 (2020).
https://doi.org/10.1103/PhysRevA.102.042613
[18] Lorenza Viola, Emanuel Knill, and Seth Lloyd. “Dynamical decoupling of open quantum systems”. Phys. Rev. Lett. 82, 2417–2421 (1999).
https://doi.org/10.1103/PhysRevLett.82.2417
[19] Sisi Zhou and Liang Jiang. “Asymptotic theory of quantum channel estimation”. PRX Quantum 2, 010343 (2021).
https://doi.org/10.1103/PRXQuantum.2.010343
[20] BM Escher, Ruynet Lima de Matos Filho, and Luiz Davidovich. “General framework for estimating the ultimate precision limit in noisy quantum-enhanced metrology”. Nature Physics 7, 406–411 (2011).
https://doi.org/10.1038/nphys1958
[21] Rafał Demkowicz-Dobrzański, Jan Kołodyński, and Mădălin Guţă. “The elusive heisenberg limit in quantum-enhanced metrology”. Nature communications 3, 1063 (2012).
https://doi.org/10.1038/ncomms2067
[22] Sisi Zhou, Chang-Ling Zou, and Liang Jiang. “Saturating the quantum cramér–rao bound using locc”. Quantum Science and Technology 5, 025005 (2020).
https://doi.org/10.1088/2058-9565/ab71f8
[23] Barbara M. Terhal and David P. DiVincenzo. “Adaptive Quantum Computation, Constant Depth Quantum Circuits and Arthur-Merlin Games”. Quant. Inf. Comput. 4, 134–145 (2004).
https://doi.org/10.26421/QIC4.2-5
[24] Hans J Briegel, David E Browne, Wolfgang Dür, Robert Raussendorf, and Maarten Van den Nest. “Measurement-based quantum computation”. Nature Physics 5, 19–26 (2009).
https://doi.org/10.1038/nphys1157
[25] Robert Raussendorf and Hans J. Briegel. “A one-way quantum computer”. Phys. Rev. Lett. 86, 5188–5191 (2001).
https://doi.org/10.1103/PhysRevLett.86.5188
[26] Jeongwan Haah, Robin Kothari, and Ewin Tang. “Optimal learning of quantum Hamiltonians from high-temperature Gibbs states” (2021). arXiv:2108.04842.
arXiv:2108.04842
[27] Dominik S. Wild and Álvaro M. Alhambra. “Classical simulation of short-time quantum dynamics”. PRX Quantum 4, 020340 (2023).
https://doi.org/10.1103/PRXQuantum.4.020340
[28] Dmitry Abanin, Wojciech De Roeck, Wen Wei Ho, and François Huveneers. “A rigorous theory of many-body prethermalization for periodically driven and closed quantum systems”. Communications in Mathematical Physics 354, 809–827 (2017).
https://doi.org/10.1007/s00220-017-2930-x
[29] Carl W. Helstrom. “Quantum detection and estimation theory”. Journal of Statistical Physics (1976).
https://doi.org/10.1007/BF01007479
[30] Samuel L. Braunstein and Carlton M. Caves. “Statistical distance and the geometry of quantum states”. Phys. Rev. Lett. 72, 3439–3443 (1994).
https://doi.org/10.1103/PhysRevLett.72.3439
[31] Sergio Boixo, Steven T. Flammia, Carlton M. Caves, and JM Geremia. “Generalized limits for single-parameter quantum estimation”. Phys. Rev. Lett. 98, 090401 (2007).
https://doi.org/10.1103/PhysRevLett.98.090401
[32] Jan Kołodyński and Rafał Demkowicz-Dobrzański. “Efficient tools for quantum metrology with uncorrelated noise”. New Journal of Physics 15, 073043 (2013).
https://doi.org/10.1088/1367-2630/15/7/073043
[33] Matteo G. A. Paris. “Quantum estimation for quantum technology”. International Journal of Quantum Information 07, 125–137 (2009).
https://doi.org/10.1142/S0219749909004839
[34] Wojciech Górecki, Rafał Demkowicz-Dobrzański, Howard M. Wiseman, and Dominic W. Berry. “${pi}$-corrected heisenberg limit”. Phys. Rev. Lett. 124, 030501 (2020).
https://doi.org/10.1103/PhysRevLett.124.030501
[35] G. Goldstein, P. Cappellaro, J. R. Maze, J. S. Hodges, L. Jiang, A. S. Sørensen, and M. D. Lukin. “Environment-assisted precision measurement”. Phys. Rev. Lett. 106, 140502 (2011).
https://doi.org/10.1103/PhysRevLett.106.140502
[36] Qing-Shou Tan, Yixiao Huang, Xiaolei Yin, Le-Man Kuang, and Xiaoguang Wang. “Enhancement of parameter-estimation precision in noisy systems by dynamical decoupling pulses”. Phys. Rev. A 87, 032102 (2013).
https://doi.org/10.1103/PhysRevA.87.032102
[37] Pavel Sekatski, Michalis Skotiniotis, and Wolfgang Dür. “Dynamical decoupling leads to improved scaling in noisy quantum metrology”. New Journal of Physics 18, 073034 (2016).
https://doi.org/10.1088/1367-2630/18/7/073034
[38] Hengyun Zhou, Joonhee Choi, Soonwon Choi, Renate Landig, Alexander M. Douglas, Junichi Isoya, Fedor Jelezko, Shinobu Onoda, Hitoshi Sumiya, Paola Cappellaro, Helena S. Knowles, Hongkun Park, and Mikhail D. Lukin. “Quantum metrology with strongly interacting spin systems”. Phys. Rev. X 10, 031003 (2020).
https://doi.org/10.1103/PhysRevX.10.031003
[39] Magdalena Szczykulska, Tillmann Baumgratz, and Animesh Datta. “Multi-parameter quantum metrology”. Advances in Physics: X 1, 621–639 (2016).
https://doi.org/10.1080/23746149.2016.1230476
[40] Alicja Dutkiewicz, Thomas E. O’Brien, and Thomas Schuster. “The advantage of quantum control in many-body Hamiltonian learning” (2023). arXiv:2304.07172.
arXiv:2304.07172
[41] Hsin-Yuan Huang, Yu Tong, Di Fang, and Yuan Su. “Learning many-body hamiltonians with heisenberg-limited scaling”. Phys. Rev. Lett. 130, 200403 (2023).
https://doi.org/10.1103/PhysRevLett.130.200403
[42] W. Dür, M. Skotiniotis, F. Fröwis, and B. Kraus. “Improved quantum metrology using quantum error correction”. Phys. Rev. Lett. 112, 080801 (2014).
https://doi.org/10.1103/PhysRevLett.112.080801
[43] G. Arrad, Y. Vinkler, D. Aharonov, and A. Retzker. “Increasing sensing resolution with error correction”. Phys. Rev. Lett. 112, 150801 (2014).
https://doi.org/10.1103/PhysRevLett.112.150801
[44] E. M. Kessler, I. Lovchinsky, A. O. Sushkov, and M. D. Lukin. “Quantum error correction for metrology”. Phys. Rev. Lett. 112, 150802 (2014).
https://doi.org/10.1103/PhysRevLett.112.150802
[45] Rafał Demkowicz-Dobrzański, Jan Czajkowski, and Pavel Sekatski. “Adaptive quantum metrology under general markovian noise”. Phys. Rev. X 7, 041009 (2017).
https://doi.org/10.1103/PhysRevX.7.041009
[46] Sisi Zhou, Mengzhen Zhang, John Preskill, and Liang Jiang. “Achieving the heisenberg limit in quantum metrology using quantum error correction”. Nature communications 9, 78 (2018).
https://doi.org/10.1038/s41467-017-02510-3
[47] Sisi Zhou, Argyris Giannisis Manes, and Liang Jiang. “Achieving metrological limits using ancilla-free quantum error-correcting codes” (2023). arXiv:2303.00881.
arXiv:2303.00881
[48] Jan Jeske, Jared H Cole, and Susana F Huelga. “Quantum metrology subject to spatially correlated markovian noise: restoring the heisenberg limit”. New Journal of Physics 16, 073039 (2014).
https://doi.org/10.1088/1367-2630/16/7/073039
[49] David Layden and Paola Cappellaro. “Spatial noise filtering through error correction for quantum sensing”. npj Quantum Information 4, 30 (2018).
https://doi.org/10.1038/s41534-018-0082-2
[50] Jan Czajkowski, Krzysztof Pawłowski, and Rafał Demkowicz-Dobrzański. “Many-body effects in quantum metrology”. New Journal of Physics 21, 053031 (2019).
https://doi.org/10.1088/1367-2630/ab1fc2
[51] Krzysztof Chabuda, Jacek Dziarmaga, Tobias J Osborne, and Rafał Demkowicz-Dobrzański. “Tensor-network approach for quantum metrology in many-body quantum systems”. Nature communications 11, 250 (2020).
https://doi.org/10.1038/s41467-019-13735-9
[52] Francisco Riberi, Leigh M Norris, Félix Beaudoin, and Lorenza Viola. “Frequency estimation under non-markovian spatially correlated quantum noise”. New Journal of Physics 24, 103011 (2022).
https://doi.org/10.1088/1367-2630/ac92a2
[53] Hai-Long Shi, Xi-Wen Guan, and Jing Yang. “Universal shot-noise limit for quantum metrology with local hamiltonians”. Phys. Rev. Lett. 132, 100803 (2024).
https://doi.org/10.1103/PhysRevLett.132.100803
[54] Elliott H. Lieb and Derek W. Robinson. “The finite group velocity of quantum spin systems”. Commun. Math. Phys. 28, 251–257 (1972).
https://doi.org/10.1007/BF01645779
[55] Chi-Fang (Anthony) Chen, Andrew Lucas, and Chao Yin. “Speed limits and locality in many-body quantum dynamics”. Reports on Progress in Physics 86, 116001 (2023).
https://doi.org/10.1088/1361-6633/acfaae
[56] S. Bravyi, M. B. Hastings, and F. Verstraete. “Lieb-robinson bounds and the generation of correlations and topological quantum order”. Phys. Rev. Lett. 97, 050401 (2006).
https://doi.org/10.1103/PhysRevLett.97.050401
[57] Jian Ma, Xiaoguang Wang, C.P. Sun, and Franco Nori. “Quantum spin squeezing”. Physics Reports 509, 89–165 (2011).
https://doi.org/10.1016/j.physrep.2011.08.003
[58] Aaron J. Friedman, Chao Yin, Yifan Hong, and Andrew Lucas. “Locality and error correction in quantum dynamics with measurement” (2022). arXiv:2206.09929.
arXiv:2206.09929
[59] Jeongwan Haah, Matthew B. Hastings, Robin Kothari, and Guang Hao Low. “Quantum algorithm for simulating real time evolution of lattice hamiltonians”. SIAM Journal on Computing 0, FOCS18–250–FOCS18–284 (0).
https://doi.org/10.1137/18M1231511
[60] Fernando GSL Brandao and Michał Horodecki. “Exponential decay of correlations implies area law”. Communications in mathematical physics 333, 761–798 (2015).
https://doi.org/10.1007/s00220-014-2213-8
[61] M. Burak Şahinoğlu, Sujeet K. Shukla, Feng Bi, and Xie Chen. “Matrix product representation of locality preserving unitaries”. Phys. Rev. B 98, 245122 (2018).
https://doi.org/10.1103/PhysRevB.98.245122
[62] Y.-Y. Shi, L.-M. Duan, and G. Vidal. “Classical simulation of quantum many-body systems with a tree tensor network”. Phys. Rev. A 74, 022320 (2006).
https://doi.org/10.1103/PhysRevA.74.022320
[63] D. Perez-Garcia, F. Verstraete, M. M. Wolf, and J. I. Cirac. “Matrix product state representations”. Quantum Info. Comput. 7, 401–430 (2007).
https://doi.org/10.26421/QIC7.5-6-1
[64] Chao Yin and Andrew Lucas. “Polynomial-time classical sampling of high-temperature quantum Gibbs states” (2023). arXiv:2305.18514.
arXiv:2305.18514
[65] Penghui Yao, Yitong Yin, and Xinyuan Zhang. “Polynomial-Time Approximation of Zero-Free Partition Functions” (2022). arXiv:2201.12772.
arXiv:2201.12772
[66] Yimu Bao, Maxwell Block, and Ehud Altman. “Finite-time teleportation phase transition in random quantum circuits”. Phys. Rev. Lett. 132, 030401 (2024).
https://doi.org/10.1103/PhysRevLett.132.030401
[67] Ken Xuan Wei, Pai Peng, Oles Shtanko, Iman Marvian, Seth Lloyd, Chandrasekhar Ramanathan, and Paola Cappellaro. “Emergent prethermalization signatures in out-of-time ordered correlations”. Phys. Rev. Lett. 123, 090605 (2019).
https://doi.org/10.1103/PhysRevLett.123.090605
[68] Pai Peng, Chao Yin, Xiaoyang Huang, Chandrasekhar Ramanathan, and Paola Cappellaro. “Floquet prethermalization in dipolar spin chains”. Nature Physics 17, 444–447 (2021).
https://doi.org/10.1038/s41567-020-01120-z
[69] Francisco Machado, Dominic V. Else, Gregory D. Kahanamoku-Meyer, Chetan Nayak, and Norman Y. Yao. “Long-range prethermal phases of nonequilibrium matter”. Phys. Rev. X 10, 011043 (2020).
https://doi.org/10.1103/PhysRevX.10.011043
[70] Chao Yin and Andrew Lucas. “Prethermalization and the local robustness of gapped systems”. Phys. Rev. Lett. 131, 050402 (2023).
https://doi.org/10.1103/PhysRevLett.131.050402
[71] Masahiro Kitagawa and Masahito Ueda. “Squeezed spin states”. Phys. Rev. A 47, 5138–5143 (1993).
https://doi.org/10.1103/PhysRevA.47.5138
[72] Michael Foss-Feig, Zhe-Xuan Gong, Alexey V Gorshkov, and Charles W Clark. “Entanglement and spin-squeezing without infinite-range interactions” (2016). arXiv:1612.07805.
arXiv:1612.07805
[73] Michael A. Perlin, Chunlei Qu, and Ana Maria Rey. “Spin squeezing with short-range spin-exchange interactions”. Phys. Rev. Lett. 125, 223401 (2020).
https://doi.org/10.1103/PhysRevLett.125.223401
[74] Maxwell Block, Bingtian Ye, Brenden Roberts, Sabrina Chern, Weijie Wu, Zilin Wang, Lode Pollet, Emily J. Davis, Bertrand I. Halperin, and Norman Y. Yao. “A Universal Theory of Spin Squeezing” (2023). arXiv:2301.09636.
arXiv:2301.09636
[75] Xi-Lin Wang, Yi-Han Luo, He-Liang Huang, Ming-Cheng Chen, Zu-En Su, Chang Liu, Chao Chen, Wei Li, Yu-Qiang Fang, Xiao Jiang, Jun Zhang, Li Li, Nai-Le Liu, Chao-Yang Lu, and Jian-Wei Pan. “18-qubit entanglement with six photons’ three degrees of freedom”. Phys. Rev. Lett. 120, 260502 (2018).
https://doi.org/10.1103/PhysRevLett.120.260502
[76] Ken X. Wei, Isaac Lauer, Srikanth Srinivasan, Neereja Sundaresan, Douglas T. McClure, David Toyli, David C. McKay, Jay M. Gambetta, and Sarah Sheldon. “Verifying multipartite entangled greenberger-horne-zeilinger states via multiple quantum coherences”. Phys. Rev. A 101, 032343 (2020).
https://doi.org/10.1103/PhysRevA.101.032343
[77] Chao Song, Kai Xu, Hekang Li, Yu-Ran Zhang, Xu Zhang, Wuxin Liu, Qiujiang Guo, Zhen Wang, Wenhui Ren, Jie Hao, Hui Feng, Heng Fan, Dongning Zheng, Da-Wei Wang, H. Wang, and Shi-Yao Zhu. “Generation of multicomponent atomic schrödinger cat states of up to 20 qubits”. Science 365, 574–577 (2019).
https://doi.org/10.1126/science.aay0600
[78] A. Omran, H. Levine, A. Keesling, G. Semeghini, T. T. Wang, S. Ebadi, H. Bernien, A. S. Zibrov, H. Pichler, S. Choi, J. Cui, M. Rossignolo, P. Rembold, S. Montangero, T. Calarco, M. Endres, M. Greiner, V. Vuletić, and M. D. Lukin. “Generation and manipulation of schrödinger cat states in rydberg atom arrays”. Science 365, 570–574 (2019).
https://doi.org/10.1126/science.aax9743
[79] I. Pogorelov, T. Feldker, Ch. D. Marciniak, L. Postler, G. Jacob, O. Krieglsteiner, V. Podlesnic, M. Meth, V. Negnevitsky, M. Stadler, B. Höfer, C. Wächter, K. Lakhmanskiy, R. Blatt, P. Schindler, and T. Monz. “Compact ion-trap quantum computing demonstrator”. PRX Quantum 2, 020343 (2021).
https://doi.org/10.1103/PRXQuantum.2.020343
[80] Sirui Lu, Mari Carmen Bañuls, and J. Ignacio Cirac. “Algorithms for quantum simulation at finite energies”. PRX Quantum 2, 020321 (2021).
https://doi.org/10.1103/PRXQuantum.2.020321
[81] Alexander Schuckert, Annabelle Bohrdt, Eleanor Crane, and Michael Knap. “Probing finite-temperature observables in quantum simulators of spin systems with short-time dynamics”. Phys. Rev. B 107, L140410 (2023).
https://doi.org/10.1103/PhysRevB.107.L140410
[82] Khaldoon Ghanem, Alexander Schuckert, and Henrik Dreyer. “Robust Extraction of Thermal Observables from State Sampling and Real-Time Dynamics on Quantum Computers”. Quantum 7, 1163 (2023).
https://doi.org/10.22331/q-2023-11-03-1163
[83] Sergey Bravyi, David Gosset, and Ramis Movassagh. “Classical algorithms for quantum mean values”. Nature Physics 17, 337–341 (2021).
https://doi.org/10.1038/s41567-020-01109-8
[84] Nolan J. Coble and Matthew Coudron. “Quasi-polynomial time approximation of output probabilities of geometrically-local, shallow quantum circuits”. In 2021 IEEE 62nd Annual Symposium on Foundations of Computer Science (FOCS). Pages 598–609. (2022).
https://doi.org/10.1109/FOCS52979.2021.00065
[85] Suchetan Dontha, Shi Jie Samuel Tan, Stephen Smith, Sangheon Choi, and Matthew Coudron. “Approximating Output Probabilities of Shallow Quantum Circuits which are Geometrically-local in any Fixed Dimension” (2022). arXiv:2202.08349.
arXiv:2202.08349
[86] Reyhaneh Aghaei Saem and Ali Hamed Moosavian. “Classical Algorithm for the Mean Value problem over Short-Time Hamiltonian Evolutions” (2023). arXiv:2301.11420.
arXiv:2301.11420
Cited by
[1] Luis Pedro García-Pintos, Kishor Bharti, Jacob Bringewatt, Hossein Dehghani, Adam Ehrenberg, Nicole Yunger Halpern, and Alexey V. Gorshkov, “Estimation of Hamiltonian parameters from thermal states”, arXiv:2401.10343, (2024).
[2] Jia-Xuan Liu, Jing Yang, Hai-Long Shi, and Sixia Yu, “Optimal Local Measurements in Many-body Quantum Metrology”, arXiv:2310.00285, (2023).
The above citations are from SAO/NASA ADS (last updated successfully 2024-03-29 03:00:21). The list may be incomplete as not all publishers provide suitable and complete citation data.
On Crossref’s cited-by service no data on citing works was found (last attempt 2024-03-29 03:00:20).
This Paper is published in Quantum under the Creative Commons Attribution 4.0 International (CC BY 4.0) license. Copyright remains with the original copyright holders such as the authors or their institutions.
- SEO Powered Content & PR Distribution. Get Amplified Today.
- PlatoData.Network Vertical Generative Ai. Empower Yourself. Access Here.
- PlatoAiStream. Web3 Intelligence. Knowledge Amplified. Access Here.
- PlatoESG. Carbon, CleanTech, Energy, Environment, Solar, Waste Management. Access Here.
- PlatoHealth. Biotech and Clinical Trials Intelligence. Access Here.
- Source: https://quantum-journal.org/papers/q-2024-03-28-1303/
- :is
- :not
- ][p
- $UP
- 003
- 07
- 08
- 1
- 10
- 11
- 12
- 120
- 125
- 13
- 130
- 14
- 15%
- 16
- 17
- 19
- 1994
- 1999
- 20
- 2001
- 2006
- 2009
- 2011
- 2012
- 2013
- 2014
- 2015
- 2016
- 2017
- 2018
- 2019
- 2020
- 2021
- 2022
- 2023
- 2024
- 22
- 23
- 24
- 25
- 250
- 26%
- 27
- 28
- 29
- 30
- 31
- 32
- 33
- 35%
- 36
- 39
- 40
- 41
- 43
- 49
- 50
- 51
- 54
- 58
- 60
- 65
- 66
- 67
- 7
- 70
- 72
- 75
- 77
- 8
- 80
- 84
- 87
- 89
- 9
- 97
- 98
- a
- Aaron
- above
- ABSTRACT
- access
- Achieves
- Adam
- adaptive
- advances
- ADvantage
- affected
- affiliations
- Alexander
- algorithm
- algorithms
- All
- an
- Ana
- Analytic
- and
- Andrew
- annual
- Anthony
- any
- approach
- ARE
- AREA
- AS
- At
- atom
- atomic
- Attainable
- attempt
- author
- authors
- based
- BE
- Bertrand
- Block
- Bound
- bounds
- Break
- by
- calculation
- calculations
- CAN
- Carl
- CAT
- Center
- chain
- chains
- chang
- Channel
- Chao-Yang Lu
- Charles
- chen
- closed
- Cluster
- CO
- codes
- Colorado
- comment
- Commons
- Communications
- complete
- computation
- computer
- computer science
- computers
- computing
- constant
- control
- copyright
- correlations
- data
- David
- Davis
- de
- degen
- del
- depth
- Derek
- Detection
- Dimension
- dimensions
- discuss
- distance
- douglas
- driven
- duration
- during
- dynamics
- e
- effects
- efficient
- Elliott
- else
- entanglement
- error
- evolution
- evolutions
- expansion
- extraction
- fan
- Federico
- feedback
- field
- filtering
- First
- fixed
- For
- found
- Foundations
- fragmentation
- Framework
- Francisco
- Freedom
- from
- functions
- Games
- gate
- General
- generation
- Group
- hans
- harvard
- higher
- holders
- Hong
- HTTPS
- huang
- i
- IEEE
- image
- Iman
- improved
- in
- independent
- info
- information
- institutions
- interacting
- interactions
- interest
- interesting
- International
- IT
- jacob
- Jan
- JavaScript
- Jian-Wei Pan
- John
- Jordan
- journal
- Last
- Law
- Leads
- learning
- Leave
- levine
- Li
- License
- LIMIT
- Limited
- limits
- List
- local
- LODE
- Low
- luiz
- Magnetic field
- Manipulation
- mar
- maria
- math
- mathematical
- Matrix
- Matter
- matthew
- max-width
- Maxwell
- May..
- mean
- measurement
- measurements
- methods
- Metrology
- Michael
- mikhail
- Month
- multiple
- Nature
- Nest
- network
- New
- no
- Noise
- of
- on
- ONE
- open
- optimal
- or
- order
- original
- output
- over
- pages
- Paper
- parameter
- parameters
- paris
- Park
- Perform
- perspective
- phase
- phases
- Photons
- Physics
- plato
- Plato Data Intelligence
- PlatoData
- possible
- possibly
- Precision
- presence
- preserving
- probabilities
- probe
- Problem
- process
- Product
- Progress
- protected
- protocol
- provide
- published
- publisher
- publishers
- Quant
- Quantum
- Quantum Computer
- quantum computers
- quantum computing
- quantum error correction
- quantum information
- quantum systems
- quantum technology
- qubits
- R
- ramanathan
- random
- real
- real-time
- references
- relies
- remains
- ren
- Reports
- representation
- Resolution
- restoring
- rigorous
- ROBERT
- Robin
- robust
- robustness
- s
- scaling
- Science
- Science and Technology
- set
- shallow
- show
- siam
- Signatures
- simulation
- SIX
- smith
- song
- Space
- Spin
- srinivasan
- State
- States
- statistical
- Stephen
- steven
- strong
- strongly
- subject
- Successfully
- such
- suitable
- Sun
- Symposium
- Systems
- tang
- Technology
- that
- The
- their
- theoretical
- theory
- thermal
- this
- thomas
- three
- Through
- time
- Title
- to
- todd
- tools
- topological quantum
- Transformation
- transition
- transitions
- tree
- ultimate
- uncorrelated
- under
- Universal
- university
- updated
- URL
- used
- using
- value
- Values
- van
- VeloCity
- via
- volume
- W
- wang
- want
- was
- which
- while
- Wild
- william
- with
- without
- Wolf
- works
- wu
- X
- xiao
- xinyuan
- Ye
- year
- youtube
- Yuan
- zephyrnet
