中文版 | English
Title

基于量子哈密顿量层析的量子表征及其实验研究

Alternative Title
QUANTUM CHARACTERIZATION BASED ON HAMILTONIAN TOMOGRAPHY AND ITS EXPERIMENTAL RESEARCH
Author
Name pinyin
WEI Chao
School number
11930019
Degree
硕士
Discipline
070203 原子与分子物理
Subject category of dissertation
07 理学
Supervisor
辛涛
Mentor unit
量子科学与工程研究院
Publication Years
2022-05-11
Submission date
2022-07-01
University
南方科技大学
Place of Publication
深圳
Abstract
量子表征是量子计算任务中的重要一环,是实现量子计算实用化不可或缺的关键技术。在早期的量子计算发展中,学界更关注的是量子比特的物理实现以及量子门电路的搭建,但随着量子计算体系中的比特数目逐渐增多,实现算法所需的量子门电路层数越来越多,计算过程中的环境噪声以及量子操控中的累积误差变得越来越不可忽视。要实现对量子设备工作精度的改进,首先我们需要将量子设备的性能进行表征。相较于量子比特的制备以及通过量子控制实现量子门操作等任务,量子表征还处于一个发展较为滞后的状态,但经过多年发展人们同样提出了多种技术方案,量子哈密顿量层析就是其中之一。
本论文将介绍两个基于量子哈密顿量层析的量子表征工作。其中,在核磁共振量子计算平台上我们进行了基于量子淬火的量子哈密顿量层析工作,对选定的两比特 Ising 模型的哈密顿量参数进行表征,得出了相当精确的实验结果。同时我们还进行了其他的传统表征实验并对比了实验结果,对比结果显示,淬火方案的量子哈密顿量层析方案得出的的实验应用有着不输于传统表征手段的表征能力。之后,为了进一步探索并优化哈密顿量层析的实现方案,我们设计了一个利用机器学习技术通过对单比特测量数据的学习估测哈密顿量参数的哈密顿量表征方案。我们选取了几个特殊的哈密顿量模型生成单比特测量数据并输入神经网络模型进行了训练,并测试了该方案面对含噪声数据时表征精度的鲁棒性。训练和测试的结果验证了我们的机器学习方案对多种模型都可以有效学习到其哈密顿量特征,并且具有极高的表征准确度和鲁棒性。
Keywords
Language
Chinese
Training classes
独立培养
Enrollment Year
2019
Year of Degree Awarded
2022-07
References List

[1] 新华社. 世界首颗量子科学实验卫星“墨子号”正式交付使用 2017 年 01 月 18 日[EB/OL].(2017-1-18)

[2017-1-18]. http://www.xinhuanet.com//photo/2017-01/18/c_1120339681.htm.

[2] ARUTE F, ARYA K, BABBUSH R, et al. Quantum supremacy using a programmable superconducting processor [J]. Nature, 2019, 574(7779): 505-510.

[3] 习近平. 习近平: 加强量子科技发展战略谋划和系统布局[N]. 人民日报海外版, 2020-10-19((1)).

[4] FEYNMAN. Simulating physics with computers [J]. International Journal Of Theoretical Physics, 1982, 21(6/7): 467–488.

[5] MANIN Y. Computable and Uncomputable [M]. Moscow: Sovetskoye Radio, 1980: 128.

[6] DEUTSCH D. Quantum theory, the Church–Turing principle and the universal quantum computer [J]. Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences, 1985, 400(1818): 97-117.

[7] BERNSTEIN E, VAZIRANI U. Quantum complexity theory [J]. SIAM Journal on computing, 1997, 26(5): 1411-1473.

[8] SHOR P W. Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer [J]. SIAM review, 1999, 41(2): 303-332.

[9] GROVER L K. Quantum mechanics helps in searching for a needle in a haystack [J]. Physical Review Letters, 1997, 79(2): 325.

[10] PRESKILL J. Quantum computing in the NISQ era and beyond [J]. Quantum, 2018, 2: 79.

[11] GOTTESMAN D. An introduction to quantum error correction and fault-tolerant quantum computation [C]//Quantum information science and its contributions to mathematics, Proceedings of Symposia in Applied Mathematics: volume 68. 2010: 13-58.

[12] CAMPBELL E T, TERHAL B M, VUILLOT C. Roads towards fault-tolerant universal quantum computation [J]. Nature, 2017, 549(7671): 172-179.

[13] DIVINCENZO D P. The physical implementation of quantum computation [J]. Fortschritte der Physik: Progress of Physics, 2000, 48(9-11): 771-783.

[14] 鲁大为. 利用核磁共振量子计算实验实现量子模拟[D]. 中国科学技术大学, 2012.

[15] 辛涛. 量子态重构与动力学时间关联的核磁共振实验研究[D]. 清华大学, 2017.

[16] LEVITT M H. Spin dynamics: basics of nuclear magnetic resonance [M]. John Wiley & Sons, 2013: 178.

[17] LLOYD S. Universal quantum simulators [J]. Science, 1996, 273(5278): 1073-1078.

[18] WALLMAN J, FLAMMIA S, HINCKS I. Quantum Characterization, Verification, and Validation [M]//Oxford Research Encyclopedia of Physics. 2018.

[19] EISERT J, HANGLEITER D, WALK N, et al. Quantum certification and benchmarking [J]. Nature Reviews Physics, 2020, 2(7): 382-390.

[20] HRADIL Z. Quantum-state estimation [J]. Physical Review A, 1997, 55(3): R1561.

[21] JAMES D F, KWIAT P G, MUNRO W J, et al. On the measurement of qubits [M]//Asymptotic Theory of Quantum Statistical Inference: Selected Papers. World Scientific, 2005: 509-538.

[22] HÄFFNER H, HÄNSEL W, ROOS C, et al. Scalable multiparticle entanglement of trapped ions [J]. Nature, 2005, 438(7068): 643-646.

[23] SONG C, XU K, LIU W, et al. 10-qubit entanglement and parallel logic operations with a superconducting circuit [J]. Physical Review Letters, 2017, 119(18): 180511.

[24] GROSS D, LIU Y K, FLAMMIA S T, et al. Quantum state tomography via compressed sensing [J]. Physical Review Letters, 2010, 105(15): 150401.

[25] KALEV A, KOSUT R L, DEUTSCH I H. Quantum tomography protocols with positivity are compressed sensing protocols [J]. Npj Quantum Information, 2015, 1(1): 1-6.

[26] GUŢĂ M, KAHN J, KUENG R, et al. Fast state tomography with optimal error bounds [J]. Journal of Physics A: Mathematical and Theoretical, 2020, 53(20): 204001.

[27] TORLAI G, MAZZOLA G, CARRASQUILLA J, et al. Neural-network quantum state tomography [J]. Nature Physics, 2018, 14(5): 447-450.

[28] CARRASQUILLA J, TORLAI G, MELKO R G, et al. Reconstructing quantum states with generative models [J]. Nature Machine Intelligence, 2019, 1(3): 155-161.

[29] WEINSTEIN Y S, HAVEL T F, EMERSON J, et al. Quantum process tomography of the quantum Fourier transform [J]. The Journal of chemical physics, 2004, 121(13): 6117-6133.

[30] EMERSON J, SILVA M, MOUSSA O, et al. Symmetrized characterization of noisy quantum processes [J]. Science, 2007, 317(5846): 1893-1896.

[31] LU D, LI H, TROTTIER D A, et al. Experimental estimation of average fidelity of a clifford gate on a 7-qubit quantum processor [J]. Physical Review Letters, 2015, 114(14): 140505.

[32] FLAMMIA S T, GROSS D, LIU Y K, et al. Quantum tomography via compressed sensing: error bounds, sample complexity and efficient estimators [J]. New Journal of Physics, 2012, 14 (9): 095022.

[33] KLIESCH M, KUENG R, EISERT J, et al. Guaranteed recovery of quantum processes from few measurements [J]. Quantum, 2019, 3: 171.

[34] CRAMER M, PLENIO M B, FLAMMIA S T, et al. Efficient quantum state tomography [J]. Nature communications, 2010, 1(1): 1-7.

[35] HÜBENER R, MARI A, EISERT J. Wick’s theorem for matrix product states [J]. Physical Review Letters, 2013, 110(4): 040401.

[36] BAUMGRATZ T, GROSS D, CRAMER M, et al. Scalable reconstruction of density matrices [J]. Physical Review Letters, 2013, 111(2): 020401.

[37] KNILL E, LEIBFRIED D, REICHLE R, et al. Randomized benchmarking of quantum gates [J]. Physical Review A, 2008, 77(1): 012307.

[38] MAGESAN E, GAMBETTA J M, JOHNSON B R, et al. Efficient measurement of quantum gate error by interleaved randomized benchmarking [J]. Physical Review Letters, 2012, 109 (8): 080505.

[39] MCKAY D C, SHELDON S, SMOLIN J A, et al. Three-qubit randomized benchmarking [J]. Physical Review Letters, 2019, 122(20): 200502.

[40] HOLZÄPFEL M, BAUMGRATZ T, CRAMER M, et al. Scalable reconstruction of unitary processes and Hamiltonians [J]. Physical Review A, 2015, 91(4): 042129.

[41] COLE J H, SCHIRMER S G, GREENTREE A D, et al. Identifying an experimental two-state Hamiltonian to arbitrary accuracy [J]. Physical Review A, 2005, 71(6): 062312.

[42] DEVITT S J, COLE J H, HOLLENBERG L C. Scheme for direct measurement of a general two-qubit Hamiltonian [J]. Physical Review A, 2006, 73(5): 052317.

[43] DI FRANCO C, PATERNOSTRO M, KIM M. Hamiltonian tomography in an access-limited setting without state initialization [J]. Physical Review Letters, 2009, 102(18): 187203.

[44] ZHANG J, SAROVAR M. Identification of open quantum systems from observable time traces [J]. Physical Review A, 2015, 91(5): 052121.

[45] HOU S Y, LI H, LONG G L. Experimental quantum Hamiltonian identification from measurement time traces [J]. Science Bulletin, 2017, 62(12): 863-868.

[46] SONE A, CAPPELLARO P. Hamiltonian identifiability assisted by a single-probe measurement [J]. Physical Review A, 2017, 95(2): 022335.

[47] SONE A, CAPPELLARO P. Exact dimension estimation of interacting qubit systems assisted by a single quantum probe [J]. Physical Review A, 2017, 96(6): 062334.

[48] QI X L, RANARD D. Determining a local hamiltonian from a single eigenstate [J]. Quantum, 2019, 3: 159.

[49] DE CLERCQ L E, OSWALD R, FLÜHMANN C, et al. Estimation of a general time-dependent Hamiltonian for a single qubit [J]. Nature communications, 2016, 7(1): 1-8.

[50] BAIREY E, ARAD I, LINDNER N H. Learning a local Hamiltonian from local measurements [J]. Physical Review Letters, 2019, 122(2): 020504.

[51] DUPONT M, MACÉ N, LAFLORENCIE N. From eigenstate to Hamiltonian: Prospects for ergodicity and localization [J]. Physical Review B, 2019, 100(13): 134201.

[52] LI Z, ZOU L, HSIEH T H. Hamiltonian tomography via quantum quench [J]. Physical Review Letters, 2020, 124(16): 160502.

[53] WANG J, PAESANI S, SANTAGATI R, et al. Experimental quantum Hamiltonian learning [J]. Nature Physics, 2017, 13(6): 551-555.

[54] KOKAIL C, VAN BIJNEN R, ELBEN A, et al. Entanglement Hamiltonian tomography in quantum simulation [J]. Nature Physics, 2021, 17(8): 936-942.

[55] XIN T, LI Y, FAN Y A, et al. Quantum Phases of Three-Dimensional Chiral Topological Insulators on a Spin Quantum Simulator [J]. Physical Review Letters, 2020, 125(9): 090502.

[56] LONG G, FENG G, SPRENGER P. Overcoming synthesizer phase noise in quantum sensing [J]. Quantum Engineering, 2019, 1(4): e27.

[57] NIE X, WEI B B, CHEN X, et al. Experimental observation of equilibrium and dynamical quantum phase transitions via out-of-time-ordered correlators [J]. Physical Review Letters, 2020, 124(25): 250601.

[58] WU X, YANG Y H, WANG Y K, et al. Determination of stabilizer states [J]. Physical Review A, 2015, 92(1): 012305.

[59] FLAMMIA S T, LIU Y K. Direct fidelity estimation from few Pauli measurements [J]. Physical Review Letters, 2011, 106(23): 230501.

[60] DA SILVA M P, LANDON-CARDINAL O, POULIN D. Practical characterization of quantum devices without tomography [J]. Physical Review Letters, 2011, 107(21): 210404.

[61] AFFLECK I, KENNEDY T, LIEB E H, et al. Rigorous results on valence-bond ground states in antiferromagnets [M]//Condensed Matter Physics and Exactly Soluble Models. Springer, 2004: 249-252.

[62] BRAVYI S, BROWNE D, CALPIN P, et al. Simulation of quantum circuits by low-rank stabilizer decompositions [J]. Quantum, 2019, 3: 181.

[63] ŻYCZKOWSKI K, PENSON K A, NECHITA I, et al. Generating random density matrices [J]. Journal of Mathematical Physics, 2011, 52(6): 062201.

[64] ZHAO D, WEI C, XUE S, et al. Characterizing quantum simulations with quantum tomography on a spin quantum simulator [J]. Physical Review A, 2021, 103(5): 052403.

[65] SAK H, SENIOR A, BEAUFAYS F. Long short-term memory based recurrent neural network architectures for large vocabulary speech recognition [J]. arXiv preprint arXiv:1402.1128, 2014.

[66] BANCHI L, GRANT E, ROCCHETTO A, et al. Modelling non-Markovian quantum processes with recurrent neural networks [J]. New Journal of Physics, 2018, 20(12): 123030.

[67] FLURIN E, MARTIN L S, HACOHEN-GOURGY S, et al. Using a recurrent neural network to reconstruct quantum dynamics of a superconducting qubit from physical observations [J].Physical Review X, 2020, 10(1): 011006.

[68] MINAKAWA T, NASU J, KOGA A. Quantum and classical behavior of spin-S Kitaev models in the anisotropic limit [J]. Physical Review B, 2019, 99(10): 104408.

[69] TAKAGI H, TAKAYAMA T, JACKELI G, et al. Concept and realization of Kitaev quantum spin liquids [J]. Nature Reviews Physics, 2019, 1(4): 264-280.

[70] XIN T. Improved quantum state tomography for systems with XX+ YY couplings and Z readouts [J]. Physical Review A, 2020, 102(5): 052410.

[71] KEITH D, HOUSE M, DONNELLY M, et al. Single-shot spin readout in semiconductors near the shot-noise sensitivity limit [J]. Physical Review X, 2019, 9(4): 041003.

[72] BRUZEWICZ C D, CHIAVERINI J, MCCONNELL R, et al. Trapped-ion quantum computing: Progress and challenges [J]. Applied Physics Reviews, 2019, 6(2): 021314.

[73] XIN T, WANG B X, LI K R, et al. Nuclear magnetic resonance for quantum computing: techniques and recent achievements [J]. Chinese Physics B, 2018, 27(2): 020308.

[74] GAMBETTA J, BRAFF W, WALLRAFF A, et al. Protocols for optimal readout of qubits using a continuous quantum nondemolition measurement [J]. Physical Review A, 2007, 76(1): 012325.

[75] NACHMAN B, URBANEK M, DE JONG W A, et al. Unfolding quantum computer readout noise [J]. Npj Quantum Information, 2020, 6(1): 1-7.

[76] CHE L, WEI C, HUANG Y, et al. Learning quantum Hamiltonians from single-qubit measurements [J]. Physical Review Research, 2021, 3(2): 023246.

Academic Degree Assessment Sub committee
量子科学与工程研究院
Domestic book classification number
TM301.2
Data Source
人工提交
Document TypeThesis
Identifierhttp://kc.sustech.edu.cn/handle/2SGJ60CL/343726
DepartmentInstitute for Quantum Science and Engineering
Recommended Citation
GB/T 7714
魏超. 基于量子哈密顿量层析的量子表征及其实验研究[D]. 深圳. 南方科技大学,2022.
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