Variational quantum state preparation via quantum data buses

Viacheslav V. Kuzmin and Pietro Silvi

Center for Quantum Physics, Faculty of Mathematics, Computer Science and Physics, University of Innsbruck, A-6020, Innsbruck, Austria
Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, A-6020 Innsbruck, Austria

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Abstract

We propose a variational quantum algorithm to prepare ground states of 1D lattice quantum Hamiltonians specifically tailored for programmable quantum devices where interactions among qubits are mediated by Quantum Data Buses (QDB). For trapped ions with the axial Center-Of-Mass (COM) vibrational mode as single QDB, our scheme uses resonant sideband optical pulses as resource operations, which are potentially faster than off-resonant couplings and thus less prone to decoherence. The disentangling of the QDB from the qubits by the end of the state preparation comes as a byproduct of the variational optimization. We numerically simulate the ground state preparation for the Su-Schrieffer-Heeger model in ions and show that our strategy is scalable while being tolerant to finite temperatures of the COM mode.

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[1] M. Endres, H. Bernien, A. Keesling, H. Levine, E. R. Anschuetz, A. Krajenbrink, C. Senko, V. Vuletic, M. Greiner, and M. D. Lukin. Atom-by-atom assembly of defect-free one-dimensional cold atom arrays. Science, 354, 1024–1027, (2016). 10.1126/​science.aah3752.
https:/​/​doi.org/​10.1126/​science.aah3752

[2] C. Gross and I. Bloch. Quantum simulations with ultracold atoms in optical lattices. Science, 357, 995–1001, (2017). 10.1126/​science.aal3837.
https:/​/​doi.org/​10.1126/​science.aal3837

[3] A. D. King, J. Carrasquilla, J. Raymond, I. Ozfidan, E. Andriyash, A. Berkley, M. Reis, T. Lanting, R. Harris, F. Altomare, K. Boothby, P. I. Bunyk, C. Enderud, A. Fréchette, E. Hoskinson, N. Ladizinsky, T. Oh, G. Poulin-Lamarre, C. Rich, Y. Sato, A. Y. Smirnov, L. J. Swenson, M. H. Volkmann, J. Whittaker, J. Yao, E. Ladizinsky, M. W. Johnson, J. Hilton, and M. H. Amin. Observation of topological phenomena in a programmable lattice of 1,800 qubits. Nature, 560, 456–460, (2018). 10.1038/​s41586-018-0410-x.
https:/​/​doi.org/​10.1038/​s41586-018-0410-x

[4] F. Hebenstreit, J. Berges, and D. Gelfand. Real-time dynamics of string breaking. Physical Review Letters, 111, 1–5, (2013). 10.1103/​PhysRevLett.111.201601.
https:/​/​doi.org/​10.1103/​PhysRevLett.111.201601

[5] P. Jurcevic, B. P. Lanyon, P. Hauke, C. Hempel, P. Zoller, R. Blatt, and C. F. Roos. Quasiparticle engineering and entanglement propagation in a quantum many-body system. Nature, 511, 202–205, (2014). 10.1038/​nature13461.
https:/​/​doi.org/​10.1038/​nature13461

[6] E. A. Martinez, C. A. Muschik, P. Schindler, D. Nigg, A. Erhard, M. Heyl, P. Hauke, M. Dalmonte, T. Monz, P. Zoller, and R. Blatt. Real-time dynamics of lattice gauge theories with a few-qubit quantum computer. Nature, 534, 516–519, (2016). 10.1038/​nature18318.
https:/​/​doi.org/​10.1038/​nature18318

[7] T. Pichler, M. Dalmonte, E. Rico, P. Zoller, and S. Montangero. Real-time dynamics in U(1) lattice gauge theories with tensor networks. Physical Review X, 6, 1–17, (2016). 10.1103/​PhysRevX.6.011023.
https:/​/​doi.org/​10.1103/​PhysRevX.6.011023

[8] M. Kitagawa and M. Ueda. Squeezed spin states. Phys. Rev. A, 47, 5138–5143, (1993). 10.1103/​PhysRevA.47.5138.
https:/​/​doi.org/​10.1103/​PhysRevA.47.5138

[9] T. Pichler, T. Caneva, S. Montangero, M. D. Lukin, and T. Calarco. Noise-resistant optimal spin squeezing via quantum control. Phys. Rev. A, 93, 013851, (2016). 10.1103/​PhysRevA.93.013851.
https:/​/​doi.org/​10.1103/​PhysRevA.93.013851

[10] R. Kaubruegger, P. Silvi, C. Kokail, R. van Bijnen, A. M. Rey, J. Ye, A. M. Kaufman, and P. Zoller. Variational Spin-Squeezing Algorithms on Programmable Quantum Sensors. Phys. Rev. Lett., 123, 260505, (2019). 10.1103/​PhysRevLett.123.260505.
https:/​/​doi.org/​10.1103/​PhysRevLett.123.260505

[11] T. Volkoff. Optimal and near-optimal probe states for quantum metrology of number-conserving two-mode bosonic Hamiltonians. Physical Review A, 94, 042327, (2016). 10.1103/​PhysRevA.94.042327.
https:/​/​doi.org/​10.1103/​PhysRevA.94.042327

[12] P. Richerme, C. Senko, J. Smith, A. Lee, S. Korenblit, and C. Monroe. Experimental performance of a quantum simulator: Optimizing adiabatic evolution and identifying many-body ground states. Phys. Rev. A, 88, 012334, (2013). 10.1103/​PhysRevA.88.012334.
https:/​/​doi.org/​10.1103/​PhysRevA.88.012334

[13] H. Bernien, S. Schwartz, A. Keesling, H. Levine, A. Omran, H. Pichler, S. Choi, A. S. Zibrov, M. Endres, M. Greiner, V. Vuletic, and M. D. Lukin. Probing many-body dynamics on a 51-atom quantum simulator. Nature, 551, 579–584, (2017). 10.1038/​nature24622.
https:/​/​doi.org/​10.1038/​nature24622

[14] P. Richerme, C. Senko, J. Smith, A. Lee, S. Korenblit, and C. Monroe. Experimental performance of a quantum simulator: Optimizing adiabatic evolution and identifying many-body ground states. Phys. Rev. A, 88, 012334, (2013). 10.1103/​PhysRevA.88.012334.
https:/​/​doi.org/​10.1103/​PhysRevA.88.012334

[15] A. Peruzzo, J. McClean, P. Shadbolt, M.-H. Yung, X.-Q. Zhou, P. J. Love, A. Aspuru-Guzik, and J. L. O'Brien. A variational eigenvalue solver on a photonic quantum processor. Nature communications, 5, 4213, (2014). 10.1038/​ncomms5213.
https:/​/​doi.org/​10.1038/​ncomms5213

[16] E. Farhi, J. Goldstone, and S. Gutmann. A quantum approximate optimization algorithm. MIT-CTP/​4610, (2014). arXiv preprint arXiv:1411.4028, (2014).
arXiv:1411.4028

[17] J. R. McClean, J. Romero, R. Babbush, and A. Aspuru-Guzik. The theory of variational hybrid quantum-classical algorithms. New Journal of Physics, 18, 023023, (2016). 10.1088/​1367-2630/​18/​2/​023023.
https:/​/​doi.org/​10.1088/​1367-2630/​18/​2/​023023

[18] A. Kandala, A. Mezzacapo, K. Temme, M. Takita, M. Brink, J. M. Chow, and J. M. Gambetta. Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature, 549, 242, (2017). 10.1038/​nature23879.
https:/​/​doi.org/​10.1038/​nature23879

[19] Z.-C. Yang, A. Rahmani, A. Shabani, H. Neven, and C. Chamon. Optimizing Variational Quantum Algorithms Using Pontryagin's Minimum Principle. Phys. Rev. X, 7, 021027, (2017). 10.1103/​PhysRevX.7.021027.
https:/​/​doi.org/​10.1103/​PhysRevX.7.021027

[20] P. Doria, T. Calarco, and S. Montangero. Optimal Control Technique for Many-Body Quantum Dynamics. Phys. Rev. Lett., 106, 190501, (2011). 10.1103/​PhysRevLett.106.190501.
https:/​/​doi.org/​10.1103/​PhysRevLett.106.190501

[21] N. Klco, E. F. Dumitrescu, A. J. McCaskey, T. D. Morris, R. C. Pooser, M. Sanz, E. Solano, P. Lougovski, and M. J. Savage. Quantum-classical computation of Schwinger model dynamics using quantum computers. Phys. Rev. A, 98, 032331, (2018). 10.1103/​PhysRevA.98.032331.
https:/​/​doi.org/​10.1103/​PhysRevA.98.032331

[22] C. Hempel, C. Maier, J. Romero, J. McClean, T. Monz, H. Shen, P. Jurcevic, B. P. Lanyon, P. Love, R. Babbush, A. Aspuru-Guzik, R. Blatt, and C. F. Roos. Quantum Chemistry Calculations on a Trapped-Ion Quantum Simulator. Phys. Rev. X, 8, 031022, (2018). 10.1103/​PhysRevX.8.031022.
https:/​/​doi.org/​10.1103/​PhysRevX.8.031022

[23] C. Kokail, C. Maier, R. van Bijnen, T. Brydges, M. K. Joshi, P. Jurcevic, C. A. Muschik, P. Silvi, R. Blatt, C. F. Roos, and P. Zoller. Self-verifying variational quantum simulation of lattice models. Nature, 569, 355–360, (2019). 10.1038/​s41586-019-1177-4.
https:/​/​doi.org/​10.1038/​s41586-019-1177-4

[24] J. Smith, A. Lee, P. Richerme, B. Neyenhuis, P. W. Hess, P. Hauke, M. Heyl, D. A. Huse, and C. Monroe. Many-body localization in a quantum simulator with programmable random disorder. Nature Physics, 12, 907–911, (2016). 10.1038/​nphys3783.
https:/​/​doi.org/​10.1038/​nphys3783

[25] A. Elben, B. Vermersch, R. van Bijnen, C. Kokail, T. Brydges, C. Maier, M. K. Joshi, R. Blatt, C. F. Roos, and P. Zoller. Cross-Platform Verification of Intermediate Scale Quantum Devices. Phys. Rev. Lett., 124, 010504, (2020). 10.1103/​PhysRevLett.124.010504.
https:/​/​doi.org/​10.1103/​PhysRevLett.124.010504

[26] J. I. Cirac and P. Zoller. Quantum Computations with Cold Trapped Ions. Physical Review Letters, 74, 4091–4094, (1995). 10.1103/​PhysRevLett.74.4091.
https:/​/​doi.org/​10.1103/​PhysRevLett.74.4091

[27] W. P. Su, J. R. Schrieffer, and A. J. Heeger. Solitons in Polyacetylene. Phys. Rev. Lett., 42, 1698–1701, (1979). 10.1103/​PhysRevLett.42.1698.
https:/​/​doi.org/​10.1103/​PhysRevLett.42.1698

[28] W. P. Su, J. R. Schrieffer, and A. J. Heeger. Soliton excitations in polyacetylene. Phys. Rev. B, 22, 2099–2111, (1980). 10.1103/​PhysRevB.22.2099.
https:/​/​doi.org/​10.1103/​PhysRevB.22.2099

[29] J. K. Asbóth, L. Oroszlány, and A. Pályi. The Su-Schrieffer-Heeger (SSH) Model, pages 1–22. Springer, (2016). 10.1007/​978-3-319-25607-8_1.
https:/​/​doi.org/​10.1007/​978-3-319-25607-8_1

[30] C. Gardiner and P. Zoller. The quantum world of ultra-cold atoms and light book II: the physics of quantum-optical devices. World Scientific Publishing Company, (2015). 10.1142/​p983.
https:/​/​doi.org/​10.1142/​p983

[31] S. Östlund and S. Rommer. Thermodynamic Limit of Density Matrix Renormalization. Phys. Rev. Lett., 75, 3537–3540, (1995). 10.1103/​PhysRevLett.75.3537.
https:/​/​doi.org/​10.1103/​PhysRevLett.75.3537

[32] F. Verstraete, D. Porras, and J. I. Cirac. Density Matrix Renormalization Group and Periodic Boundary Conditions: A Quantum Information Perspective. Phys. Rev. Lett., 93, 227205, (2004). 10.1103/​PhysRevLett.93.227205.
https:/​/​doi.org/​10.1103/​PhysRevLett.93.227205

[33] R. Blatt and D. Wineland. Entangled states of trapped atomic ions. Nature, 453, 1008–1015, (2008). 10.1038/​nature07125.
https:/​/​doi.org/​10.1038/​nature07125

[34] C. Monroe and J. Kim. Scaling the Ion Trap Quantum Processor. Science, 339, 1164–1169, (2013). 10.1126/​science.1231298.
https:/​/​doi.org/​10.1126/​science.1231298

[35] J. D. Hood, A. Goban, A. Asenjo-Garcia, M. Lu, S. P. Yu, D. E. Chang, and H. J. Kimble. Atom-atom interactions around the band edge of a photonic crystal waveguide. Proceedings of the National Academy of Sciences of the United States of America, 113, 10507–10512, (2016). 10.1073/​pnas.1603788113.
https:/​/​doi.org/​10.1073/​pnas.1603788113

[36] S. P. Yu, J. A. Muniz, C. L. Hung, and H. J. Kimble. Two-dimensional photonic crystals for engineering atom–light interactions. Proceedings of the National Academy of Sciences of the United States of America, 116, 12743–12751, (2019). 10.1073/​pnas.1822110116.
https:/​/​doi.org/​10.1073/​pnas.1822110116

[37] A. J. Kollár, A. T. Papageorge, V. D. Vaidya, Y. Guo, J. Keeling, and B. L. Lev. Supermode-density-wave-polariton condensation with a Bose-Einstein condensate in a multimode cavity. Nature Communications, 8, 1–10, (2017). 10.1038/​ncomms14386.
https:/​/​doi.org/​10.1038/​ncomms14386

[38] I. Cohen and K. Mølmer. Deterministic quantum network for distributed entanglement and quantum computation. Phys. Rev. A, 98, 030302, (2018). 10.1103/​PhysRevA.98.030302.
https:/​/​doi.org/​10.1103/​PhysRevA.98.030302

[39] V. D. Vaidya, Y. Guo, R. M. Kroeze, K. E. Ballantine, A. J. Kollár, J. Keeling, and B. L. Lev. Tunable-Range, Photon-Mediated Atomic Interactions in Multimode Cavity QED. Physical Review X, 8, 11002, (2018). 10.1103/​PhysRevX.8.011002.
https:/​/​doi.org/​10.1103/​PhysRevX.8.011002

[40] S. Welte, B. Hacker, S. Daiss, S. Ritter, and G. Rempe. Photon-Mediated Quantum Gate between Two Neutral Atoms in an Optical Cavity. Phys. Rev. X, 8, 011018, (2018). 10.1103/​PhysRevX.8.011018.
https:/​/​doi.org/​10.1103/​PhysRevX.8.011018

[41] M. Fitzpatrick, N. M. Sundaresan, A. C. Li, J. Koch, and A. A. Houck. Observation of a dissipative phase transition in a one-dimensional circuit QED lattice. Physical Review X, 7, 1–8, (2017). 10.1103/​PhysRevX.7.011016.
https:/​/​doi.org/​10.1103/​PhysRevX.7.011016

[42] J. M. Fink, A. Dombi, A. Vukics, A. Wallraff, and P. Domokos. Observation of the photon-blockade breakdown phase transition. Physical Review X, 7, 1–9, (2017). 10.1103/​PhysRevX.7.011012.
https:/​/​doi.org/​10.1103/​PhysRevX.7.011012

[43] C. Song, K. Xu, W. Liu, C.-p. Yang, S.-B. Zheng, H. Deng, Q. Xie, K. Huang, Q. Guo, L. Zhang, P. Zhang, D. Xu, D. Zheng, X. Zhu, H. Wang, Y.-A. Chen, C.-Y. Lu, S. Han, and J.-W. Pan. 10-Qubit Entanglement and Parallel Logic Operations with a Superconducting Circuit. Physical Review Letters, 119, 180511, (2017). 10.1103/​PhysRevLett.119.180511.
https:/​/​doi.org/​10.1103/​PhysRevLett.119.180511

[44] M. J. A. Schuetz, B. Vermersch, G. Kirchmair, L. M. K. Vandersypen, J. I. Cirac, M. D. Lukin, and P. Zoller. Quantum simulation and optimization in hot quantum networks. Phys. Rev. B, 99, 241302, (2019). 10.1103/​PhysRevB.99.241302.
https:/​/​doi.org/​10.1103/​PhysRevB.99.241302

[45] T. Shi, D. E. Chang, and J. I. Cirac. Multiphoton-scattering theory and generalized master equations. Physical Review A, 92, 053834, (2015). 10.1103/​PhysRevA.92.053834.
https:/​/​doi.org/​10.1103/​PhysRevA.92.053834

[46] M. A. Sillanpää, J. I. Park, and R. W. Simmonds. Coherent quantum state storage and transfer between two phase qubits via a resonant cavity. Nature, 449, 438–442, (2007). 10.1038/​nature06124.
https:/​/​doi.org/​10.1038/​nature06124

[47] A. Lemmer, A. Bermudez, and M. B. Plenio. Driven geometric phase gates with trapped ions. New Journal of Physics, 15, 083001, (2013). 10.1088/​1367-2630/​15/​8/​083001.
https:/​/​doi.org/​10.1088/​1367-2630/​15/​8/​083001

[48] S. Debnath, N. M. Linke, S. T. Wang, C. Figgatt, K. A. Landsman, L. M. Duan, and C. Monroe. Observation of Hopping and Blockade of Bosons in a Trapped Ion Spin Chain. Physical Review Letters, 120, 73001, (2018). 10.1103/​PhysRevLett.120.073001.
https:/​/​doi.org/​10.1103/​PhysRevLett.120.073001

[49] K. Mølmer and A. Sørensen. Multiparticle Entanglement of Hot Trapped Ions. Physical Review Letters, 82, 1835–1838, (1999). 10.1103/​PhysRevLett.82.1835.
https:/​/​doi.org/​10.1103/​PhysRevLett.82.1835

[50] D. Porras and J. I. Cirac. Effective Quantum Spin Systems with Trapped Ions. Phys. Rev. Lett., 92, 207901, (2004). 10.1103/​PhysRevLett.92.207901.
https:/​/​doi.org/​10.1103/​PhysRevLett.92.207901

[51] J. Majer, J. M. Chow, J. M. Gambetta, J. Koch, B. R. Johnson, J. A. Schreier, L. Frunzio, D. I. Schuster, A. A. Houck, A. Wallraff, A. Blais, M. H. Devoret, S. M. Girvin, and R. J. Schoelkopf. Coupling superconducting qubits via a cavity bus. Nature, 449, 443–447, (2007). 10.1038/​nature06184.
https:/​/​doi.org/​10.1038/​nature06184

[52] J. S. Douglas, H. Habibian, C. L. Hung, A. V. Gorshkov, H. J. Kimble, and D. E. Chang. Quantum many-body models with cold atoms coupled to photonic crystals. Nature Photonics, 9, 326–331, (2015). 10.1038/​nphoton.2015.57.
https:/​/​doi.org/​10.1038/​nphoton.2015.57

[53] C. A. Sackett, D. Kielpinski, B. E. King, C. Langer, V. Meyer, C. J. Myatt, M. Rowe, Q. A. Turchette, W. M. Itano, D. J. Wineland, and C. Monroe. Experimental entanglement of four particles. Nature, 404, 256–259, (2000). 10.1038/​35005011.
https:/​/​doi.org/​10.1038/​35005011

[54] N. Friis, O. Marty, C. Maier, C. Hempel, M. Holzäpfel, P. Jurcevic, M. B. Plenio, M. Huber, C. Roos, R. Blatt, and B. Lanyon. Observation of Entangled States of a Fully Controlled 20-Qubit System. Phys. Rev. X, 8, 021012, (2018). 10.1103/​PhysRevX.8.021012.
https:/​/​doi.org/​10.1103/​PhysRevX.8.021012

[55] I. M. Georgescu, S. Ashhab, and F. Nori. Quantum simulation. Reviews of Modern Physics, 86, 153–185, (2014). 10.1103/​RevModPhys.86.153.
https:/​/​doi.org/​10.1103/​RevModPhys.86.153

[56] U. Schollwöck. The density-matrix renormalization group in the age of matrix product states. Annals of Physics, 326, 96–192, (2011). 10.1016/​j.aop.2010.09.012.
https:/​/​doi.org/​10.1016/​j.aop.2010.09.012

[57] R. Orús. A practical introduction to tensor networks: Matrix product states and projected entangled pair states. Annals of Physics, 349, 117–158, (2014). 10.1016/​j.aop.2014.06.013.
https:/​/​doi.org/​10.1016/​j.aop.2014.06.013

[58] W. Huggins, P. Patel, K. B. Whaley, and E. M. Stoudenmire. Towards Quantum Machine Learning with Tensor Networks. Quantum Science and Technology, 4, 024001, (2018). 10.1088/​2058-9565/​aaea94.
https:/​/​doi.org/​10.1088/​2058-9565/​aaea94

[59] C. Schön, K. Hammerer, M. M. Wolf, J. I. Cirac, and E. Solano. Sequential generation of matrix-product states in cavity QED. Phys. Rev. A, 75, 032311, (2007). 10.1103/​PhysRevA.75.032311.
https:/​/​doi.org/​10.1103/​PhysRevA.75.032311

[60] S.-J. Ran. Efficient Encoding of Matrix Product States into Quantum Circuits of One-and Two-Qubit Gates. arXiv preprint arXiv:1908.07958, (2019). 10.1103/​PhysRevA.101.032310.
https:/​/​doi.org/​10.1103/​PhysRevA.101.032310
arXiv:1908.07958

[61] J.-G. Liu, Y.-H. Zhang, Y. Wan, and L. Wang. Variational quantum eigensolver with fewer qubits. Phys. Rev. Research, 1, 023025, (2019). 10.1103/​PhysRevResearch.1.023025.
https:/​/​doi.org/​10.1103/​PhysRevResearch.1.023025

[62] C. Roos, T. Zeiger, H. Rohde, H. C. Nägerl, J. Eschner, D. Leibfried, F. Schmidt-Kaler, and R. Blatt. Quantum State Engineering on an Optical Transition and Decoherence in a Paul Trap. Phys. Rev. Lett., 83, 4713–4716, (1999). 10.1103/​PhysRevLett.83.4713.
https:/​/​doi.org/​10.1103/​PhysRevLett.83.4713

[63] V. M. Schäfer, C. J. Ballance, K. Thirumalai, L. J. Stephenson, T. G. Ballance, A. M. Steane, and D. M. Lucas. Fast quantum logic gates with trapped-ion qubits. Nature, 555, 75–78, (2018). 10.1038/​nature25737.
https:/​/​doi.org/​10.1038/​nature25737

[64] V. S. Borkar, V. R. Dwaracherla, and N. Sahasrabudhe. Gradient Estimation with Simultaneous Perturbation and Compressive Sensing. Journal of Machine Learning Research, 18, 1–27, (2015).

[65] L. Prashanth, S. Bhatnagar, M. Fu, and S. Marcus. Adaptive system optimization using random directions stochastic approximation. IEEE Transactions on Automatic Control, 62, 2223–2238, (2016). 10.1109/​TAC.2016.2600643.
https:/​/​doi.org/​10.1109/​TAC.2016.2600643

[66] Z. Leng, P. Mundada, S. Ghadimi, and A. Houck. Robust and efficient algorithms for high-dimensional black-box quantum optimization. arXiv preprint arXiv:1910.03591, (2019).
arXiv:1910.03591

[67] P. Nicholas. A dividing rectangles algorithm for stochastic simulation optimization. In Proc. INFORMS Comput. Soc. Conf., volume 14, pages 47–61, (2014). 10.1287/​ics.2015.0004.
https:/​/​doi.org/​10.1287/​ics.2015.0004

[68] H. Liu, S. Xu, X. Wang, J. Wu, and Y. Song. A global optimization algorithm for simulation-based problems via the extended DIRECT scheme. Engineering Optimization, 47, 1441–1458, (2015). 10.1080/​0305215X.2014.971777.
https:/​/​doi.org/​10.1080/​0305215X.2014.971777

[69] S. R. White. Density matrix formulation for quantum renormalization groups. Phys. Rev. Lett., 69, 2863–2866, (1992). 10.1103/​PhysRevLett.69.2863.
https:/​/​doi.org/​10.1103/​PhysRevLett.69.2863

[70] R. Bowler, J. Gaebler, Y. Lin, T. R. Tan, D. Hanneke, J. D. Jost, J. P. Home, D. Leibfried, and D. J. Wineland. Coherent Diabatic Ion Transport and Separation in a Multi-Zone Trap Array. Physical Review Letters, 109, 1–4, (2012). 10.1103/​PhysRevLett.109.080502.
https:/​/​doi.org/​10.1103/​PhysRevLett.109.080502

[71] T. A. Baart, T. Fujita, C. Reichl, W. Wegscheider, and L. M. K. Vandersypen. Coherent spin-exchange via a quantum mediator. Nature Nanotechnology, 12, 26–30, (2017). 10.1038/​nnano.2016.188.
https:/​/​doi.org/​10.1038/​nnano.2016.188

[72] P. Lodahl, S. Mahmoodian, S. Stobbe, P. Schneeweiss, J. Volz, A. Rauschenbeutel, H. Pichler, and P. Zoller. Chiral Quantum Optics. Nature, 541, 473–480, (2016). 10.1038/​nature21037.
https:/​/​doi.org/​10.1038/​nature21037

[73] M. P. Zaletel and F. Pollmann. Isometric Tensor Network States in Two Dimensions. arXiv preprint arXiv:1902.05100, (2019). 10.1103/​PhysRevLett.124.037201.
https:/​/​doi.org/​10.1103/​PhysRevLett.124.037201
arXiv:1902.05100

[74] R. Haghshenas, M. J. O'Rourke, and G. K.-L. Chan. Conversion of projected entangled pair states into a canonical form. Phys. Rev. B, 100, 054404, (2019). 10.1103/​PhysRevB.100.054404.
https:/​/​doi.org/​10.1103/​PhysRevB.100.054404

[75] A. Rivas and S. F. Huelga. Open quantum systems. Springer, (2012). 10.1007/​978-3-642-23354-8.
https:/​/​doi.org/​10.1007/​978-3-642-23354-8

[76] P. W. Shor. Scheme for reducing decoherence in quantum computer memory. Phys. Rev. A, 52, R2493–R2496, (1995). 10.1103/​PhysRevA.52.R2493.
https:/​/​doi.org/​10.1103/​PhysRevA.52.R2493

[77] F. Reiter, A. S. Sørensen, P. Zoller, and C. A. Muschik. Dissipative quantum error correction and application to quantum sensing with trapped ions. Nature Communications, 8, 1822, (2017). 10.1038/​s41467-017-01895-5.
https:/​/​doi.org/​10.1038/​s41467-017-01895-5

[78] D. J. Wales and J. P. Doye. Global optimization by basin-hopping and the lowest energy structures of Lennard-Jones clusters containing up to 110 atoms. The Journal of Physical Chemistry A, 101, 5111–5116, (1997). 10.1021/​jp970984n.
https:/​/​doi.org/​10.1021/​jp970984n

[79] B. Olson, I. Hashmi, K. Molloy, and A. Shehu. Basin hopping as a general and versatile optimization framework for the characterization of biological macromolecules. Advances in Artificial Intelligence, 2012, 3, (2012). 10.1155/​2012/​674832.
https:/​/​doi.org/​10.1155/​2012/​674832

[80] C. G. Broyden. The convergence of a class of double-rank minimization algorithms 1. general considerations. IMA Journal of Applied Mathematics, 6, 76–90, (1970). doi.org/​10.1093/​imamat/​6.1.76.
https:/​/​doi.org/​doi.org/​10.1093/​imamat/​6.1.76

[81] R. Fletcher. A new approach to variable metric algorithms. The computer journal, 13, 317–322, (1970). 10.1093/​comjnl/​13.3.317.
https:/​/​doi.org/​10.1093/​comjnl/​13.3.317

[82] D. Goldfarb. A family of variable-metric methods derived by variational means. Mathematics of computation, 24, 23–26, (1970). 10.1090/​S0025-5718-1970-0258249-6.
https:/​/​doi.org/​10.1090/​S0025-5718-1970-0258249-6

[83] D. F. Shanno. Conditioning of quasi-Newton methods for function minimization. Mathematics of computation, 24, 647–656, (1970). 10.1090/​S0025-5718-1970-0274029-X.
https:/​/​doi.org/​10.1090/​S0025-5718-1970-0274029-X

[84] J. I. Colless, V. V. Ramasesh, D. Dahlen, M. S. Blok, M. E. Kimchi-Schwartz, J. R. McClean, J. Carter, W. A. De Jong, and I. Siddiqi. Computation of Molecular Spectra on a Quantum Processor with an Error-Resilient Algorithm. Physical Review X, 8, 11021, (2018). 10.1103/​PhysRevX.8.011021.
https:/​/​doi.org/​10.1103/​PhysRevX.8.011021

Cited by

[1] Tyler Volkoff and Patrick J. Coles, "Large gradients via correlation in random parameterized quantum circuits", arXiv:2005.12200.

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