Quantum simulations of materials on near-term quantum computers
Source abstract
Abstract
Abstract Quantum computers hold promise to enable efficient simulations of the properties of molecules and materials; however, at present they only permit ab initio calculations of a few atoms, due to a limited number of qubits. In order to harness the power of near-term quantum computers for simulations of larger systems, it is desirable to develop hybrid quantum-classical methods where the quantum computation is restricted to a small portion of the system. This is of particular relevance for molecules and solids where an active region requires a higher level of theoretical accuracy than its environment. Here, we present a quantum embedding theory for the calculation of strongly-correlated electronic states of active regions, with the rest of the system described within density functional theory. We demonstrate the accuracy and effectiveness of the approach by investigating several defect quantum bits in semiconductors that are of great interest for quantum information technologies. We perform calculations on quantum computers and show that they yield results in agreement with those obtained with exact diagonalization on classical architectures, paving the way to simulations of realistic materials on near-term quantum computers.
Source: crossref · Quality: baseline
Research context
OpenAlex topics: Quantum Computing Algorithms and Architecture · Quantum and electron transport phenomena · Quantum-Dot Cellular Automata
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
References (87)
Show source-provided references
1. Cohen, A. J., Mori-Sánchez, P. & Yang, W. Insights into current limitations of density functional theory. Science 321, 792–794 (2008).10.1126/science.1158722 ↗
2. Su, N. Q., Li, C. & Yang, W. Describing strong correlation with fractional-spin correction in density functional theory. Proc. Natl Acad. Sci. USA. 115, 9678–9683 (2018).10.1073/pnas.1807095115 ↗
3. Georges, A., Kotliar, G., Krauth, W. & Rozenberg, M. J. Dynamical mean-field theory of strongly correlated fermion systems and the limit of infinite dimensions. Rev. Mod. Phys. 68, 13–125 (1996).10.1103/RevModPhys.68.13 ↗
4. Kotliar, G. et al. Electronic structure calculations with dynamical mean-field theory. Rev. Mod. Phys. 78, 865–951 (2006).10.1103/RevModPhys.78.865 ↗
5. Ceperley, D. & Alder, B. Quantum monte carlo. Science 231, 555–560 (1986).10.1126/science.231.4738.555 ↗
6. Wagner, L. K. & Ceperley, D. M. Discovering correlated fermions using quantum monte carlo. Rep. Prog. Phys. 79, 094501 (2016).10.1088/0034-4885/79/9/094501 ↗
7. Sun, Q. et al. Py SCF: the python-based simulations of chemistry framework. Wiley Interdiscip. Rev.: Comput. Mol. Sci. 8, e1340 (2017).
8. Aspuru-Guzik, A. Simulated quantum computation of molecular energies. Science 309, 1704–1707 (2005).10.1126/science.1113479 ↗
9. Bravyi, S., Gambetta, J. M., Mezzacapo, A. & Temme, K. Tapering off qubits to simulate fermionic hamiltonians. Preprint at https://arxiv.org/abs/1701.08213 (2017).
10. Babbush, R. et al. Low-depth quantum simulation of materials. Phys. Rev. X 8, 011044 (2018).
11. Kivlichan, I. D. et al. Quantum simulation of electronic structure with linear depth and connectivity. Phys. Rev. Lett. 120, 110501 (2018).10.1103/PhysRevLett.120.110501 ↗
12. Motta, M. et al. Determining eigenstates and thermal states on a quantum computer using quantum imaginary time evolution. Nat. Phys. 16, 205–210 (2020).10.1038/s41567-019-0704-4 ↗
13. Ollitrault, P. J. et al. Quantum equation of motion for computing molecular excitation energies on a noisy quantum processor. Preprint at https://arxiv.org/abs/1910.12890 (2019).
14. Cao, Y. et al. Quantum chemistry in the age of quantum computing. Chem. Rev. 119, 10856–10915 (2019).10.1021/acs.chemrev.8b00803 ↗
15. Smart, S. E. & Mazziotti, D. A. Quantum-classical hybrid algorithm using an error-mitigating n-representability condition to compute the mott metal-insulator transition. Phys. Rev. A 100, 022517 (2019).10.1103/PhysRevA.100.022517 ↗
16. Smart, S. E., Schuster, D. I. & Mazziotti, D. A. Experimental data from a quantum computer verifies the generalized pauli exclusion principle. Commun. Phys. 2, 1–6 (2019).10.1038/s42005-019-0110-3 ↗
17. Bauer, B., Bravyi, S., Motta, M. & Chan, G. K.-L. Quantum algorithms for quantum chemistry and quantum materials science. Preprint at https://arxiv.org/abs/2001.03685 (2020).
18. Preskill, J. Quantum Computing in the NISQ era and beyond. Quantum 2, 79 (2018).10.22331/q-2018-08-06-79 ↗
19. Rubin, N. C. A hybrid classical/quantum approach for large-scale studies of quantum systems with density matrix embedding theory. Preprint at https://arxiv.org/abs/1610.06910 (2016).
20. Yamazaki, T., Matsuura, S., Narimani, A., Saidmuradov, A. & Zaribafiyan, A. Towards the practical application of near-term quantum computers in quantum chemistry simulations: a problem decomposition approach. Preprint at https://arxiv.org/abs/1806.01305 (2018).
21. Bauer, B., Wecker, D., Millis, A. J., Hastings, M. B. & Troyer, M. Hybrid quantum-classical approach to correlated materials. Phys. Rev. X 6, 031045 (2016).
22. Kreula, J. M. et al. Few-qubit quantum-classical simulation of strongly correlated lattice fermions. EPJ Quantum Technol. 3, 1–19 (2016).10.1140/epjqt/s40507-016-0049-1 ↗
23. Rungger, I. et al. Dynamical mean field theory algorithm and experiment on quantum computers. Preprint at arXiv: https://arxiv.org/abs/1910.04735 (2019).
24. Davies, G. & Hamer, M. F. Optical studies of the 1.945 eV vibronic band in diamond. Proc. R. Soc. A348, 285–298 (1976).10.1098/rspa.1976.0039 ↗
25. Rogers, L. J., Armstrong, S., Sellars, M. J. & Manson, N. B. Infrared emission of the NV centre in diamond: Zeeman and uniaxial stress studies. N. J. Phys. 10, 103024 (2008).10.1088/1367-2630/10/10/103024 ↗
26. Doherty, M. W., Manson, N. B., Delaney, P. & Hollenberg, L. C. L. The negatively charged nitrogen-vacancy centre in diamond: the electronic solution. N. J. Phys. 13, 025019 (2011).10.1088/1367-2630/13/2/025019 ↗
27. Maze, J. R. et al. Properties of nitrogen-vacancy centers in diamond: the group theoretic approach. N. J. Phys. 13, 025025 (2011).10.1088/1367-2630/13/2/025025 ↗
28. Choi, S., Jain, M. & Louie, S. G. Mechanism for optical initialization of spin in NV-center in diamond. Phys. Rev. B 86, 041202 (2012).10.1103/PhysRevB.86.041202 ↗
29. Doherty, M. W. et al. The nitrogen-vacancy colour centre in diamond. Phys. Rep. 528, 1–45 (2013).10.1016/j.physrep.2013.02.001 ↗
30. Goldman, M. L. et al. State-selective intersystem crossing in nitrogen-vacancy centers. Phys. Rev. B 91, 165201 (2015).10.1103/PhysRevB.91.165201 ↗
31. D’Haenens-Johansson, U. F. S. et al. Optical properties of the neutral silicon split-vacancy center in diamond. Phys. Rev. B 84, 245208 (2011).10.1103/PhysRevB.84.245208 ↗
32. Gali, A. & Maze, J. R. Ab initio study of the split silicon-vacancy defect in diamond: Electronic structure and related properties. Phys. Rev. B 88, 235205 (2013).10.1103/PhysRevB.88.235205 ↗
33. Green, B. L. et al. Neutral silicon-vacancy center in diamond: Spin polarization and lifetimes. Phys. Rev. Lett. 119, 096402 (2017).10.1103/PhysRevLett.119.096402 ↗
34. Rose, B. C. et al. Observation of an environmentally insensitive solid-state spin defect in diamond. Science 361, 60–63 (2018).10.1126/science.aao0290 ↗
35. Green, B. L. et al. Electronic structure of the neutral silicon-vacancy center in diamond. Phys. Rev. B 99, 161112 (2019).10.1103/PhysRevB.99.161112 ↗
36. Thiering, G. & Gali, A. The (eg ⊗ eu) ⊗ eg product jahn–teller effect in the neutral group-IV vacancy quantum bits in diamond. npj Comput. Mater. 5, 18 (2019).10.1038/s41524-019-0158-3 ↗
37. Son, N. T. et al. Photoluminescence and zeeman effect in chromium-doped 4h and 6h SiC. J. Appl. Phys. 86, 4348–4353 (1999).10.1063/1.371368 ↗
38. Koehl, W. F. et al. Resonant optical spectroscopy and coherent control of Cr4+ spin ensembles in sic and gan. Phys. Rev. B 95, 035207 (2017).10.1103/PhysRevB.95.035207 ↗
39. Diler, B. et al. Coherent control and high-fidelity readout of chromium ions in commercial silicon carbide. npj Quantum Inf. 6, 11 (2020).10.1038/s41534-020-0247-7 ↗
40. Weber, J. R. et al. Quantum computing with defects. Proc. Natl Acad. Sci. USA. 107, 8513–8518 (2010).10.1073/pnas.1003052107 ↗
41. Seo, H., Govoni, M. & Galli, G. Design of defect spins in piezoelectric aluminum nitride for solid-state hybrid quantum technologies. Sci. Rep. 6, 20803 (2016).
42. Seo, H., Ma, H., Govoni, M. & Galli, G. Designing defect-based qubit candidates in wide-gap binary semiconductors for solid-state quantum technologies. Phys. Rev. Mater. 1, 075002 (2017).10.1103/PhysRevMaterials.1.075002 ↗
43. Ivády, V., Abrikosov, I. A. & Gali, A. First principles calculation of spin-related quantities for point defect qubit research. npj Comput. Mater. 4, 76 (2018).10.1038/s41524-018-0132-5 ↗
44. Dreyer, C. E., Alkauskas, A., Lyons, J. L., Janotti, A. & Van de Walle, C. G. First-principles calculations of point defects for quantum technologies. Annu. Rev. Mater. Res. 48, 1–26 (2018).10.1146/annurev-matsci-070317-124453 ↗
45. Anderson, C. P. et al. Electrical and optical control of single spins integrated in scalable semiconductor devices. Science 366, 1225–1230 (2019).10.1126/science.aax9406 ↗
46. Abraham, H. et al. Qiskit: an open-source framework for quantum computing. Zenodo. https://doi.org/10.5281/zenodo.2562111 (2019).10.5281/zenodo.2562111 ↗
47. 5-qubit backend: IBM Q team, \IBM Q 5 Yorktown backend speci cation V1.1.0". https://quantum-computing.ibm.com (2018).
48. Abrams, D. S. & Lloyd, S. Simulation of many-body fermi systems on a universal quantum computer. Phys. Rev. Lett. 79, 2586 (1997).10.1103/PhysRevLett.79.2586 ↗
49. Peruzzo, A. et al. A variational eigenvalue solver on a photonic quantum processor. Nat. Commun. 5, 4213 (2014).10.1038/ncomms5213 ↗
50. McClean, J. R., Romero, J., Babbush, R. & Aspuru-Guzik, A. The theory of variational hybrid quantum-classical algorithms. N. J. Phys. 18, 023023 (2016).10.1088/1367-2630/18/2/023023 ↗
51. Kandala, A. et al. Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549, 242–246 (2017).10.1038/nature23879 ↗
52. Sun, Q. & Chan, G. K.-L. Quantum embedding theories. Acc. Chem. Res. 49, 2705–2712 (2016).10.1021/acs.accounts.6b00356 ↗
53. Huang, C., Pavone, M. & Carter, E. A. Quantum mechanical embedding theory based on a unique embedding potential. J. Chem. Phys. 134, 154110 (2011).10.1063/1.3577516 ↗
54. Goodpaster, J. D., Barnes, T. A., Manby, F. R. & Miller, T. F. Accurate and systematically improvable density functional theory embedding for correlated wavefunctions. J. Chem. Phys. 140, 18A507 (2014).10.1063/1.4864040 ↗
55. Jacob, C. R. & Neugebauer, J. Subsystem density-functional theory. Wiley Interdiscip. Rev.: Comput. Mol. Sci. 4, 325–362 (2014).
56. Genova, A., Ceresoli, D. & Pavanello, M. Periodic subsystem density-functional theory. J. Chem. Phys. 141, 174101 (2014).10.1063/1.4897559 ↗
57. Wen, X., Graham, D. S., Chulhai, D. V. & Goodpaster, J. D. Absolutely localized projection-based embedding for excited states. J. Chem. Theory Comput. 16, 385–398 (2020).10.1021/acs.jctc.9b00959 ↗
58. Knizia, G. & Chan, G. K.-L. Density matrix embedding: a simple alternative to dynamical mean-field theory. Phys. Rev. Lett. 109, 186404 (2012).10.1103/PhysRevLett.109.186404 ↗
59. Wouters, S., Jiménez-Hoyos, C. A., Sun, Q. & Chan, G. K.-L. A practical guide to density matrix embedding theory in quantum chemistry. J. Chem. Theory Comput. 12, 2706–2719 (2016).10.1021/acs.jctc.6b00316 ↗
60. Pham, H. Q., Hermes, M. R. & Gagliardi, L. Periodic electronic structure calculations with density matrix embedding theory. J. Chem. Theory Comput. 16, 130–140 (2020).10.1021/acs.jctc.9b00939 ↗
61. Lan, T. N., Kananenka, A. A. & Zgid, D. Rigorous ab initio quantum embedding for quantum chemistry using green’s function theory: screened interaction, nonlocal self-energy relaxation, orbital basis, and chemical accuracy. J. Chem. Theory Comput. 12, 4856–4870 (2016).10.1021/acs.jctc.6b00638 ↗
62. Dvorak, M. & Rinke, P. Dynamical configuration interaction: Quantum embedding that combines wave functions and green’s functions. Phys. Rev. B 99, 115134 (2019).10.1103/PhysRevB.99.115134 ↗
63. Zhu, T., Cui, Z.-H. & Chan, G. K.-L. Efficient formulation of ab initio quantum embedding in periodic systems: Dynamical mean-field theory. J. Chem. Theory Comput. 16, 141–153 (2019).10.1021/acs.jctc.9b00934 ↗
64. Cui, Z.-H., Zhu, T. & Chan, G. K.-L. Efficient implementation of ab initio quantum embedding in periodic systems: Density matrix embedding theory. J. Chem. Theory Comput. 16, 119–129 (2019).10.1021/acs.jctc.9b00933 ↗
65. Aryasetiawan, F. et al. Frequency-dependent local interactions and low-energy effective models from electronic structure calculations. Phys. Rev. B 70, 195104 (2004).10.1103/PhysRevB.70.195104 ↗
66. Miyake, T., Aryasetiawan, F. & Imada, M. Ab initio procedure for constructing effective models of correlated materials with entangled band structure. Phys. Rev. B 80, 155134 (2009).10.1103/PhysRevB.80.155134 ↗
67. Hirayama, M., Miyake, T., Imada, M. & Biermann, S. Low-energy effective hamiltonians for correlated electron systems beyond density functional theory. Phys. Rev. B 96, 075102 (2017).10.1103/PhysRevB.96.075102 ↗
68. Wilson, H. F., Gygi, F. & Galli, G. Efficient iterative method for calculations of dielectric matrices. Phys. Rev. B 78, 113303 (2008).10.1103/PhysRevB.78.113303 ↗
69. Govoni, M. & Galli, G. Large scale GW calculations. J. Chem. Theory Comput. 11, 2680–2696 (2015).10.1021/ct500958p ↗
70. Ma, H., Govoni, M., Gygi, F. & Galli, G. A finite-field approach for GW calculations beyond the random phase approximation. J. Chem. Theory Comput. 15, 154–164 (2018).10.1021/acs.jctc.8b00864 ↗
71. Nguyen, N. L., Ma, H., Govoni, M., Gygi, F. & Galli, G. Finite-field approach to solving the bethe-salpeter equation. Phys. Rev. Lett. 122, 237402 (2019).10.1103/PhysRevLett.122.237402 ↗
72. Bockstedte, M., Schütz, F., Garratt, T., Ivády, V. & Gali, A. Ab initio description of highly correlated states in defects for realizing quantum bits. npj Quantum Mater. 3, 31 (2018).10.1038/s41535-018-0103-6 ↗
73. Skone, J. H., Govoni, M. & Galli, G. Self-consistent hybrid functional for condensed systems. Phys. Rev. B 89, 195112 (2014).10.1103/PhysRevB.89.195112 ↗
74. Heitz, R. et al. Identification of the 1.19-eV luminescence in hexagonal GaN. Phys. Rev. B 52, 16508–16515 (1995).10.1103/PhysRevB.52.16508 ↗
75. Anisimov, V. I., Aryasetiawan, F. & Lichtenstein, A. First-principles calculations of the electronic structure and spectra of strongly correlated systems: the lda+ u method. J. Phys. Condens. Matter 9, 767 (1997).10.1088/0953-8984/9/4/002 ↗
76. Kandala, A. et al. Error mitigation extends the computational reach of a noisy quantum processor. Nature 567, 491 (2019).10.1038/s41586-019-1040-7 ↗
77. Giannozzi, P. et al. QUANTUM ESPRESSO: a modular and open-source software project for quantum simulations of materials. J. Phys. Condens. Matter 21, 395502 (2009).10.1088/0953-8984/21/39/395502 ↗
78. Schlipf, M. & Gygi, F. Optimization algorithm for the generation of ONCV pseudopotentials. Comput. Phys. Commun. 196, 36–44 (2015).10.1016/j.cpc.2015.05.011 ↗
79. Perdew, J. P., Burke, K. & Ernzerhof, M. Generalized gradient approximation made simple. Phys. Rev. Lett. 77, 3865–3868 (1996).10.1103/PhysRevLett.77.3865 ↗
80. Pham, T. A. et al. Electronic structure of aqueous solutions: bridging the gap between theory and experiments. Sci. Adv. 3, e1603210 (2017).10.1126/sciadv.1603210 ↗
81. Smart, T. J., Wu, F., Govoni, M. & Ping, Y. Fundamental principles for calculating charged defect ionization energies in ultrathin two-dimensional materials. Phys. Rev. Mater. 2, 124002 (2018).10.1103/PhysRevMaterials.2.124002 ↗
82. Gerosa, M., Gygi, F., Govoni, M. & Galli, G. The role of defects and excess surface charges at finite temperature for optimizing oxide photoabsorbers. Nat. Mater. 17, 1122–1127 (2018).10.1038/s41563-018-0192-4 ↗
83. Gygi, F. Architecture of qbox: a scalable first-principles molecular dynamics code. IBM J. Res. Dev. 52, 137–144 (2008).10.1147/rd.521.0137 ↗
84. Knowles, P. & Handy, N. A new determinant-based full configuration interaction method. Chem. Phys. Lett. 111, 315–321 (1984).10.1016/0009-2614(84)85513-X ↗
85. Jordan, P. & Wigner, E. P. About the pauli exclusion principle. Z. Phys. 47, 631–651 (1928).10.1007/BF01331938 ↗
86. Powell, M. J. A direct search optimization method that models the objective and constraint functions by linear interpolation. In Advances in optimization and numerical analysis, 51–67 (Springer, Dordrecht, 1994).10.1007/978-94-015-8330-5_4 ↗
87. Govoni, M. et al. Qresp, a tool for curating, discovering and exploring reproducible scientific papers. Sci. Data 6, 190002 (2019).10.1038/sdata.2019.2 ↗