Skip to main content
Log in

NMR Quantum Information Processing: Indian Contributions and Perspectives

  • Review Article
  • Published:
Journal of the Indian Institute of Science Aims and scope

Abstract

Quantum processors based on NMR architectures, which use nuclear spins as qubits and radio frequency pulses to implement unitary quantum gates, came into existence nearly two decades ago. Since their first proof-of-principle demonstrations as a testbed quantum processors, NMR quantum processors have contributed significantly to advances in various subareas of quantum information processing. Indian researchers have been working in this field since its inception and have continued to contribute to novel developments. This article begins by delineating the basic building blocks of an NMR quantum processor and evaluating the advantages and disadvantages of this quantum technology. Contributions of NMR quantum information processing techniques in the areas of the state initialization and quantum control, experimental implementation of quantum algorithms, entanglement detection and characterization, foundational tests of quantum mechanics, quantum state and process tomography, noise characterization and decoherence mitigation protocols, quantum simulation, and quantum thermodynamics are described. The article traces the historical development of this area, with an emphasis on Indian contributions and perspectives.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Figure 1:
Figure 2:
Figure 3:
Figure 4:
Figure 5:
Figure 6:

Similar content being viewed by others

References

  1. Ernst RR, Bodehausen G, Wokaun A (1990) Principles of Nuclear Magnetic Resonance in One and Two Dimensions. Clarendon, Oxford OX2 8DP, UK

  2. Cory DG, Price MD, Havel TF (1998) Nuclear magnetic resonance spectroscopy: An experimentally accessible paradigm for quantum computing. Physica D 120(1):82–101. https://doi.org/10.1016/S0167-2789(98)00046-3

    Article  CAS  Google Scholar 

  3. Nielsen MA, Chuang IL (2010) Quantum Computation and Quantum Information. Cambridge University Press, Cambridge UK

    Google Scholar 

  4. Oliveira IS, Bonagamba TJ, Sarthour RS, Freitas JCC, deAzevedo ER (2007) NMR Quantum Information Processing. Elsevier, Linacre House, Jordan Hill, Oxford OX2 8DP, UK

  5. Quantum computation using NMR (2000) Dorai, K., Mahesh, T.S., Arvind, Kumar, A. Curr Sci 79:1447–1458

    Google Scholar 

  6. Vandersypen LMK, Chuang IL (2005) NMR techniques for quantum control and computation. Rev Mod Phys 76:1037–1069. https://doi.org/10.1103/RevModPhys.76.1037

    Article  Google Scholar 

  7. Ramanathan C, Boulant N, Chen Z, Cory DG, Chuang I, Steffen M (2004) NMR quantum information processing. Quantum Inf Process 3(1):15–44. https://doi.org/10.1007/s11128-004-3668-x

    Article  CAS  Google Scholar 

  8. Cory DG, Laflamme R, Knill E, Viola L, Havel TF, Boulant N, Boutis G, Fortunato E, Lloyd S, Martinez R, Negrevergne C, Pravia M, Sharf Y, Teklemariam G, Weinstein YS, Zurek WH (2000) NMR based quantum information processing: Achievements and prospects. Fortschritte der Physik 48(9–11):875–907. https://doi.org/10.1002/1521-3978(200009)48:9/11<875::AID-PROP875>3.0.CO;2-V

  9. Suter D, Mahesh TS (2008) Spins as qubits: Quantum information processing by nuclear magnetic resonance. J Chem Phys 128(5):052206. https://doi.org/10.1063/1.2838166

    Article  CAS  Google Scholar 

  10. Serra RM, Oliveira IS (2012) Nuclear magnetic resonance quantum information processing. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 370(1976):4615–4619. https://doi.org/10.1098/rsta.2012.0332

    Article  CAS  Google Scholar 

  11. Modi K, Fazio R, Pascazio S, Vedral V, Yuasa K (2012) Classical to quantum in large-number limit. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 370(1976):4810–4820. https://doi.org/10.1098/rsta.2011.0353

    Article  Google Scholar 

  12. Soares-Pinto DO, Auccaise R, Maziero J, Gavini-Viana A, Serra RM, Celeri LC (2012) On the quantumness of correlations in nuclear magnetic resonance. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 370(1976):4821–4836. https://doi.org/10.1098/rsta.2011.0364

    Article  CAS  Google Scholar 

  13. Teles J, DeAzevedo ER, Freitas JCC, Sarthour RS, Oliveira IS, Bonagamba TJ (2012) Quantum information processing by nuclear magnetic resonance on quadrupolar nuclei. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 370(1976):4770–4793. https://doi.org/10.1098/rsta.2011.0365

    Article  CAS  Google Scholar 

  14. Franzoni MB, Acosta RH, Pastawski HM, Levstein PR (2012) Storage of quantum coherences as phase-labelled local polarization in solid-state nuclear magnetic resonance. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 370(1976):4713–4733. https://doi.org/10.1098/rsta.2011.0363

    Article  CAS  Google Scholar 

  15. Schulte-Herbrüggen T, Marx R, Fahmy A, Kauffman L, Lomonaco S, Khaneja N, Glaser SJ (2012) Control aspects of quantum computing using pure and mixed states. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 370(1976):4651–4670. https://doi.org/10.1098/rsta.2011.0513

    Article  Google Scholar 

  16. Rowland B, Jones JA (2012) Implementing quantum logic gates with gradient ascent pulse engineering: principles and practicalities. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 370(1976):4636–4650. https://doi.org/10.1098/rsta.2011.0361

    Article  Google Scholar 

  17. Souza AM, Álvarez GA, Suter D (2012) Robust dynamical decoupling. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 370(1976):4748–4769. https://doi.org/10.1098/rsta.2011.0355

    Article  Google Scholar 

  18. Qiu C, Nie X, Lu D (2021) Quantum simulations with nuclear magnetic resonance system. Chin Phys B 30(4):048201. https://doi.org/10.1088/1674-1056/abe299

    Article  CAS  Google Scholar 

  19. Rong X, Lu D, Kong X, Geng J, Wang Y, Shi F, Duan C-K, Du J (2017) Harnessing the power of quantum systems based on spin magnetic resonance: from ensembles to single spins. Advances in Physics: X 2(1):125–168. https://doi.org/10.1080/23746149.2016.1266914

    Article  CAS  Google Scholar 

  20. Lu D, Xu B, Xu N, Li Z, Chen H, Peng X, Xu R, Du J (2012) Quantum chemistry simulation on quantum computers: theories and experiments. Phys Chem Chem Phys 14:9411–9420. https://doi.org/10.1039/C2CP23700H

    Article  CAS  Google Scholar 

  21. Lu D, Xu N, Xu B, Li Z, Chen H, Peng X, Xu R, Du J (2012) Experimental study of quantum simulation for quantum chemistry with a nuclear magnetic resonance simulator. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 370(1976):4734–4747. https://doi.org/10.1098/rsta.2011.0360

    Article  CAS  Google Scholar 

  22. Criger B, Passante G, Park D, Laflamme R (2012) Recent advances in nuclear magnetic resonance quantum information processing. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 370(1976):4620–4635. https://doi.org/10.1098/rsta.2011.0352

    Article  CAS  Google Scholar 

  23. Xin T, Wang B-X, Li K-R, Kong X-Y, Wei S-J, Wang T, Ruan D, Long G-L (2018) Nuclear magnetic resonance for quantum computing: Techniques and recent achievements. Chin Phys B 27(2):020308. https://doi.org/10.1088/1674-1056/27/2/020308

    Article  Google Scholar 

  24. Mahesh TS (2015) Quantum information processing by NMR. Resonance 20(11):1053–1065. https://doi.org/10.1007/s12045-015-0273-5

    Article  CAS  Google Scholar 

  25. Dorai K, Arvind Kumar A (2000) Implementing quantum-logic operations, pseudopure states, and the Deutsch-Jozsa algorithm using noncommuting selective pulses in NMR. Phys. Rev. A 61, 042306. https://doi.org/10.1103/PhysRevA.61.042306

  26. Mahesh TS, Dorai K, Arvind Kumar A (2001) Implementing logic gates and the Deutsch-Jozsa quantum algorithm by two-dimensional NMR using spin- and transition-selective pulses. Journal of Magnetic Resonance 148(1), 95–103. https://doi.org/10.1006/jmre.2000.2225

  27. Mahesh TS, Kumar A (2001) Ensemble quantum-information processing by NMR: Spatially averaged logical labeling technique for creating pseudopure states. Phys Rev A 64:012307. https://doi.org/10.1103/PhysRevA.64.012307

    Article  CAS  Google Scholar 

  28. Sinha N, Mahesh TS, Ramanathan KV, Kumar A (2001) Toward quantum information processing by nuclear magnetic resonance: Pseudopure states and logical operations using selective pulses on an oriented spin 3/2 nucleus. J Chem Phys 114(10):4415–4420. https://doi.org/10.1063/1.1346645

    Article  CAS  Google Scholar 

  29. Das R, Mahesh TS, Kumar A (2002) Implementation of conditional phase-shift gate for quantum information processing by NMR, using transition-selective pulses. J Magn Reson 159(1):46–54. https://doi.org/10.1016/S1090-7807(02)00009-5

    Article  CAS  Google Scholar 

  30. Mahesh TS, Sinha N, Ramanathan KV, Kumar A (2002) Ensemble quantum-information processing by NMR: Implementation of gates and the creation of pseudopure states using dipolar coupled spins as qubits. Phys Rev A 65:022312. https://doi.org/10.1103/PhysRevA.65.022312

    Article  CAS  Google Scholar 

  31. Kumar A, Ramanathan KV, Mahesh TS, Sinha N, Murali KVRM (2002) Developments in quantum information processing by nuclear magnetic resonance: Use of quadrupolar and dipolar couplings. Pramana 59(2):243–254. https://doi.org/10.1007/s12043-002-0114-4

    Article  CAS  Google Scholar 

  32. Mahesh TS, Sinha N, Ghosh A, Das R, Suryaprakash N, Levitt MH, Ramanathan KV, Kumar A (2003) Quantum information processing by NMR using strongly coupled spins. Curr Sci 85(7):932–944

    CAS  Google Scholar 

  33. Das R, Mitra A, Kumar SV, Kumar A (2003) Quantum information processing by NMR: Preparation of pseudopure states and implementation of unitary operations in a single qutrit system. Int. J. Quantum Inf. 01(03):387–394. https://doi.org/10.1142/S0219749903000292

    Article  Google Scholar 

  34. Murali KVRM, Sinha N, Mahesh TS, Levitt MH, Ramanathan KV, Kumar A (2002) Quantum-information processing by nuclear magnetic resonance: Experimental implementation of half-adder and subtractor operations using an oriented spin-7/2 system. Phys Rev A 66:022313. https://doi.org/10.1103/PhysRevA.66.022313

    Article  CAS  Google Scholar 

  35. Das R, Kumar A (2003) Use of quadrupolar nuclei for quantum-information processing by nuclear magnetic resonance: Implementation of a quantum algorithm. Phys Rev A 68:032304. https://doi.org/10.1103/PhysRevA.68.032304

    Article  CAS  Google Scholar 

  36. Das R, Bhattacharyya R, Kumar A (2004) Quantum information processing by NMR using a 5-qubit system formed by dipolar coupled spins in an oriented molecule. J Magn Reson 170(2):310–321. https://doi.org/10.1016/j.jmr.2004.07.008

    Article  CAS  Google Scholar 

  37. Das R, Chakraborty S, Rukmani K, Kumar A (2004) Search for optimum labeling schemes in qubit systems for quantum-information processing by nuclear magnetic resonance. Phys Rev A 70:012314. https://doi.org/10.1103/PhysRevA.70.012314

    Article  CAS  Google Scholar 

  38. Dogra S, Dorai K (2018) Arvind: Majorana representation, qutrit hilbert space and NMR implementation of qutrit gates. J Phys B: At Mol Opt Phys 51(4):045505. https://doi.org/10.1088/1361-6455/aaa69f

    Article  CAS  Google Scholar 

  39. Das R, Kumar SKK, Kumar A (2005) Use of non-adiabatic geometric phase for quantum computing by NMR. J Magn Reson 177(2):318–328. https://doi.org/10.1016/j.jmr.2005.07.025

    Article  CAS  Google Scholar 

  40. Ghosh A, Kumar A (2006) Experimental measurement of mixed state geometric phase by quantum interferometry using NMR. Phys Lett A 349(1):27–36. https://doi.org/10.1016/j.physleta.2005.08.092

    Article  CAS  Google Scholar 

  41. Gopinath T, Kumar A (2006) Geometric quantum computation using fictitious spin-\(\frac{1}{2}\) subspaces of strongly dipolar coupled nuclear spins. Phys Rev A 73:022326. https://doi.org/10.1103/PhysRevA.73.022326

    Article  CAS  Google Scholar 

  42. Roy SS, Mahesh TS (2010) Initialization of NMR quantum registers using long-lived singlet states. Phys Rev A 82:052302. https://doi.org/10.1103/PhysRevA.82.052302

    Article  CAS  Google Scholar 

  43. Manu VS, Kumar A (2012) Singlet-state creation and universal quantum computation in NMR using a genetic algorithm. Phys Rev A 86:022324. https://doi.org/10.1103/PhysRevA.86.022324

    Article  CAS  Google Scholar 

  44. Devra A, Prabhu P, Singh H, Arvind Dorai K (2018) Efficient experimental design of high-fidelity three-qubit quantum gates via genetic programming. Quantum Information Processing 17(3), 1–24. https://doi.org/10.1007/s11128-018-1835-8

  45. Batra P, Krithika VR, Mahesh TS (2020) Push-pull optimization of quantum controls. Phys. Rev. Research 2:013314. https://doi.org/10.1103/PhysRevResearch.2.013314

    Article  CAS  Google Scholar 

  46. Ram MH, Krithika VR, Batra P, Mahesh TS (2022) Robust quantum control using hybrid pulse engineering. Phys Rev A 105:042437. https://doi.org/10.1103/PhysRevA.105.042437

    Article  CAS  Google Scholar 

  47. Pande VR, Bhole G, Khurana D, Mahesh TS (2017) Strong algorithmic cooling in large star-topology quantum registers. Phys Rev A 96:012330. https://doi.org/10.1103/PhysRevA.96.012330

    Article  Google Scholar 

  48. Mahesh TS, Khurana D, Krithika VR, Sreejith GJ, Kumar CSS (2021) Star-topology registers: NMR and quantum information perspectives. J Phys: Condens Matter 33(38):383002. https://doi.org/10.1088/1361-648x/ac0dd3

    Article  CAS  Google Scholar 

  49. Chakraborty T, Bhattacharya R, Anjusha VS, Nesladek M, Suter D, Mahesh TS (2022) Magnetic-field-assisted spectral decomposition and imaging of charge states of \(N\)-\(V\) centers in diamond. Phys. Rev. Applied 17:024046. https://doi.org/10.1103/PhysRevApplied.17.024046

    Article  CAS  Google Scholar 

  50. Dorai K, Arvind Kumar A (2001) Implementation of a Deutsch-like quantum algorithm utilizing entanglement at the two-qubit level on an NMR quantum-information processor. Phys. Rev. A 63, 034101. https://doi.org/10.1103/PhysRevA.63.034101

  51. Arvind Dorai K, Kumar A (2001) Quantum entanglement in the NMR implementation of the Deutsch-Jozsa algorithm. Pramana 56(5), 705–713. https://doi.org/10.1007/s12043-001-0095-8

  52. Das R, Mahesh TS, Kumar A (2003) Experimental implementation of Grover’s search algorithm using efficient quantum state tomography. Chem Phys Lett 369(1):8–15. https://doi.org/10.1016/S0009-2614(02)01895-X

    Article  CAS  Google Scholar 

  53. Das R, Kumar A (2006) Experimental implementation of a quantum algorithm in a multiqubit NMR system formed by an oriented 7/2 spin. App. Phys. Lett. 89(2), 024107. https://doi.org/10.1063/1.2218323

  54. Das R, Kumar A (2004) Spectral implementation of some quantum algorithms by one- and two-dimensional nuclear magnetic resonance. J Chem Phys 121(16):7601–7613. https://doi.org/10.1063/1.1795674

    Article  CAS  Google Scholar 

  55. Gopinath T, Das R, Kumar A (2005) Programmable quantum-state discriminator by nuclear magnetic resonance. Phys Rev A 71:042307. https://doi.org/10.1103/PhysRevA.71.042307

    Article  CAS  Google Scholar 

  56. Bhattacharyya R, Das R, Ramanathan KV, Kumar A (2005) Implementation of parallel search algorithms using spatial encoding by nuclear magnetic resonance. Phys Rev A 71:052313. https://doi.org/10.1103/PhysRevA.71.052313

    Article  CAS  Google Scholar 

  57. Gopinath T, Kumar A (2006) Hadamard NMR spectroscopy for two-dimensional quantum information processing and parallel search algorithms. J Magn Reson 183(2):259–268. https://doi.org/10.1016/j.jmr.2006.09.001

    Article  CAS  Google Scholar 

  58. Mitra A, Ghosh A, Das R, Patel A, Kumar A (2005) Experimental implementation of local adiabatic evolution algorithms by an NMR quantum information processor. J Magn Reson 177(2):285–298. https://doi.org/10.1016/j.jmr.2005.08.004

    Article  CAS  Google Scholar 

  59. Dorai K, Suter D (2005) Efficient implementations of the quantum Fourier transform: An experimental perspective. International Journal of Quantum Information 03(02):413–424. https://doi.org/10.1142/S0219749905000967

    Article  Google Scholar 

  60. Mitra A, Sivapriya K, Kumar A (2007) Experimental implementation of a three qubit quantum game with corrupt source using nuclear magnetic resonance quantum information processor. J Magn Reson 187(2):306–313. https://doi.org/10.1016/j.jmr.2007.05.013

    Article  CAS  Google Scholar 

  61. Mahesh TS, Rajendran N, Peng X, Suter D (2007) Factorizing numbers with the Gauss sum technique: NMR implementations. Phys Rev A 75:062303. https://doi.org/10.1103/PhysRevA.75.062303

    Article  CAS  Google Scholar 

  62. Gopinath T, Kumar A (2008) Implementation of controlled phase shift gates and Collins version of Deutsch-Jozsa algorithm on a quadrupolar spin-7/2 nucleus using non-adiabatic geometric phases. J Magn Reson 193(2):168–176. https://doi.org/10.1016/j.jmr.2008.04.018

    Article  CAS  Google Scholar 

  63. Mitra A, Mahesh TS, Kumar A (2008) NMR implementation of adiabatic SAT algorithm using strongly modulated pulses. J Chem Phys 128(12):124110. https://doi.org/10.1063/1.2835542

    Article  CAS  Google Scholar 

  64. Roy SS, Shukla A, Mahesh TS (2012) NMR implementation of a quantum delayed-choice experiment. Phys Rev A 85:022109. https://doi.org/10.1103/PhysRevA.85.022109

    Article  CAS  Google Scholar 

  65. Dogra S, Arvind Dorai K (2014) Determining the parity of a permutation using an experimental NMR qutrit. Physics Letters A 378(46), 3452–3456. https://doi.org/10.1016/j.physleta.2014.10.003

  66. Bhole G, Shukla A, Mahesh TS (2015) Benford analysis: A useful paradigm for spectroscopic analysis. Chem Phys Lett 639:36–40. https://doi.org/10.1016/j.cplett.2015.08.061

    Article  CAS  Google Scholar 

  67. Dogra S, Arvind Dorai K (2015) Implementation of the quantum Fourier transform on a hybrid qubit-qutrit NMR quantum emulator. International Journal of Quantum Information 13(07), 1550059. https://doi.org/10.1142/S0219749915500598

  68. Bhole G, Anjusha VS, Mahesh TS (2016) Steering quantum dynamics via bang-bang control: Implementing optimal fixed-point quantum search algorithm. Phys Rev A 93:042339. https://doi.org/10.1103/PhysRevA.93.042339

    Article  CAS  Google Scholar 

  69. Pal S, Moitra S, Anjusha VS, Kumar A, Mahesh TS (2019) Hybrid scheme for factorisation: Factoring 551 using a 3-qubit NMR quantum adiabatic processor. Pramana 92(2):26. https://doi.org/10.1007/s12043-018-1684-0

    Article  Google Scholar 

  70. Roy SS, Mahesh TS, Agarwal GS (2011) Storing entanglement of nuclear spins via Uhrig dynamical decoupling. Phys Rev A 83:062326. https://doi.org/10.1103/PhysRevA.83.062326

    Article  CAS  Google Scholar 

  71. Katiyar H, Roy SS, Mahesh TS, Patel A (2012) Evolution of quantum discord and its stability in two-qubit NMR systems. Phys Rev A 86:012309. https://doi.org/10.1103/PhysRevA.86.012309

    Article  CAS  Google Scholar 

  72. Dogra S, Dorai K (2015) Arvind: Experimental construction of generic three-qubit states and their reconstruction from two-party reduced states on an NMR quantum information processor. Phys Rev A 91:022312. https://doi.org/10.1103/PhysRevA.91.022312

    Article  CAS  Google Scholar 

  73. Das D, Dogra S, Dorai K (2015) Arvind: Experimental construction of a W superposition state and its equivalence to the Greenberger-Horne-Zeilinger state under local filtration. Phys Rev A 92:022307. https://doi.org/10.1103/PhysRevA.92.022307

    Article  CAS  Google Scholar 

  74. Singh A, Arvind Dorai K (2016) Entanglement detection on an NMR quantum-information processor using random local measurements. Phys. Rev. A 94, 062309. https://doi.org/10.1103/PhysRevA.94.062309

  75. Singh A, Arvind Dorai K (2017) Witnessing nonclassical correlations via a single-shot experiment on an ensemble of spins using nuclear magnetic resonance. Phys. Rev. A 95, 062318. https://doi.org/10.1103/PhysRevA.95.062318

  76. Singh A, Dorai K (2018) Arvind: Experimentally identifying the entanglement class of pure tripartite states. Quantum Inf Process 17(12):334. https://doi.org/10.1007/s11128-018-2105-5

    Article  Google Scholar 

  77. Singh A, Singh H, Dorai K (2018) Arvind: Experimental classification of entanglement in arbitrary three-qubit pure states on an NMR quantum information processor. Phys Rev A 98:032301. https://doi.org/10.1103/PhysRevA.98.032301

    Article  CAS  Google Scholar 

  78. Pal S, Nishad N, Mahesh TS, Sreejith GJ (2018) Temporal order in periodically driven spins in star-shaped clusters. Phys Rev Lett 120:180602. https://doi.org/10.1103/PhysRevLett.120.180602

    Article  CAS  Google Scholar 

  79. Singh H, Arvind Dorai K (2018) Evolution of tripartite entangled states in a decohering environment and their experimental protection using dynamical decoupling. Phys. Rev. A 97, 022302. https://doi.org/10.1103/PhysRevA.97.022302

  80. Singh A, Gautam A, Arvind Dorai K (2019) Experimental detection of qubit-ququart pseudo-bound entanglement using three nuclear spins. Physics Letters A 383(14), 1549–1554. https://doi.org/10.1016/j.physleta.2019.02.027

  81. Singh A, Singh D, Gulati V, Dorai K (2020) Arvind: Experimental detection of non-local correlations using a local measurement-based hierarchy on an NMR quantum processor. The European Physical Journal D 74(8):168. https://doi.org/10.1140/epjd/e2020-10173-9

    Article  CAS  Google Scholar 

  82. Gautam A, Pande VR, Singh A, Dorai K (2020) Arvind: Simulating the effect of weak measurements by a phase damping channel and determining different measures of bipartite correlations in nuclear magnetic resonance. Phys Lett A 384(30):126760. https://doi.org/10.1016/j.physleta.2020.126760

    Article  CAS  Google Scholar 

  83. Batra P, Singh A, Mahesh TS (2021) Efficient characterization of quantum evolutions via a recommender system. Quantum 5, 598. https://doi.org/10.22331/q-2021-12-06-598

  84. Pal S, Batra P, Krisnanda T, Paterek T, Mahesh TS (2021) Experimental localisation of quantum entanglement through monitored classical mediator. Quantum 5, 478. https://doi.org/10.22331/q-2021-06-17-478

  85. Sharmila B, Krithika VR, Pal S, Mahesh TS, Lakshmibala S, Balakrishnan V (2022) Tomographic entanglement indicators from NMR experiments. J Chem Phys 156(15):154102. https://doi.org/10.1063/5.0087032

    Article  CAS  Google Scholar 

  86. Gautam A, Dorai K (2022) Arvind: Experimental demonstration of the dynamics of quantum coherence evolving under a PT-symmetric hamiltonian on an NMR quantum processor. Quantum Inf Process 21(9):329. https://doi.org/10.1007/s11128-022-03669-5

    Article  Google Scholar 

  87. Gulati V, Arvind Dorai K (2022) Classification and measurement of multipartite entanglement by reconstruction of correlation tensors on an NMR quantum processor. The European Physical Journal D 76(10), 194. https://doi.org/10.1140/epjd/s10053-022-00527-y

  88. Samal JR, Gupta M, Panigrahi PK, Kumar A (2010) Non-destructive discrimination of Bell states by NMR using a single ancilla qubit. J Phys B: At Mol Opt Phys 43(9):095508. https://doi.org/10.1088/0953-4075/43/9/095508

    Article  CAS  Google Scholar 

  89. Samal JR, Pati AK, Kumar A (2011) Experimental test of the quantum no-hiding theorem. Phys Rev Lett 106:080401. https://doi.org/10.1103/PhysRevLett.106.080401

    Article  CAS  Google Scholar 

  90. Athalye V, Roy SS, Mahesh TS (2011) Investigation of the Leggett-Garg inequality for precessing nuclear spins. Phys Rev Lett 107:130402. https://doi.org/10.1103/PhysRevLett.107.130402

    Article  CAS  Google Scholar 

  91. Katiyar H, Shukla A, Rao KRK, Mahesh TS (2013) Violation of entropic Leggett-Garg inequality in nuclear spins. Phys Rev A 87:052102. https://doi.org/10.1103/PhysRevA.87.052102

    Article  CAS  Google Scholar 

  92. Karthik HS, Katiyar H, Shukla A, Mahesh TS, Devi ARU, Rajagopal AK (2013) Inversion of moments to retrieve joint probabilities in quantum sequential measurements. Phys Rev A 87:052118. https://doi.org/10.1103/PhysRevA.87.052118

    Article  CAS  Google Scholar 

  93. Dogra S, Dorai K (2016) Arvind: Experimental demonstration of quantum contextuality on an NMR qutrit. Phys Lett A 380(22):1941–1946. https://doi.org/10.1016/j.physleta.2016.04.015

    Article  CAS  Google Scholar 

  94. Katiyar H, Kumar CSS, Mahesh TS (2016) NMR investigation of contextuality in a quantum harmonic oscillator via pseudospin mapping. Europhys Lett 113(2):20003. https://doi.org/10.1209/0295-5075/113/20003

    Article  CAS  Google Scholar 

  95. Singh D, Singh J, Dorai K (2019) Arvind: Experimental demonstration of fully contextual quantum correlations on an NMR quantum information processor. Phys Rev A 100:022109. https://doi.org/10.1103/PhysRevA.100.022109

    Article  CAS  Google Scholar 

  96. Singh D, Arvind Dorai K (2022) Experimental simulation of a monogamy relation between quantum contextuality and nonlocality on an NMR quantum processor. Journal of Magnetic Resonance Open 10-11, 100058. https://doi.org/10.1016/j.jmro.2022.100058

  97. Singh D, Arvind Dorai K (2022) Experimental demonstration of the violation of the temporal Peres-Mermin inequality using contextual temporal correlations and noninvasive measurements. Phys. Rev. A 105, 022216. https://doi.org/10.1103/PhysRevA.105.022216

  98. Das R, Mahesh TS, Kumar A (2003) Efficient quantum-state tomography for quantum-information processing using a two-dimensional Fourier-transform technique. Phys Rev A 67:062304. https://doi.org/10.1103/PhysRevA.67.062304

    Article  CAS  Google Scholar 

  99. Singha Roy S, Mahesh TS (2010) Density matrix tomography of singlet states. J Magn Reson 206(1):127–133. https://doi.org/10.1016/j.jmr.2010.06.014

    Article  CAS  Google Scholar 

  100. Shukla A, Rao KRK, Mahesh TS (2013) Ancilla-assisted quantum state tomography in multiqubit registers. Phys Rev A 87:062317. https://doi.org/10.1103/PhysRevA.87.062317

    Article  CAS  Google Scholar 

  101. Sudheer Kumar CS, Shukla A, Mahesh TS (2016) Discriminating between Lüders and Von Neumann measuring devices: An NMR investigation. Phys Lett A 380(43):3612–3616. https://doi.org/10.1016/j.physleta.2016.09.004

    Article  CAS  Google Scholar 

  102. Singh H, Arvind Dorai K (2016) Constructing valid density matrices on an NMR quantum information processor via maximum likelihood estimation. Physics Letters A 380(38), 3051–3056. https://doi.org/10.1016/j.physleta.2016.07.046

  103. Shukla A, Mahesh TS (2014) Single-scan quantum process tomography. Phys Rev A 90:052301. https://doi.org/10.1103/PhysRevA.90.052301

    Article  CAS  Google Scholar 

  104. Gaikwad A, Rehal D, Singh A, Arvind Dorai K (2018) Experimental demonstration of selective quantum process tomography on an NMR quantum information processor. Phys. Rev. A 97, 022311. https://doi.org/10.1103/PhysRevA.97.022311

  105. Gaikwad A, Shende K, Arvind Dorai K (2022) Implementing efficient selective quantum process tomography of superconducting quantum gates on IBM quantum experience. Scientific Reports 12(1), 3688. https://doi.org/10.1038/s41598-022-07721-3

  106. Gaikwad A, Shende K, Dorai K (2021) Experimental demonstration of optimized quantum process tomography on the IBM quantum experience. International Journal of Quantum Information 19(07):2040004. https://doi.org/10.1142/S0219749920400043

    Article  Google Scholar 

  107. Gaikwad A, Arvind Dorai K (2021) True experimental reconstruction of quantum states and processes via convex optimization. Quantum Information Processing 20(1). https://doi.org/10.1007/s11128-020-02930-z

  108. Sudheer Kumar CS, Mahesh TS (2018) Ancilla-induced amplification of quantum Fisher information. Eur. Phys. J. Plus 133(11):460. https://doi.org/10.1140/epjp/i2018-12260-2

    Article  Google Scholar 

  109. Gaikwad A, Arvind, Dorai K (2022) Simulating open quantum dynamics on an NMR quantum processor using the Sz.-Nagy dilation algorithm. Phys. Rev. A 106, 022424. https://doi.org/10.1103/PhysRevA.106.022424

  110. Ghosh A, Kumar A (2005) Relaxation of pseudo pure states: the role of cross-correlations. J Magn Reson 173(1):125–133. https://doi.org/10.1016/j.jmr.2004.11.013

    Article  CAS  Google Scholar 

  111. Hegde SS, Mahesh TS (2014) Engineered decoherence: Characterization and suppression. Phys Rev A 89:062317. https://doi.org/10.1103/PhysRevA.89.062317

    Article  CAS  Google Scholar 

  112. Khurana D, Unnikrishnan G, Mahesh TS (2016) Spectral investigation of the noise influencing multiqubit states. Phys Rev A 94:062334. https://doi.org/10.1103/PhysRevA.94.062334

    Article  Google Scholar 

  113. Singh H, Arvind Dorai K (2020) Using a Lindbladian approach to model decoherence in two coupled nuclear spins via correlated phase damping and amplitude damping noise channels. Pramana 94(1), 160. https://doi.org/10.1007/s12043-020-02027-3

  114. Singh H, Arvind Dorai K (2014) Experimental protection against evolution of states in a subspace via a super-Zeno scheme on an NMR quantum information processor. Phys. Rev. A 90, 052329. https://doi.org/10.1103/PhysRevA.90.052329

  115. Singh H, Arvind Dorai K (2017) Experimental protection of arbitrary states in a two-qubit subspace by nested Uhrig dynamical decoupling. Phys. Rev. A 95, 052337. https://doi.org/10.1103/PhysRevA.95.052337

  116. Singh H, Arvind Dorai K (2017) Experimentally freezing quantum discord in a dephasing environment using dynamical decoupling. EPL (Europhysics Letters) 118(5), 50001. https://doi.org/10.1209/0295-5075/118/50001

  117. Khurana D, Mahesh TS (2017) Bang-bang optimal control of large spin systems: Enhancement of 13C–13C singlet-order at natural abundance. J Magn Reson 284:8–14. https://doi.org/10.1016/j.jmr.2017.09.006

    Article  CAS  Google Scholar 

  118. Khurana D, Agarwalla BK, Mahesh TS (2019) Experimental emulation of quantum non-markovian dynamics and coherence protection in the presence of information backflow. Phys Rev A 99:022107. https://doi.org/10.1103/PhysRevA.99.022107

    Article  CAS  Google Scholar 

  119. Rao KRK, Kumar A (2012) Entanglement in a 3-spin Heisenberg-XY chain with nearest-neighbor interactions, simulated in an NMR quantum simulator. Int. J. Quantum Inf. 10(04):1250039. https://doi.org/10.1142/S0219749912500396

    Article  Google Scholar 

  120. Ajoy A, Rao RK, Kumar A, Rungta P (2012) Algorithmic approach to simulate Hamiltonian dynamics and an NMR simulation of quantum state transfer. Phys Rev A 85:030303. https://doi.org/10.1103/PhysRevA.85.030303

    Article  CAS  Google Scholar 

  121. Manu VS, Kumar A (2014) Quantum simulation using fidelity-profile optimization. Phys Rev A 89:052331. https://doi.org/10.1103/PhysRevA.89.052331

    Article  CAS  Google Scholar 

  122. Hegde SS, Katiyar H, Mahesh TS, Das A (2014) Freezing a quantum magnet by repeated quantum interference: An experimental realization. Phys Rev B 90:174407. https://doi.org/10.1103/PhysRevB.90.174407

    Article  CAS  Google Scholar 

  123. Rao KRK, Katiyar H, Mahesh TS, Sen (De) A, Sen U, Kumar A (2013) Multipartite quantum correlations reveal frustration in a quantum Ising spin system. Phys. Rev. A 88, 022312. https://doi.org/10.1103/PhysRevA.88.022312

  124. Rao KRK, Mahesh TS, Kumar A (2014) Efficient simulation of unitary operators by combining two numerical algorithms: An NMR simulation of the mirror-inversion propagator of an \(XY\) spin chain. Phys Rev A 90:012306. https://doi.org/10.1103/PhysRevA.90.012306

    Article  CAS  Google Scholar 

  125. Joshi S, Shukla A, Katiyar H, Hazra A, Mahesh TS (2014) Estimating Franck-Condon factors using an NMR quantum processor. Phys Rev A 90:022303. https://doi.org/10.1103/PhysRevA.90.022303

    Article  CAS  Google Scholar 

  126. Shankar R, Hegde SS, Mahesh TS (2014) Quantum simulations of a particle in one-dimensional potentials using NMR. Phys Lett A 378(1):10–15. https://doi.org/10.1016/j.physleta.2013.10.029

    Article  CAS  Google Scholar 

  127. V.S., A., Hegde SS, Mahesh TS (2016) NMR investigation of the quantum pigeonhole effect. Phys. Lett. A 380(4), 577–580. https://doi.org/10.1016/j.physleta.2015.12.011

  128. Krithika VR, Anjusha VS, Bhosale UT, Mahesh TS (2019) NMR studies of quantum chaos in a two-qubit kicked top. Phys Rev E 99:032219. https://doi.org/10.1103/PhysRevE.99.032219

    Article  CAS  Google Scholar 

  129. Krithika VR, Pal S, Nath R, Mahesh TS (2021) Observation of interaction induced blockade and local spin freezing in a NMR quantum simulator. Phys. Rev. Research 3:033035. https://doi.org/10.1103/PhysRevResearch.3.033035

    Article  CAS  Google Scholar 

  130. Pal S, Mahesh TS, Agarwalla BK (2019) Experimental demonstration of the validity of the quantum heat-exchange fluctuation relation in an NMR setup. Phys Rev A 100:042119. https://doi.org/10.1103/PhysRevA.100.042119

    Article  CAS  Google Scholar 

  131. Pal S, Saryal S, Segal D, Mahesh TS, Agarwalla BK (2020) Experimental study of the thermodynamic uncertainty relation. Phys. Rev. Research 2:022044. https://doi.org/10.1103/PhysRevResearch.2.022044

    Article  CAS  Google Scholar 

Download references

Acknowledgements

A. acknowledges financial support from DST/ICPS/QuST/Theme-1/2019/Q-68. K .D. acknowledges financial support from DST/ICPS/QuST/Theme-2/2019/Q-74.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Arvind.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Dorai, K., Arvind NMR Quantum Information Processing: Indian Contributions and Perspectives. J Indian Inst Sci 103, 569–589 (2023). https://doi.org/10.1007/s41745-022-00353-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s41745-022-00353-6

Keywords

Navigation