nLab nuclear magnetic resonance

Idea

In physics, by nuclear magnetic resonance (NMR) one refers to resonant control of the spin of atomic nuclei through an external electromagnetic field.

One way to realize qbits (in quantum information theory and quantum computing) is as spin-quantum states manipulated via spin resonance: spin resonance qbits. A prominent example of spin resonance qbit realizations uses a nitrogen-vacancy center in diamond.

Related concepts

• nitrogen-vacancy center in diamond

• spin resonance qbit

• quantum computing

• quantum sensing

References

General

See also

• Wikipedia, Nuclear magnetic resonance

On Floquet theory? in nuclear magnetic resonance:

• Konstantin L. Ivanov, Kaustubh R. Mote, Matthias Ernst, Asif Equbal, Perunthiruthy K. Madhu, Floquet theory in magnetic resonance: Formalism and applications, Progress in Nuclear Magnetic Resonance Spectroscopy, 126–127 (2021) 17-58 [doi:10.1016/j.pnmrs.2021.05.002]

Further developments:

• Navin Khaneja et al., Optimal control of coupled spin dynamics: design of NMR pulse sequences by gradient ascent algorithms, Journal of Magnetic Resonance 172 2 (2005) 296-305 [doi:10.1016/j.jmr.2004.11.004]

• Asif Equbal et al., Role of electron spin dynamics and coupling network in designing dynamic nuclear polarization, Progress in Nuclear Magnetic Resonance Spectroscopy 126–127 (2021) 1-16 [doi:10.1016/j.pnmrs.2021.05.003]

Spin resonance qbits

The idea of spin resonance qbits, i.e. of qbits realized on quantum mechanical spinors (e.g. electron-spin or nucleus-spin) and manipulated via spin resonance:

• Daniel Loss, David P. DiVincenzo, Quantum Computation with Quantum Dots, Phys. Rev. A 57 120 (1998) $[$arXiv:cond-mat/9701055, doi:10.1103/PhysRevA.57.120$]$

The very first proof-of-principle quantum computations were made with nuclear magnetic resonance-technology:

• D. G. Cory et al, NMR Based Quantum Information Processing: Achievements and Prospects, Fortsch. Phys. 48 9-11 (2000) 875-907 $[$arXiv:quant-ph/0004104$]$

• Jonathan A. Jones, Quantum Computing and Nuclear Magnetic Resonance, PhysChemComm 11 (2001) $[$doi:10.1039/b103231n, arXiv:quant-ph/0106067$]$

• Jonathan A. Jones, Quantum Computing with NMR, Prog. NMR Spectrosc. 59 (2011) 91-120 $[$doi:10.1016/j.pnmrs.2010.11.001, arXiv:1011.1382$]$

• Dorothea Golze, Maik Icker, Stefan Berger, Implementation of two-qubit and three-qubit quantum computers using liquid-state nuclear magnetic resonance, Concepts in Magnetic Resonance 40A 1 (2012) 25-37 $[$doi:10.1002/cmr.a.21222$]$

• NMR Quantum Computing (2012) $[$slides pdf$]$

• Tao Xin et al., Nuclear magnetic resonance for quantum computing: Techniques and recent achievements (Topic Review - Solid-state quantum information processing), Chinese Physics B 27 020308 $[$doi:10.1088/1674-1056/27/2/020308$]$

See also:

• Lieven Vandersypen, Mark Eriksson: Quantum computing with semiconductor spins, Physics Today 72 8 (2019) 38 [doi:10.1063/PT.3.4270]

Monograph:

• Chen, Church, Englert, Henkel, Rohwedder, Scully, Zubairy, section 10 of: Quantum Computing Devices – Principles, Designs, and Analysis, Routledge (2007) [ISBN:9780367390372]

Exposition, review and outlook:

• Raymond Laflamme, Emanuel Knill, et al., Introduction to NMR Quantum Information Processing, Proceedings of the International School of Physics “Enrico Fermi” 148 Experimental Quantum Computation and Information [arXiv:quant-ph/0207172]

• Asif Equbal, Molecular spin qubits for future quantum technology, talk at CQTS (Nov 2022) [slides: pdf, video: rec]

• Jonathan A. Jones, Controlling NMR spin systems for quantum computation, Spectroscopy 140–141 (2024) 49-85 [doi:10.1016/j.pnmrs.2024.02.002, arXiv:2402.01308]

  “Nuclear magnetic resonance is arguably both the best available quantum technology for implementing simple quantum computing experiments and the worst technology for building large scale quantum computers that has ever been seriously put forward. After a few years of rapid growth, leading to an implementation of Shor’s quantum factoring algorithm in a seven-spin system, the field started to reach its natural limits and further progress became challenging. […] the user friendliness of NMR implementations means that they remain popular for proof-of-principle demonstrations of simple quantum information protocols.”

See also:

• Wikipedia, Spin qbit quantum computer

• Wikipedia, Nuclear magnetic resonance quantum computer

More on implementation of quantum logic gates on qbits realized on nucleon-spin, via pulse protocols in NMR-technology:

• Price, Somaroo, Tseng, Gore, Fahmy,, Havel, Cory: Construction and Implementation of NMR Quantum Logic Gates for Two Spin Systems, Journal of Magnetic Resonance 140 2 (1999) 371-378 $[$doi;10.1006/jmre.1999.1851$]$

and analogously on electron-spin:

• M. Yu. Volkov and K. M. Salikhov, Pulse Protocols for Quantum Computing with Electron Spins as Qubits, Appl Magn Reson 41 (2011) 145–154 $[$doi:10.1007/s00723-011-0297-2$]$

For references on spin resonance qbits realized on a nitrogen-vacancy center in diamond, see there.

There exist toy desktop quantum computers for educational purposes, operating on a couple of nuclear magnetic resonance qbits at room temperature :

• CIQTEK: Diamond Quantum Computer for Education

• SpinQ: SpinQ Triangulum: a commercial three-qubit desktop quantum computer $[$arXiv:2202.02983$]$