nLab qbit




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In quantum information theory and quantum computing, by a q-bit (or qubit) one means a quantum state in a 2-dimensional complex Hilbert space of states.

Hence the quantum data type QBitQBit is the 2-dimensional complex vector space equipped with its canonical quantum measurement-basis

2|0|1. \mathbb{C}^2 \,\simeq\, \mathbb{C} \cdot \vert 0 \rangle \oplus \mathbb{C} \cdot \vert 1 \rangle \,.

Analogous higher- but still finite- dd-dimensional quantum data (types) are called qdits (“qtrits” for d=3d = 3).


In terms of geometric quantization

In geometric quantization qbits are naturally understood as the states given by the geometric quantization of the 2-sphere for prequantum line bundle (plus metaplectic correction) being of unit first Chern class. See at geometric quantization of the 2-sphere – The space of quantum states.



The term q-bit goes back to

and was popularized by early adoption such as in

Textbook account:

See also:

Laboratoy-realizations of qbits for use in quantum computers:

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:

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

See also:

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

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]]

See also:

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 :

Superconducting qbits

On realizing qbits and quantum gates (hence quantum computation) via quantum states of magnetic flux through (Josephson junctions in) superconductors, manipulated via electromagnetic pulses:

  • M. H. Devoret, A. Wallraff, J. M. Martinis, Superconducting Qubits: A Short Review [[arXiv:cond-mat/0411174]]

  • John Clarke, Frank K. Wilhelm, Superconducting quantum bits, Nature 453 (2008) 1031–1042 [[doi:10.1038/nature07128]]

  • Jerry Moy Chow, Quantum Information Processing with Superconducting Qubits (2010) [[pdf]]

  • Jay M. Gambetta, Jerry M. Chow, Matthias Steffen, Building logical qubits in a superconducting quantum computing system, npj Quantum Information 3 2 (2017) [[doi:10.1038/s41534-016-0004-0]]

  • Morten Kjaergaard et al. Superconducting Qubits: Current State of Play, Annual Review of Condensed Matter Physics 11 (2019) 369-395 [[doi:10.1146/annurev-conmatphys-031119-050605]]

  • He-Liang Huang, Dachao Wu, Daojin Fan, Xiaobo Zhu, Superconducting Quantum Computing: A Review, Science China Information Sciences 63 8 (2020) 1-32 [[arXiv:2006.10433, doi:10.1007/s11432-020-2881-9]]

  • S. Kwon et al., Gate-based superconducting quantum computing, Journal of Applied Physics 129 (2021) 041102 [[doi:10.1063/5.0029735]]

Fine detail of the pulse control:

  • M. Werninghaus, D. J. Egger, F. Roy, S. Machnes, F. K. Wilhelm, S. Filipp: Leakage reduction in fast superconducting qubit gates via optimal control, npj Quantum Information 7 14 (2021) [[doi:10.1038/s41534-020-00346-2]]

  • M. Carroll, S. Rosenblatt, P. Jurcevic, I. Lauer & A. Kandala. Dynamics of superconducting qubit relaxation times, npj Quantum Information 8 132 (2022) [[doi:10.1038/s41534-022-00643-y]]

  • Elisha Siddiqui Matekole, Yao-Lung L. Fang, Meifeng Lin, Methods and Results for Quantum Optimal Pulse Control on Superconducting Qubit Systems, 2022 IEEE International Parallel and Distributed Processing Symposium Workshops (2022) [[arXiv:2202.03260, doi:10.1109/IPDPSW55747.2022.00102]]

Corrections due to quasiparticle-excitations:

Last revised on January 20, 2024 at 13:21:54. See the history of this page for a list of all contributions to it.