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qbit in nLab

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Contents

Context

Computation

constructive mathematics, realizability, computability

intuitionistic mathematics

propositions as types, proofs as programs, computational trinitarianism

Constructive mathematics

Realizability

Computability

Quantum systems

quantum logic

quantum physics

quantum probability theory – observables and states

quantum information

quantum technology

quantum computing

Contents

Idea

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

ℂ 2≃ℂ⋅|0⟩⊕ℂ⋅|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).

Properties

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.

References

General

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]

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:

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:

Monograph:

  • Chen, Church, Englert, Henkel, Rohwedder, Scully, Zubairy, section 9 of: Quantum Computing Devices Principles, Designs, and Analysis, Routledge (2007) [ISBN:9780367390372]

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.