constructive mathematics, realizability, computability
propositions as types, proofs as programs, computational trinitarianism
quantum algorithms:
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 is the 2-dimensional complex vector space equipped with its canonical quantum measurement-basis
Analogous higher- but still finite- -dimensional quantum data (types) are called qdits (“qtrits” for ).
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:
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:
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:
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:
and analogously on electron-spin:
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 :
SpinQ: SpinQ Triangulum: a commercial three-qubit desktop quantum computer arXiv:2202.02983
On realizing qbits and quantum gates (hence quantum computation) via quantum states of magnetic flux through (Josephson junctions in) superconductors, manipulated via electromagnetic pulses:
Michel 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
Michel H. Devoret, R. J. Schoelkopf, Superconducting Circuits for Quantum Information: An Outlook, Science 339 6124 (2013) 1169-1174 [doi:10.1126/science.1231930]
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
Olivier Ezratty, Perspective on superconducting qubit quantum computing, Eur. Phys. J. A 59 94 (2023) [doi:10.1140/epja/s10050-023-01006-7]
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.