constructive mathematics, realizability, computability
propositions as types, proofs as programs, computational trinitarianism
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quantum probability theory – observables and states
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quantum algorithms:
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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 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
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:
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:
Revision on August 24, 2023 at 16:10:16 by Urs Schreiber See the history of this page for a list of all contributions to it.