Physical and logical qubits

In quantum computing, a qubit is a unit of information analogous to a bit (binary digit) in classical computing, but it is affected by quantum mechanical properties such as superposition and entanglement which allow qubits to be in some ways more powerful than classical bits for some tasks. Qubits are used in quantum circuits and quantum algorithms composed of quantum logic gates to solve computational problems, where they are used for input/output and intermediate computations.

A physical qubit is a physical device that behaves as a two-state quantum system, used as a component of a computer system.[1][2] A logical qubit is a physical or abstract qubit that performs as specified in a quantum algorithm or quantum circuit[3] subject to unitary transformations, has a long enough coherence time to be usable by quantum logic gates (c.f. propagation delay for classical logic gates).[1][4][5]

As of September 2018, most technologies used to implement qubits face issues of stability, decoherence,[6][7] fault tolerance[8][9] and scalability.[6][9][10] Because of this, many physical qubits are needed for the purposes of error-correction to produce an entity which behaves logically as a single qubit would in a quantum circuit or algorithm; this is the subject of quantum error correction.[3][11] Thus, contemporary logical qubits typically consist of many physical qubits to provide stability, error-correction and fault tolerance needed to perform useful computations.[1][7][11]


1-bit and 2-bit quantum gate operations have been shown to be universal.[12][13][14][15] A quantum algorithm can be instantiated as a quantum circuit.[16][17]

A logical qubit specifies how a single qubit should behave in a quantum algorithm, subject to quantum logic operations which can be built out of quantum logic gates. However, issues in current technologies preclude single two-state quantum systems, which can be used as physical qubits, from reliably encoding and retaining this information for long enough to be useful. Therefore, current attempts to produce scalable quantum computers require quantum error correction, and multiple (currently many) physical qubits must be used to create

The quantum threshold theorem

Topological quantum computing

The approach of topological qubits, which takes advantage of topological effects in quantum mechanics, has been proposed as needed many fewer or even a single physical qubit per logical qubit.[10] Topological qubits rely on a class of particles called anyons which have spin that is neither half-integral (fermions) nor integral (bosons), and therefore obey neither the Fermi–Dirac statistics nor the Bose–Einstein statistics of particle behavior.[18] Anyons exhibit braid symmetry in their world lines, which has desirable properties for the stability of qubits. Notably, anyons must exist in systems constrained to two spatial dimensions or fewer, according to the spin–statistics theorem, which states that in 3 or more spatial dimensions, only fermions and bosons are possible.[18]

See also


  1. Shaw, Bilal; Wilde, Mark M.; Oreshkov, Ognyan; Kremsky, Isaac; Lidar, Daniel A. (2008-07-18). "Encoding One Logical Qubit Into Six Physical Qubits". Physical Review A. 78 (1): 012337. arXiv:0803.1495. doi:10.1103/PhysRevA.78.012337. ISSN 1050-2947.
  2. Viola, Lorenza; Knill, Emanuel; Laflamme, Raymond (2001-09-07). "Constructing Qubits in Physical Systems". Journal of Physics A: Mathematical and General. 34 (35): 7067–7079. arXiv:quant-ph/0101090. doi:10.1088/0305-4470/34/35/331. ISSN 0305-4470.
  3. Heeres, Reinier W.; Reinhold, Philip; Ofek, Nissim; Frunzio, Luigi; Jiang, Liang; Devoret, Michel H.; Schoelkopf, Robert J. (2016-08-08). "Implementing a Universal Gate Set on a Logical Qubit Encoded in an Oscillator". Nature Communications. 8 (1): 94. arXiv:1608.02430. doi:10.1038/s41467-017-00045-1. ISSN 2041-1723. PMC 5522494. PMID 28733580.
  4. "Logical Qubits (LogiQ)". Intelligence Advanced Research Projects Activity. Retrieved 2018-09-18.
  5. "Logical Qubits (LogiQ)". Retrieved 2018-10-04.
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  7. Kapit, Eliot (2016-04-12). "A Very Small Logical Qubit". Physical Review Letters. 116 (15): 150501. arXiv:1510.06117. doi:10.1103/PhysRevLett.116.150501. ISSN 0031-9007. PMID 27127945.
  8. Nigg, Daniel; Mueller, Markus; Martinez, Esteban A.; Schindler, Philipp; Hennrich, Markus; Monz, Thomas; Martin-Delgado, Miguel A.; Blatt, Rainer (2014-07-18). "Experimental Quantum Computations on a Topologically Encoded Qubit". Science. 345 (6194): 302–305. arXiv:1403.5426. doi:10.1126/science.1253742. ISSN 0036-8075. PMID 24925911.
  9. "Achieving scalability in quantum computing". Microsoft Cloud Blogs. Microsoft. 2018-05-16. Retrieved 2018-09-18.
  10. Mishmash, Ryan; Alicea, Jason (2017-08-16). "Topological qubits: Arriving in 2018?". Quantum Frontiers. Retrieved 2018-09-17.
  11. Jones, Cody; Fogarty, Michael A.; Morello, Andrea; Gyure, Mark F.; Dzurak, Andrew S.; Ladd, Thaddeus D. (2018-06-01). "A logical qubit in a linear array of semiconductor quantum dots". Physical Review X. 8 (2): 021058. arXiv:1608.06335. doi:10.1103/PhysRevX.8.021058. ISSN 2160-3308.
  12. DiVincenzo, David P. (1995-02-01). "Two-bit gates are universal for quantum computation". Physical Review A. 51 (2): 1015–1022. arXiv:cond-mat/9407022. Bibcode:1995PhRvA..51.1015D. doi:10.1103/PhysRevA.51.1015. PMID 9911679.
  13. Deutsch, David; Barenco, Adriano; Ekert, Artur (1995-06-08). "Universality in Quantum Computation". Proceedings of the Royal Society of London A: Mathematical and Physical Sciences. 449 (1937): 669–677. arXiv:quant-ph/9505018. Bibcode:1995RSPSA.449..669D. CiteSeerX doi:10.1098/rspa.1995.0065. ISSN 1471-2946.
  14. Barenco, Adriano (1995-06-08). "A Universal Two-Bit Gate for Quantum Computation". Proceedings of the Royal Society of London A: Mathematical and Physical Sciences. 449 (1937): 679–683. arXiv:quant-ph/9505016. Bibcode:1995RSPSA.449..679B. doi:10.1098/rspa.1995.0066. ISSN 1471-2946.
  15. Lloyd, Seth (1995-07-10). "Almost Any Quantum Logic Gate is Universal". Physical Review Letters. 75 (2): 346–349. Bibcode:1995PhRvL..75..346L. doi:10.1103/PhysRevLett.75.346. PMID 10059671.
  16. Yazdani, Maryam; Zamani, Morteza Saheb; Sedighi, Mehdi (2013-06-09). "A Quantum Physical Design Flow Using ILP and Graph Drawing". Quantum Information Processing Journal. arXiv:1306.2037.
  17. Whitney, Mark; Isailovic, Nemanja; Patel, Yatish; Kubiatowicz, John (2007-04-02). "Automated Generation of Layout and Control for Quantum Circuits". ACM Computing Frontiers. arXiv:0704.0268.
  18. Wilczek, Frank (2018-02-27). "How 'Anyon' Particles Emerge From Quantum Knots | Quanta Magazine". Quanta Magazine. Retrieved 2018-09-18.
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