Since the development of the first quantum computer in 1998, 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]
In 2023, Google researchers showed how quantum error correction can improve logical qubit performance by increasing the physical qubit count.[12] These results found that a larger logical qubit (49 physical qubits) had a lower error rate, about 2.9 percent per round of error correction, compared to a rate of about 3.0 percent for the smaller logical qubit (17 physical qubits).[13]
In 2024, IBM researchers created a quantum error correction code 10 times more efficient than previous research, protecting 12 logical qubits for roughly a million cycles of error checks using 288 qubits.[14][15] The work demonstrates error correction on near-term devices while reducing overhead – the number of physical qubits required to keep errors low.[16]
In 2024, Microsoft and Quantinuum announced experimental results that showed logical qubits could be created with significantly fewer physical qubits.[17] The team used quantum error correction techniques developed by Microsoft and Quantinuum's trapped ion hardware to use 30 physical qubits to form four logical qubits. Scientists used a qubit virtualization system and active syndrome extraction—also called repeated error correction to accomplish this.[18] This work defines how to achieve logical qubits within quantum computation.[19]
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 a single, error-tolerant logical qubit. Depending on the error-correction scheme used, and the error rates of each physical qubit, a single logical qubit could be formed of up to 1,000 physical qubits.[26]
^ abcShaw, 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. Bibcode:2008PhRvA..78a2337S. doi:10.1103/PhysRevA.78.012337. ISSN 1050-2947. S2CID 40040752.
^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. Bibcode:2001JPhA...34.7067V. doi:10.1088/0305-4470/34/35/331. ISSN 0305-4470. S2CID 14713492.
^ abHeeres, 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. PMC5522494. PMID 28733580.
^"Logical Qubits (LogiQ)". Intelligence Advanced Research Projects Activity. Retrieved 2018-09-18.
^ ab"Achieving scalability in quantum computing". Microsoft Cloud Blogs. Microsoft. 2018-05-16. Retrieved 2018-09-18.
^ abMishmash, Ryan; Alicea, Jason (2017-08-16). "Topological qubits: Arriving in 2018?". Quantum Frontiers. Retrieved 2018-09-17.
^ abJones, 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. Bibcode:2018PhRvX...8b1058J. doi:10.1103/PhysRevX.8.021058. ISSN 2160-3308. S2CID 119108989.
^Swayne, Matt (2024-03-28). "IBM Reports 10 Times More Efficient Error-Correcting Method Brings Practical Quantum Computers Closer To Reality". The Quantum Insider. Retrieved 2024-07-09.
^Crane, Leah (2023-08-18). "IBM has just made error correction easier for quantum computers". New Scientist. Retrieved 2024-07-09.
^Choi, Charles (2024-04-03). "Microsoft Tests New Path to Reliable Quantum Computers - 1,000 physical qubits for each logical one? Try a dozen, says Redmond". IEEE Spectrum. Retrieved 2024-07-09.
^Timmer, John (2024-04-03). "Quantum error correction used to actually correct errors". Ars Technica. Retrieved 2024-07-09.
^Sutor, Bob (2024-04-05). "Quantum in Context: Microsoft & Quantinuum Create Real Logical Qubits". The Futurum Group. Retrieved 2024-07-09.
^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. S2CID 2317415.
^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. CiteSeerX10.1.1.54.2646. doi:10.1098/rspa.1995.0065. ISSN 1471-2946. S2CID 15088854.
^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. S2CID 119447556.
^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.
^Yazdani, Maryam; Zamani, Morteza Saheb; Sedighi, Mehdi (2013-06-09). "A Quantum Physical Design Flow Using ILP and Graph Drawing". Quantum Information Processing Journal. 12 (10): 3239. arXiv:1306.2037. Bibcode:2013QuIP...12.3239Y. doi:10.1007/s11128-013-0597-6. S2CID 12195937.
^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.
^Fowler, Austin G.; Mariantoni, Matteo; Martinis, John M.; Cleland, Andrew N. (2012). "Surface codes: Towards practical large-scale quantum computation". Physical Review A. 86 (3): 032324. arXiv:1208.0928. Bibcode:2012PhRvA..86c2324F. doi:10.1103/PhysRevA.86.032324. ISSN 1050-2947. S2CID 119277773.
^ abWilczek, Frank (2018-02-27). "How 'Anyon' Particles Emerge From Quantum Knots | Quanta Magazine". Quanta Magazine. Retrieved 2018-09-18.