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}}</ref> subject to [[unitary transformation (quantum mechanics)|unitary transformation]]s, has a long enough [[coherence time]] to be usable by quantum logic gates (c.f. [[propagation delay#Electronics|propagation delay]] for classical logic gates).<ref name="SixPhysicalQubits" /><ref>{{Cite web|url=https://www.iarpa.gov/index.php/research-programs/logiq/logical-qubits|title=Logical Qubits (LogiQ)|website=Intelligence Advanced Research Projects Activity|language=en-us|access-date=2018-09-18}}</ref><ref>{{Cite web|url=https://www.iarpa.gov/index.php/research-programs/logiq/logical-qubits|title=Logical Qubits (LogiQ)|website=www.iarpa.gov|language=en-us|access-date=2018-10-04}}</ref>
|journal=Nature Communications|volume=6|issue=1|pages=6983|doi=10.1038/ncomms7983|pmid=25923318|pmc=4421804|issn=2041-1723}}</ref><ref name="A Very Small Logical Qubit">{{Cite journal|last=Kapit|first=Eliot|date=2016-04-12
|title=A Very Small Logical Qubit
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|arxiv = 1608.06335
|journal=Physical Review X|volume=8|issue=2|pages=021058|doi=10.1103/PhysRevX.8.021058|bibcode=2018PhRvX...8b1058J|s2cid=119108989|issn=2160-3308}}</ref> Thus, contemporary logical qubits [[Qubit#Physical implementations|typically consist of]] many physical qubits to provide stability, error-correction and fault tolerance needed to perform useful computations.<ref name="SixPhysicalQubits" /><ref name="A Very Small Logical Qubit" /><ref name=":4" />
In 2023, Google researchers showed how quantum error correction can improve logical qubit performance by increasing the physical qubit count.<ref name="Suppressing quantum errors">{{Cite journal|last=Acharya|first=Rajeev|date=2023-02-22
|title=Suppressing quantum errors by scaling a surface code logical qubit
|arxiv = 2207.06431
|journal=Nature |volume=614 |issue=7949 |pages=676-681|doi=10.1038/s41586-022-05434-1|pmid=36813892 |pmcid=9946823|issn=1476-4687}}</ref> 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).<ref>{{Cite web |last=Conover |first=Emily |date=2023-02-22 |title=Google's quantum computer reached an error-correcting milestone |website=ScienceNews |language=en-US |url=https://www.sciencenews.org/article/google-quantum-computer-sycamore-milestone |access-date=2024-07-09}}</ref>
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.<ref name="High-threshold and low-overhead">{{Cite journal| last=Bravyi |first=Sergei |date=2024-03-27
|title=High-threshold and low-overhead fault-tolerant quantum memory
|arxiv = 2308.07915
|journal=Nature |volume=627 |issue=8005 |pages=pages778–782|doi=10.1038/s41586-024-07107-7 |pmid=38538939 |pmcid=10972743 |issn=1476-4687}}</ref><ref>{{Cite web |last=Swayne |first=Matt |date=2024-03-28 |title=IBM Reports 10 Times More Efficient Error-Correcting Method Brings Practical Quantum Computers Closer To Reality |website=The Quantum Insider |language=en-US |url=https://thequantuminsider.com/2024/03/28/ibm-reports-10-times-more-efficient-error-correcting-method-brings-practical-quantum-computers-closer-to-reality/ |access-date=2024-07-09}}</ref> The work demonstrates error correction on near-term devices while reducing overhead – the number of physical qubits required to keep errors low.<ref>{{Cite web |last=Crane |first=Leah |date=2023-08-18 |title=IBM has just made error correction easier for quantum computers |website=New Scientist |language=en-US |url=https://www.newscientist.com/article/2388191-ibm-has-just-made-error-correction-easier-for-quantum-computers/ |access-date=2024-07-09}}</ref>
In 2024, Microsoft and Quantinuum announced experimental results that showed logical qubits could be created with significantly fewer physical qubits.<ref>{{Cite web |last=Choi |first=Charles |date=2024-04-03 |title=Microsoft Tests New Path to Reliable Quantum Computers - 1,000 physical qubits for each logical one? Try a dozen, says Redmond |website=IEEE Spectrum |language=en-US |url=https://spectrum.ieee.org/microsoft-quantum-computer-quantinuum |access-date=2024-07-09}}</ref> 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.<ref>{{Cite web |last=Timmer |first=John |date=2024-04-03 |title=Quantum error correction used to actually correct errors |website=Ars Technica |language=en-US |url=https://arstechnica.com/science/2024/04/quantum-error-correction-used-to-actually-correct-errors/ |access-date=2024-07-09}}</ref> This work defines how to achieve logical qubits within quantum computation.<ref>{{Cite web |last=Sutor |first=Bob |date=2024-04-05 |title=Quantum in Context: Microsoft & Quantinuum Create Real Logical Qubits |website=The Futurum Group |language=en-US |url=https://futurumgroup.com/insights/quantum-in-context-microsoft-quantinuum-create-real-logical-qubits/ |access-date=2024-07-09}}</ref>
== Overview ==
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