Quantinuum Logical Qubits
Early research on quantum error correction demonstrated that a complex entangled state known as a “logical qubit,” which was created by mixing several noisy physical qubits, could endure for an infinitely long period of time. The search for codes that work effectively as “quantum memories,” as they are known, is a major focus for QEC researchers. Though this is only half the story, numerous potential coding families have been discovered.
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Long-term qubit retention is one thing, but quantum circuit operation is required to achieve the potential benefits of quantum computing. Additionally, these circuits must be operated on the logical qubits of their code to ensure that noise does not interfere with their processing. Since the implementation of these “logical gates” frequently involves numerous physical operations, this is frequently far more difficult than performing gates on the actual qubits of Quantinuum device. Converting a physical circuit into a logical circuit can be challenging since it is frequently not immediately clear which logical gates a code contains.
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Certain codes, such as the well-known surface code, have simple logical gates and are also good quantum memory. The disadvantage is that a high number of physical qubits are needed to accomplish massive logical algorithms, and the ratio of physical qubits to logical qubits (the “encoding rate”) is low. There are also high-rate codes that are good quantum memories, but they are significantly harder to compute on. In a sense, a high-rate code with simple logical gates and a good quantum memory would be the holy grail of QEC. Here, by creating a new code with those characteristics, they further that goal.
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Improvements to earlier error-correcting codes
Genon codes were recently introduced by Quantinuum QEC experts. These codes were constructed using an underlying technique known as the “symplectic double cover,” which also offered a means of obtaining logical gates that are well adapted to the QCCD architecture of Quantinuum. Specifically, single qubit operations and relabeling the device’s physical qubits are used to accomplish these “SWAP-transversal” gates. This relabeling can be accomplished in software almost for free because of the all-to-all communication made possible by qubit movement on the QCCD architecture. The resulting logical gates are equally high fidelity when combined with single-qubit operations of exceptionally high fidelity (~1.2 x10-5).
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They further develop these codes in light of their potential. It uses a process known as “code concatenation” to merge the symplectic double codes with the [[4,2,2]] Iceberg code. Concatenated codes are similar to nesting dolls in that they have an exterior code that contains codes inside of it, and these codes may also contain codes. Technically speaking, the logical qubits of one code function as the physical qubits of another code when they are concatenated.
It refers to these new codes as “concatenated symplectic double codes” because they were created with a large number of these readily implementable SWAP-transversal gates. It demonstrates how the concatenation method enables us to “upgrade” logical gates in terms of their ease of implementation, which is essential to their development. This process could offer insights for creating additional codes with practical logical gates. Interestingly, this code’s SWAP-transversal gate set is so strong that universal computation only requires two more operations (logical T and S). In addition, it provides numerical proof that these codes are good quantum memory and feature a large number of logical qubits.
Quantinuum didn’t have to give up speed to use concatenated symplectic double codes, which feature one of the simplest logical computing strategies. By 2029, it hopes to have hundreds of logical qubits with a logical error rate of about 1x 10-8. With the help of these codes, Quantinuum can make the most of its hardware’s best features and produce a product that will give us a genuine competitive edge.
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