We reported last year about Quantinuum’s research into non-Abelian topological states to develop more efficient error correction codes. They now have further implemented further research to develop a new error correction code that they call Genon Braiding. The goal is to find a code that provides a more efficient Physical-to-Logical qubit ratio (lower is better) that is well-suited to the physical characteristics of their hardware. Achieving this can allow them to get to quantum advantage sooner, because it would allow a user to implement a useful algorithm with fewer physical qubits.
Quantinuum’s approach is based upon topological concepts, in particular a concept called braiding. They are also taking advantage of some of the physical characteristics of their H1-1 processor including the very high gate fidelities they have achieved as well as its capability of implementing all-to-all qubit coupling. Other tricks they use for this code Relabelling which logical renames qubit 1 to qubit 2 rather than physically swapping the qubits together. This is analogous to a concept in classical computing architecture called register renaming which was first used in the 1960’s with the IBM System/360 Model 91 supercomputer. They also have developed a technique for creating symplectic double codes which can take a [[n, k, d]] code and create a [[2n, 2k, ≥ d]] code with twice the number of qubits. In this nomenclature, the first number stands for the number of physical qubits in the code, the second stands for the number of logical qubits, and the third stands for the distance between codewords. Note that a distance of two is required to detect an error and a distance of three is required to correct an error in one of the qubits. And to correct errors in more than one qubit, one would need an even higher distance.
In the paper, Quantinuum used this code to test out three different variations on the H1-1 processor. The first implemented a [[4,1,2]] code to test out fidelities improvements on logical single qubit Clifford gates. The second implemented a [[8,2,2]] code to test out fidelities with a logical two qubit CX gate. And the third test out a [[10,2,3]] implementation with a logical g = CX0,1 · SWAP gate.
Like several other error correction code demonstrations we have reported on recently, this research is certainly a step in the right direction, but it is not what we call a “Sputnik Moment” in that it does not show a fully functional error corrected machine. One of the biggest things that has yet to be demonstrated is the ability to provide error correction for a universal gate set. This research shows that Quantinuum has successfully generated implementation of the Clifford gate set, but to have a quantum computer that can process any quantum program, it needs to implement non-Clifford gates too. Specifically, this would mean implementing either a T-gate or a Toffoli gate which combined with the Clifford gates would provide a universal gate set. Implementing the non-Clifford gates is quite complicated and would require something like Magic State Distillation in T-state factories. In addition, a distance of code distance of three would not provide enough error correction capability to successfully implement some of the large use cases being investigated in the DARPA Benchmarking program we just reported on. The paper showed a number of different theoretical variations of this genon braiding code with one using 85 physical qubits to create one logical qubit with a code distance of 13 and denoted as [[85,1,13]]. So there is certainly a lot of room for further development and we look forward to seeing more results in the future.
Quantinuum has issued a press release summarizing this research available here and you can access the preprint of the technical paper on arXiv here.
June 22, 2024