![]() This is a very long paper (over 100 pages), but the first 15to 20 pages or so, including the In a nutshell section can be consulted for a brief high-level view of the topic of this paper. A graph neural network (GNN) is constructed and trained with a purpose of using it as a quantum error correction decoder for depolarized noise on the. Great detail about QEC can be found in the technical papers listed in the References and bibliography section of this paper. 3.2 Tree diagram illustrating the possible paths of the Flag 1-FTEC Protocol. That said, various details of QEC will invariably crop up from time to time. One of the most surprising scientific discoveries of the last few decades is that this is, in fact, not the case, thanks to two basic ideas: quantum error. With a plethora of quantum error correcting codes that can be used in. The focus here is the impact of QEC and logical qubits on algorithms and applications. To be clear, this informal paper won’t endeavor to do a deep dive on the technical details of quantum error correction. ![]() After this, we will introduce the stabilizer formalism, which allows efficient resource management while constructing the QEC codes. I have endeavored to cover all of the issues and questions of concern to me, but others may have additional issues and questions. And then, we will study types of quantum errors and construct respective codes to correct them. The emphasis in this informal paper is on preliminary thoughts, with no attempt to be completely comprehensive and fully exhaustive of all areas of logical qubits, quantum error correction, and fault-tolerant quantum computing. Figure 1: Quantum circuit for the quantum error-correction protocol described and implemented in this work as one would compose it of single-bit rotations, Hadamard gates, and controlled-not. Absent perfect qubits, automatic and transparent quantum error correction (QEC) is needed to achieve fault-tolerant qubits - logical qubits - to support fault-tolerant quantum computing (FTQC.) This informal paper will explore many of the issues and questions involved with achieving fault-tolerant logical qubits, but will stop short of diving too deep into the very arcane technical details of quantum error correction itself. NISQ has been a great way to make a lot of rapid progress in quantum computing, but its limitations, particularly its noisiness and lack of robust, automatic, and transparent error correction, preclude it from being a viable path to true, dramatic, and compelling quantum advantage for compute-intensive applications which can be developed by non-elite developers which would simply not be feasible using classical computing. Finally, errors in quantum information are intrinsically continuous (. Preliminary Thoughts on Fault-Tolerant Quantum Computing, Quantum Error Correction, and Logical Qubits Hence any error correction procedure needs to be able to simultaneously correct for both.
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