Repetition code: The simplest quantum error correction code, where a single qubit is encoded into multiple qubits by repeating it multiple times. The repetition code can correct bit flip errors, but not phase flip errors. Shor code: The first quantum error correction code, developed by Peter ...
Nested Quantum Error Correction CodesI describe a method for pasting together certain quantum error-correcting codes that correct one error to make a single larger one-error quantum code. I show how to construct codes encoding 7 qubits in 13 qubits using the method, as well as 15 qubits in ...
The description of quantum error correction suggests a close analogy with classical error correction, and, indeed, several subspace quantum codes are based on classical error correcting code. Quantum error correction requires a multi-qubit measurement that does not disturb the quantum information in the...
A quantum error correction code (QECC) that encodes K qubits into N qubits, denoted as [N,K], is defined by an encoding mapping U from the K-qubit Hilbert space H2K onto a 2K-dimensional subspace Cq of the N-qubit Hilbert space H2N. From: Quantum Information Processing and Quantum Err...
9.4 量子错误校正(Quantum Error Correction) 首先需要指出,量子演化是一个连续的过程,与经典计算这种离散的过程是很不一样的。其次,编码操作无法对量子态进行多个备份。最后,被编码的量子态的损坏无法通过对所有qubits进行测量来检测。 考虑单个qubit,其状态为 |0\rangle ,在与状态为 |E\rangle 的环境交互后,会产...
The three qubit bit flip code (Quantum error-correction) 上述仅仅在经典中进行介绍,在量子中也存在 quantum error-correction code,但由于一些基本问题,可能存在一些不同。 No cloning: 在量子中,通过独立的备份量子态来纠错的方法,因为 no-cloning theorem 而无法实现。
code distance by 2, culminating in a 101-qubit distance-7 code with 0.143% ± 0.003 per cent error per cycle of error correction. This logical memory is also beyond breakeven, exceeding the lifetime of its best physical qubit by a factor of 2.4 ± 0.3. Our system maintains ...
code. This is possible because the code encodes more information into the same number of physical qubits, while still showing excellent performance at error rates below 0.001. Furthermore, each qubit is coupled to six others, a reasonable hardware requirement for realizing the error correction ...
Here we demonstrate quantum error correction using the surface code, which is known for its exceptionally high tolerance to errors3,4,5,6. Using 17 physical qubits in a superconducting circuit, we encode quantum information in a distance-three logical qubit, building on recent distance-two error...
PyMatching: A Python/C++ library for decoding quantum error correcting codes with minimum-weight perfect matching. quantum-error-correctionsurface-codeminimum-weight-perfect-matching UpdatedSep 5, 2023 C++ yaleqc/qtcodes Star83 Code Issues Pull requests ...