Example: The three-qubit code This article explains the basics of quantum error correction, the types of quantum errors, and some common quantum error correction codes. It also provides an example of how to correct errors using the three-qubit code. What is quantum error correction? Quantum ...
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 ...
Quantum error correction codeHamming codeFault-toleranceQuantum measurementHigh-dimensional quantum error correction codes (QECCs) are widely used to enhance the security and coding capabilities of the entire quantum systems. While these codes show promise in achieving reliable quantum computing by ...
The logical error rate of our larger quantum memory is suppressed by a factor of Λ = 2.14 ± 0.02 when increasing the 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 ...
The three qubit bit flip code (Classical error correction) 噪声是导致量子信息处理过程失败的主要原因之一。我们无法消灭噪声,但我们可以使得噪声尽量小,来保证运算过程的准确性。同时通过 error-correction 技术来一定层度纠正噪声的影响。 The key idea is that if we wish to protect a message against the ef...
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...
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...
9.1 经典错误校正(Classical Error Correction) 错误模型(error model):它描述了一个比特集合的演化过程。 信道(channel):无误差(error-free)信道称为恒等信道(identity channel),其不会对bit产生影响。 最经典的错误模型是比特翻转(bit-flip)模型,其以一定的概率 p 对原有值进行翻转,如下图所示: 在电路上将错误...
Furthermore we generalize the error models to the case of not-so-perfectly-protected qubits and introduce the quantity infidelity as a figure of merit and show that our code outperforms also the ordinary quantum error-correcting codes.doi:10.48550/arXiv.0801.1379Ying Dong...
Below we present a perfect (i.e., capable of correcting all one-bit errors with the minimum number of extra qubits) quantum error correction code using only five qubits (shown to be the smallest possible number). Our code is not a classical linear code [11] but a truly quantum code....