Quantum errors corrected

Guangjun Xie

The 3-qubit error-correction quantum circuit is realized and optimized in the non-measuring condition.The modular thought is presented to design and optimize the quantum error-correction circuit. With the quantum bits increasing,the error-correction circuit of 3-qubits can be used in the error-correction circuit of 5-qubits as a module.The error-correction circuit of 5-qubits can be used in the error-correction circuit of 7-qubits.By parity of reasoning,the error-correction circuit of a few quantum bits can be used in the error-correction circuit of multiple quantum bits.The quantum error-correction circuit can be simplified and the redundant qubits can be reduced using the method.It can also make the quantum cost lower.

Ray LaPierre

Ming-Xia Huo, Ying Li

Quantum error correction is important to quantum information processing, which allows us to reliably process information encoded in quantum error correction codes. Efficient quantum error correction benefits from the knowledge of error rates. We propose a protocol for monitoring error rates in real time without interrupting the quantum error correction. Any adaptation of the quantum error correction code or its implementation circuit is not required. The protocol can be directly applied to the most advanced quantum error correction techniques, e.g. surface code. A Gaussian processes algorithm is used to estimate and predict error rates based on error correction data in the past. We find that using these estimated error rates, the probability of error correction failures can be significantly reduced by a factor increasing with the code distance.

Belal Ehsan Baaquie, L. C. Kwek

Venkateswaran Kasirajan

Ri Qu, Bing-jian Shang, Yan-ru Bao +1 more

Operator quantum error correction provides a unified framework for the known techniques of quantum error correction such as the standard error correction model, the method of decoherence-free subspaces, and the noiseless subsystem method. We first show an example of a new quantum error correction scheme which can not be described by operation quantum error correction. Then we introduce a different notion of noiseless subsystems according to the example. Base on this notion, we present a more unified approach which incorporates operator quantum error correction as a special case. Moreover, we also give a sufficient and necessary condition of quantum error correction using this approach. We show that this approach provides more recovery operations than operator quantum error correction, which possibly leads to simpler decoding procedures.