A Novel Approach for Asymmetric Quantum Error Correction With Syndrome Measurement

Abstract

Most of the quantum error correction methods are symmetric. Symmetric methods are implemented by considering the amplitude of bit flip(X) and phase flip(Z) errors as same. With the quantum experiments, it is observed that the amplitude of Z errors are more compared to X errors. Due to which the need of asymmetric error correction has increased. This paved a path for the development of asymmetric error correction methods. In this paper, we discussed the concept of asymmetric quantum error correction (AQEC) and proposed an efficient approach for AQEC with encoding, syndrome measurement and decoding operations with increased fidelity to 85.89% and reduced circuit depth to 48%.

Quantum Error Correction Via Noise Guessing Decoding

“…Our work considers a system model with perfect encoding and perfect measurements, focusing on correcting the errors that arise in the communication channel, which is a common model used in the literature [50], [51]. By making use of the key features of GRAND, this work shows how to take advantage of QRLCs to construct stabilizer codes that are shown, via semi-analytical simulation, to be near-capacity achieving and decodable in practice, leading to quantum error correction codes able to cope with large channel error rates, even at reasonably high code rates.…”

“…Syndrome measurement setups are a central building block in QEEC [40], [41], [51]. As in classical GRAND, the syndrome measurement step of the stabilizer code may be considered simply as a membership test, accepting the quantum state if the syndrome s is zero, and rejecting the error-affected state if s = 0 (see Fig.…”