MBE-CQEC A New Continuous Quantum Error Correction Scheme

As the number of quantum bits increases, quantum computers will be able to process information much faster than classical computers. But quantum bits are fragile. They change state very quickly, for example, and are affected by environmental factors such as temperature, which can introduce many errors. Researchers have been working to develop an effective way to correct these errors in real time. This is the quantum error correction (QEC) scheme.

Environmental factors - called decoherence - cause random rotations of quantum bits. For example, the rotation of the central quantum bit in the figure (center) represents a quantum error. the task of the QEC scheme is to detect and correct this error so that the quantum bit can return to its initial state.

Jason Twamley's team at Okinawa Institute of Science and Technology (OIST) in Japan, together with collaborators at Trinity College Dublin in Ireland and the University of Queensland in Brisbane, Australia, have proposed a new error correction technique, a measurement-based estimator scheme for continuous quantum error correction. The paper has been published in Physical Review Research [1].

The implementation of QEC requires the collection of multiple quantum bits using the properties of entanglement. In order to detect errors occurring in quantum bits, the QEC scheme must apply a series of measurements called syndrome measurements (MS). These measurements evaluate whether two nearest neighboring quantum bits are aligned in the same direction. The results of these measurements are called syndrome, and then based on them, errors in the quantum bits can be detected and subsequently corrected [2].

Common QEC schemes are usually slow and they also lead to a rapid loss of information stored in the quantum bits due to the inability to capture and correct errors in real time. In addition, such QEC methods use a traditional quantum measurement method called projection measurement to obtain the syndrome. This method requires several additional quantum bits, making it resource-intensive.

These schemes, called discrete quantum error correction (DQEC), use projected von Neumann measurements on stabilizers to discretize the error syndrome into a finite set and apply fast yougates to recover the corrupted information. In contrast, continuous quantum error correction (CQEC) can in principle be performed faster than DQEC and save resources.

Now, OIST has developed a measurement-based estimator scheme called continuous quantum error correction (MBE-CQEC), which can quickly and efficiently detect and correct errors from partially noisy syndrome measurements. They use a powerful classical computer as an external controller (or estimator) that estimates errors in the quantum system, filters out the noise perfectly, and applies feedback to correct them.

MBE-CQEC scheme for three quantum bits. Quantum bits in a quantum computer (left) are measured continuously by an estimator (right) run by a classical computer. The estimator detects errors by making syndrome measurements, which are then corrected with appropriate feedback.

However, the scheme works only for bit flips, one of the two types of errors in quantum computing. Moreover, the theoretical model on which the scheme is based still needs to be experimentally verified on a quantum computer. In addition, it has the important limitation that the real-time simulation speed of the estimator decreases exponentially as the number of quantum bits in the system increases.

Reference links：

[1]https://journals.aps.org/prresearch/abstract/10.1103/PhysRevResearch.4.033207

[2]https://www.oist.jp/news-center/press-releases/mbe-cqec-new-scheme-correct-quantum-errors