A framework for constructing quantum spherical codes

To reliably perform complex, large-scale calculations, computer systems rely on so-called error correction systems, techniques designed to protect information from errors. These techniques are perhaps even more essential when it comes to quantum computers, devices that perform calculations leveraging the principles of quantum mechanics.

Indeed, quantum computers are very sensitive to errors, because qubits (i.e. their information units) can lose their quantum state due to interactions with the environment. Error correction systems for quantum computers should be adapted to quantum mechanical processes, taking into account the unique vulnerabilities of quantum computing systems.

Most error-correcting codes developed so far are designed to mitigate errors in qubit-based systems. However, these schemes are often not compatible with other quantum devices storing information in bosonic systems, such as photonic resonators.

NIST/University of Maryland researchers recently introduced a new framework for constructing quantum codes that could also be applied to bosonic quantum systems. Their framework, described in an article published in Natural physicsspecifically proposes the construction of quantum codes defined on spheres.

“In graduate school, I was part of a team of researchers working on feline codes, which are used to store quantum information using light,” said Victor V. Albert, lead author of the article, at Phys.org. “As such, these codes are an instance of photonic or, more generally, bosonic codes. The information would be stored in the superposition of two classical electromagnetic signals. Such signals would have different amplitudes, but they would be the same length d ‘wave.”

After the development of these so-called cat codes, Albert and some of his peers began to explore the possibility of generalizing them so that they could be applied to multiple electromagnetic signals of different wavelengths. Although they were able to develop some system-specific codes, Albert felt that they still had not developed a unified framework that could be generalized to different systems.

“Since then, the simplest cat codes have grown in importance and become relevant to the computing systems implemented by Amazon AWS, Yale Quantum Circuits Inc and Alice&Bob in France,” Albert said. “As part of our new study, we set out to develop a way to define and study extensions of cat codes to electromagnetic signals of multiple amplitudes and frequencies.”

All quantum codes require the superposition of something, and Albert and his colleagues realized that it made sense to superimpose well-separated points on a sphere. Their framework builds on a previously proposed method for mapping electromagnetic signals of any frequency into points on a sphere.

“There is an old and very general technique from the founder of information theory, Claude Shannon, which maps an arbitrary electromagnetic signal of fixed amplitude but of any of them frequency at one point on the sphere,” Albert explained. “This means that sending classical information efficiently using light means packing as many points on the sphere as possible while ensuring that noise causes them to overlap. “

Researchers took this idea and attempted to translate it to apply to quantum computing. Their efforts resulted in the development of their new theoretical framework for constructing quantum spherical codes.

“We realized that the quantum version is to consider superimposing the sets of points that people have previously determined to be good for transmitting classical information. In low dimensions, these sets include the corners of the famous Platonic solids,” he said. explained Albert. “In higher dimensions, some sets are linked to exotic networks and binary codes.”

In their paper, Albert and his colleagues describe different ways of superimposing points in these sets to obtain high-performance quantum codes. Although their work so far is primarily theoretical, it opens a potential new avenue for creating photonic quantum codes made up of superpositions of a set of electromagnetic signals.

“As the simplest examples continue to be studied by experimental groups in industry and academia, this framework could give rise to other equally relevant codes,” Albert said. “The practical relevance, however, depends on future experimental advances in the control of quantum devices. Regardless of this, this framework should provide a fun playground for theorists in the meantime.”

This recent study by Albert and colleagues highlights a potential avenue for protecting bosonic quantum systems against noise. In the future, this could pave the way for more studies aimed at developing quantum analogues of classical spherical codes and testing their performance.

“Quantum computing is not about storing quantum information, but about manipulating it,” Albert added. “Having defined the codes, we now want to perform operations on them. We are also studying other classes of codes that are not described by our framework. This is a pretty exciting time in photonic coding theory.”

© 2024 Science X Network