Quantinuum Demonstrates Quantum Error Detection, Not Fully Fault Tolerant

Recently, Quantinuum published an interesting paper on arXiv entitled "Demonstrating Bayesian Quantum Phase Estimation with Quantum Error Detection", describing An interesting paper published in arXiv entitled "Demonstrating Bayesian Quantum Phase Estimation with Quantum Error Detection" describes a simulation of a quantum phase estimation algorithm to calculate the ground state energy of the hydrogen molecule (H2).

Sketch of the entire QPE encoding circuit

While simulations of hydrogen molecules have been done before, this project is unique in that it also incorporates error detection as part of the algorithm. This research uses [6, 4, 2] encoding: that is, 6 physical quantum bits are used to encode 4 logical quantum bits with a coding distance of 2. When the coding distance is 2, it means that the encoding can detect single-bit errors, but cannot correct single-bit errors, and may not even be able to detect two-bit errors. Assuming that single-bit errors are the most common errors, the correct answer can be obtained by running the algorithm over and over again until the code shows that no errors have occurred.

This research is unrelated to an earlier experiment published by Quantinuum to create and manipulate non-Abelian arbitraries to produce topological quantum bits. The two experiments are completely different.

Although it is not well understood in the popular press, there is a big difference between error detection and error correction. Most of the codes that researchers are working on, such as surface coding, color coding, GKP coding, LDPC coding, etc., not only detect errors but also correct them. These types of codes are the only way to achieve fully fault-tolerant machines: the machines in question are capable of running the thousands of quantum bits and millions of gates of algorithms required for most quantum applications. Even with the excellent quantum bit quality of Quantinuum's ion trap machines, the chances of achieving error-free performance when running these very large algorithms are close to zero. As a result, error detection algorithms need to be run repeatedly millions or billions of times before zero errors (if any) are finally achieved. Error-correcting codes don't have this problem because they correct errors as they occur and then continue to execute the rest of the algorithm.

Ilyas Khan, Quantinuum's chief product officer, affirmed the above in an interview, which is just the first implementation of Quantum Phase Estimation (QPE) technology on logic quantum bits. "Unlike VQE, QPE scales up and provides a long-term theoretical quantum advantage," he said, "While this work is not a fully error-tolerant computation, it is an important step toward that goal."

However, this method of error detection could be useful in the future, especially in low-depth algorithms - as the probability of running them without any errors is reasonable.

Reference link:

[1] https://quantumcomputingreport.com/quantinuum-demonstrates-quantum-error-detection-but-its-not-what-we-would-call-full-fault- tolerance/

[2]https://arxiv.org/pdf/2306.16608.pdf

[3]https://www.quantinuum.com/news/for-the-first-time-ever-quantinuums-new-h2-quantum-computer-has-created-non-abelian-topological -quantum-matter-and-braided-its-anyons

[4]https://www.eetimes.eu/quantum-computing-breakthrough-in-simulating-chemical-molecules/