Earlier this week, the Google AI Quantum team announced it has made additional progress on quantum error correction and had just published a paper in Nature magazine with the technical details. In brief, to solve the problem of relatively high error rates in a single quantum physical qubit, engineers can group together several of the physical qubits together to create a single logical qubit which, if done properly, will show a decreased error rate from the physical qubit.

What Google demonstrated was that the logical error rate of a logical qubit composed of 49 physical qubits (code distance 5) was lower than the error rate of a logical qubit composed of 17 physical qubits (code distance 3). While it may appear obvious that when you scale up the number of physical qubits the error rate will decrease, in practice it is not so easy because the more physical qubits you add, the higher the probability that some of those physical qubits will incur errors and the larger code won’t show an improvement in the error rate. What the Google AI team demonstrated for the first time is that with careful engineering it is indeed possible to scale the error correction codes. In their experiment, they reduce the logical error rate from 3.028% for a 17 physical qubit implementation to 2.914% for a 49 physical qubit implementation. Although the improvement is extremely small and nowhere near what would be needed for a practical error corrected quantum computer, it is at least, going in the right direction.

Although a lot of hoopla was generated in the popular press about this, regular readers of the Quantum Computing Report may remember that we first reported on this research in our July 2022 Research Roundup report when this was first posted on arXiv as a pre-print paper. It’s still an impressive accomplishment, but should still be regarded as one of many milestones that the industry will need to achieve in order to have a fully corrected fault tolerant quantum computer. This one accomplishment won’t change the industry overnight and it will still take many years to reach the final goal.

We should note that error correction is one of the most active areas of research within quantum computing and many groups have also achieved significant results. (However, those other teams may not have spent as much money as the Google PR team did in promoting the accomplishments!) Notable papers we have seen in the past few years include one from IonQ, University of Maryland, and Duke University titled Fault-Tolerant Operation of a Quantum Error-Correction Code which encoded a logical qubit from 13 physical qubits to show an improvement. Another one came from Quantinuum titled Implementing Fault-tolerant Entangling Gates on the Five-qubit Code and the Color Code which demonstrated entangling gates between two logical qubits done in a fully fault-tolerant manner using real-time error correction. And also a previous Google paper titled Exponential suppression of bit or phase errors with cyclic error correction which demonstrated an improvement in reducing either bit-flip error or phase-flip errors, but not both at the same time.

We expect to see many more similar papers from multiple parties over the next few years with each making one more step forward. To put the magnitude of the problem in perspective, some of the really significant quantum applications that we always talk about will require programs that contain hundreds of thousands of logical gates with each gate having a logical qubit error rate of perhaps 10-15. Today, we are roughly at the 10-3 level so an improvement of over 10 orders of magnitude is still required. So a lot of research and hard work will be required in pretty much all areas of the system including architecture, algorithms, material science, fabrication, control electronics, mechanicals, and integration with the classical processor.

February 25, 2023