Quantum Error Correction goes FOOM

In this post: why I expect the maximum achievable qubit quality to increase drastically in the next few years. In 2014, the John Martinis group at UCSB performed an experiment where they stored a classical bit using their quantum computer. They protected the bit with a 9 qubit quantum repetition code . The protected bit had a half life of roughly 100 microseconds. Clearly that’s not competitive with classical storage... but the goal of the experiment wasn’t to hit a high number. The goal was to perform a demonstration of the fledgling power of quantum error correction. In particular, the 9 qubit rep code had a longer lifetime than the individual physical qubits, and also a longer lifetime than the 5 qubit rep code that they also tried. It hinted that qubit quality could be solved using qubit quantity. Later experiments by the same group (now at Google) improved on this starting point. In 2021, it was a 21 qubit rep code with a half life of 3 milliseconds. Then, in 2023, it was a 51 qubit rep code with a half life of 300 milliseconds. Most recently, in 2024, it was a 59 qubit rep code with a half life of 2 hours. Let’s plot this data: ( view with semilog scale instead) That’s quite the plot, right? There’s a huge lull and then... FOOM! It took nearly a decade for the half life to approach one second, and then one year later it’s suddenly measured in hours?! I know why it happens, but I still find it surprising. Here’s a simple model that explains the FOOM. The lifetime $L$ of a repetition code grows like $L = C \lambda^q$ (see equation 11 of “Surface codes: Towards practical large-scale quantum computation” ). Here $q$ is the number of physical qubits, $\lambda$ is a measure of qubit quality, and $C$ is a starting constant. Suppose quality is held fixed at $\lambda = 2$ and qubit count doubles each year (meaning $q = 2^t$). Then $L$ grows superexponentially : The first stacked exponential is qubit count vs years, due to the assumed Moore’s-law-like growth. The second stacked exponential is error rate vs qubit count, due to technical details of how quantum error correction works that I’m not going to go into. What do you get when you stack two exponentials? A lull followed by a FOOM. In practice, things are a bit more complex than a superexponential. There are “hurdles” that place ceilings on the lifetime of error corrected objects. You discover these QEC hurdles due to the superexponential not holding, and you get mini FOOMs as you fix them. A mundane example of a QEC hurdle is, if you don’t have backup generators, your qubits can’t live longer than the time between power outages. Installing backup generators would allow the lifetime to increase, until it becomes limited by whatever the next QEC hurdle is (such as asteroid strikes). An important QEC hurdle is leakage. During operation, superconducting transmons can get...

Preview: ~500 words