| When you save a file on your computer and step away for a few minutes, you don't need to worry that your work will be utterly garbled when you return. Things are not so simple for researchers building quantum computers. These machines, powered by the counterintuitive laws of quantum physics, can theoretically solve certain problems far faster than their ordinary "classical" cousins. But their elementary building blocks, called quantum bits or qubits, are extremely fussy — the slightest disturbance can induce errors that can easily derail a computation. To realize the promise of quantum computing, researchers will need to get these errors under control by using quantum error correction.
The heart of quantum error correction is a simple principle: redundancy, redundancy, redundancy. The first step is to devise a recipe, called a quantum error-correcting code, that uses many error-prone "physical" qubits to encode each of the "logical" qubits that actually perform computations. Researchers can then use clever tricks to diagnose and correct errors. The same basic idea is routinely used to protect ordinary classical information on CDs and hard drives, as I discussed in this newsletter last August.
Yet quantum error correction is far more challenging than its classical counterpart. One reason is simply that qubits are more delicate than classical computing hardware. It's not just a matter of shielding qubits from environmental disturbances. Every act in a computation, including those involved in error correction, can trigger new errors. In addition, qubit errors come in two distinct flavors, each of which requires a different kind of error correction. Finally, quantum measurement is inherently disruptive — checking any qubit to diagnose errors will spoil any quantum computation in progress. That means researchers must snoop for errors indirectly, without ever measuring the qubits that store their data. Researchers have concocted many different quantum error-correcting codes to tackle these challenges. In 2021, Katie McCormick explained how one of the most iconic codes works.
These are formidable challenges, and researchers still have a long way to go. But quantum error correction is one of the most active areas of quantum computing research. Industry labs are steadily driving error rates down and scaling up error-correcting codes to work with ever-larger arrays of qubits, while academic researchers are devising new codes and uncovering curious connections to far-flung areas of math and physics.
What's New and Noteworthy
The promise of quantum error correction hinges on one critical assumption: The more physical qubits you use to encode each logical qubit, the more robust your logical qubits will be. But adding more qubits also introduces more potential sources of errors. Scaling up to bigger codes only helps when the error rates of individual physical qubits are below a threshold that's specific to each code. Last year, I covered a milestone result in which a team of Google researchers presented clear evidence that they'd crossed this error threshold for a popular error-correcting code called the surface code. They compared progressively larger versions of the surface code and saw that adding more qubits reduced the error rate.
The surface code used in the Google team's demonstration has many attractive features, including a relatively high error threshold. But it requires a lot of qubits to reduce error rates to the extremely low levels that quantum algorithms demand — thousands of physical qubits for each logical qubit. In 2023, Charlie Wood wrote about a promising development for an alternative approach based on "low-density parity check" (LDPC) codes. Two groups of researchers used computer simulations to show that LDPC codes can get away with far fewer physical qubits than surface codes. It remains to be seen whether researchers can realize this promise with real hardware.
The study of quantum error correction has also led researchers to some surprising places. In 2019, Natalie Wolchover wrote about intriguing hints that the mathematics of quantum error correction might help researchers understand the origins of space-time. And last year, I wrote about two researchers who discovered a link between quantum error correction and aperiodic tilings — geometric patterns that can cover an infinite plane without ever repeating, and which have their own connections to fundamental physics. "There are deep roots connecting these different things," the physicist Felix Flicker told me. "This tantalizing set of connections is begging to be worked out." | 
