Never-Repeating Patterns of Tiles Can Safeguard Quantum Information

This excessive fragility would possibly make quantum computing sound hopeless. But in 1995, the utilized mathematician Peter Shor found a intelligent method to retailer quantum data. His encoding had two key properties. First, it may tolerate errors that solely affected particular person qubits. Second, it got here with a process for correcting errors as they occurred, stopping them from piling up and derailing a computation. Shor’s discovery was the primary instance of a quantum error-correcting code, and its two key properties are the defining options of all such codes.

The first property stems from a easy precept: Secret data is much less susceptible when it’s divided up. Spy networks make use of an analogous technique. Each spy is aware of little or no in regards to the community as an entire, so the group stays protected even when any particular person is captured. But quantum error-correcting codes take this logic to the acute. In a quantum spy community, no single spy would know something in any respect, but collectively they’d know loads.

Each quantum error-correcting code is a selected recipe for distributing quantum data throughout many qubits in a collective superposition state. This process successfully transforms a cluster of bodily qubits right into a single digital qubit. Repeat the method many occasions with a big array of qubits, and also you’ll get many digital qubits that you should utilize to carry out computations.

The bodily qubits that make up every digital qubit are like these oblivious quantum spies. Measure any one in every of them and also you’ll study nothing in regards to the state of the digital qubit it’s part of—a property referred to as native indistinguishability. Since every bodily qubit encodes no data, errors in single qubits gained’t destroy a computation. The data that issues is one way or the other in all places, but nowhere specifically.

“You can’t pin it down to any individual qubit,” Cubitt mentioned.

All quantum error-correcting codes can soak up a minimum of one error with none impact on the encoded data, however they are going to all finally succumb as errors accumulate. That’s the place the second property of quantum error-correcting codes kicks in—the precise error correction. This is carefully associated to native indistinguishability: Because errors in particular person qubits don’t destroy any data, it’s at all times potential to reverse any error utilizing established procedures particular to every code.

Taken for a Ride

Zhi Li, a postdoc on the Perimeter Institute for Theoretical Physics in Waterloo, Canada, was effectively versed within the idea of quantum error correction. But the topic was removed from his thoughts when he struck up a dialog together with his colleague Latham Boyle. It was the autumn of 2022, and the 2 physicists have been on a night shuttle from Waterloo to Toronto. Boyle, an professional in aperiodic tilings who lived in Toronto on the time and is now on the University of Edinburgh, was a well-known face on these shuttle rides, which regularly bought caught in heavy visitors.

“Normally they could be very miserable,” Boyle mentioned. “This was like the greatest one of all time.”

Before that fateful night, Li and Boyle knew of one another’s work, however their analysis areas didn’t straight overlap, they usually’d by no means had a one-on-one dialog. But like numerous researchers in unrelated fields, Li was interested by aperiodic tilings. “It’s very hard to be not interested,” he mentioned.