Non-repeating tile patterns can protect quantum information

This extreme fragility may make quantum computing seem hopeless. But in 1995, applied mathematician Peter Shor Discover A smart way to store quantum information. His coding had two main characteristics. First, it can tolerate errors that only affect individual qubits. Second, it came with a procedure for correcting errors when they occur, preventing them from accumulating and derailing the calculation process. Shor's discovery was the first example of a quantum error-correcting code, and its key properties are the hallmarks of all such codes.

The first property stems from a simple principle: confidential information is less vulnerable when it is divided. Spy networks use a similar strategy. Each spy knows very little about the network as a whole, so the organization remains safe even if an individual is caught. But quantum error correction codes take this logic to the extreme. In a quantum espionage network, no spy would know anything at all, yet they would know a lot together.

Each quantum error correction code is a specific recipe for distributing quantum information across many qubits in a collective superposition. This procedure effectively converts an array of physical qubits into a single virtual qubit. Repeat the process several times with a large set of qubits, and you will get many virtual qubits that you can use to perform calculations.

The physical qubits that make up each virtual qubit are like those unsuspecting quantum spies. Measure any one of them and you will know nothing about the state of the virtual qubit it is part of, a property called local indistinguishability. Since each physical qubit does not encode any information, errors in individual qubits will not corrupt the computation. Important information is everywhere in one way or another, but nowhere in particular.

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“You can't bind it to any individual qubit,” Cubitt said.

All quantum error correction codes can accommodate at least one error without any impact on the encoded information, but they will all eventually give up as errors accumulate. And here begins the second feature of quantum error correction codes, which is actual error correction. This is closely related to local indistinguishability: since errors in individual qubits do not destroy any information, it is always possible Reverse any error Using established procedures for each code.

Taken for a ride

Zhi Li, a postdoctoral researcher at the Peripheral Institute for Theoretical Physics in Waterloo, Canada, was well versed in quantum error correction theory. But the topic was far from his mind when he started a conversation with his colleague Latham Boyle. It was the fall of 2022, and the two physicists were on an evening shuttle from Waterloo to Toronto. Boyle, an expert in non-cyclical tiling who lived in Toronto at the time and now works at the University of Edinburgh, was a familiar face on those shuttles, which often get stuck in heavy traffic.

“Normally they can be pretty miserable,” Boyle said. “This was like the greatest ever.”

Before that fateful evening, Lee and Boyle were aware of each other's work, but their areas of research did not directly overlap, and they had never had a one-on-one conversation. But like countless researchers in unrelated fields, Lee was interested in non-periodic tiles. “It's very hard not to be interested,” he said.

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