Quanta: “Neven’s Law” forecasts quantum supremacy

Rapid improvement at Google’s Quantum AI Lab has led to what’s being called “Neven’s law,” a new kind of rule to describe how quickly quantum computers are gaining on classical ones. The rule began as an in-house observation before Hartmut Neven, director of the Lab, mentioned it in May at the Google Quantum Spring Symposium. There, he said that quantum computers are gaining computational power relative to classical ones at a “doubly exponential” rate — a staggeringly fast clip.

With double exponential growth, “it looks like nothing is happening, nothing is happening, and then whoops, suddenly you’re in a different world,” Neven said. “That’s what we’re experiencing here.”

The doubly exponential rate at which, according to Neven, quantum computers are gaining on classical ones is a result of two exponential factors combined with each other. The first is that quantum computers have an intrinsic exponential advantage over classical ones: If a quantum circuit has four quantum bits, for example, it takes a classical circuit with 16 ordinary bits to achieve equivalent computational power. This would be true even if quantum technology never improved.

The second exponential factor comes from the rapid improvement of quantum processors. Neven says that Google’s best quantum chips have recently been improving at an exponential rate. (This rapid improvement has been driven by a reduction in the error rate in the quantum circuits. Reducing the error rate has allowed the engineers to build larger quantum processors, Neven said.) If classical computers require exponentially more computational power to simulate quantum processors, and those quantum processors are growing exponentially more powerful with time, you end up with this doubly exponential relationship between quantum and classical machines.

“I think the undeniable reality of this progress puts the ball firmly in the court of those who believe scalable quantum computing can’t work,” wrote Scott Aaronson, a computer scientist at the University of Texas, Austin, in an email. “They’re the ones who need to articulate where and why the progress will stop.”

[Ed. note: Fintech Capital Markers attended a Cyber Week event focused on quantum security, where the topic of this article came up, and with very cynical overtones. Referring to projects in anticipation of the risks of quantum computers to cryptography, a speaker said: “Don’t allow the hype/math/physics/science-oriented arguments to distort the priorities as a risk manager.” In other words, keep the risks of the threat in perspective to what’s actually happening in practice, which requires far more testing and engineering. At the same time, the CISO of a European bank was a delegate, and speaking on the sidelines told us that quantum security is a concern, and steps are being taken to address the inevitable, now. The conversations we hear around “quantum supremacy” sound eerily familiar to those of the “Singularity” in the artificial intelligence context.]

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