Google makes “magic states” 40 times more reliable on its Willow quantum chip

Eight attempts in a hundred. That is the share Google’s Willow chip keeps at the end of the process; the other 92 are thrown away. The waste is deliberate, and it is the price of a result Google Quantum AI published in Science on Thursday, October 15: “T-states” with a logical fidelity of 99.99%, meaning at most one error in 10,000, and roughly 40 times fewer errors than without the technique. It is called magic state cultivation.

The same day, Alphabet chief executive Sundar Pichai posted on X: “Some magical progress towards ‘magic state’ in quantum!” The pun hides a real engineering problem, identified as far back as 2004, that researchers have been chipping away at for some twenty years.

An essential ingredient that can be used only once

A quantum computer cannot compute with just any operations. Some of them are easy to shield from errors, the curse of these machines, where the slightest temperature shift or electrical interference knocks qubits off course. But those “easy” operations are not enough. A classical computer can readily simulate a program built only from them, which means they offer no advantage on their own.

The missing piece is the so-called T gate. It cannot be carried out reliably in a direct way; instead, it is performed by consuming a quantum state prepared separately, the magic state. Each one works only once. A machine running a serious algorithm would therefore have to churn them out continuously, like a factory feeding an assembly line. By some estimates cited by Google, as much as 95% of a quantum computer’s capacity could go to that production alone.

The standard approach, “distillation”, takes several imperfect states and extracts a single purer one, at the cost of a large number of qubits. Cultivation, proposed in 2024 by Google researchers Craig Gidney, Noah Shutty and Cody Jones, works more like a sieve. A noisy state is injected into a small region of the chip and put through a series of coordinated measurements that catch defects; failed attempts are discarded, and the survivor is “grown” into a larger error-correcting code. Until now, the idea had only been tested in theory and simulation.

Months lost to a measuring tool

The result did not come easily. In a post on Google’s blog, Emma Rosenfeld, a research scientist at Google Quantum AI, and Craig Gidney recount that early data seemed to contradict physics. It took months to trace the cause to a wrong assumption in the benchmarking method itself. Drift in electrical equipment and temperature swings in the lab produced slow noise that skewed comparisons and could make the states look better than they were.

The team tightened control of the chip and devised a benchmarking technique that uses cultivation to measure itself, yielding a lower bound on fidelity rather than a flattering figure. It also handed the final tuning step to a reinforcement-learning algorithm, which improved both the circuit’s error probability and the share of retained attempts by about an order of magnitude, according to The Quantum Insider.

« We still need to demonstrate magic state cultivation at a larger scale. »

Emma Rosenfeld and Craig Gidney, Google Quantum AI, on Google’s blog

The authors are open about the limits. When states were held through long rounds of error correction, the logical error rate came out about seven times higher than simulations predicted. The likely culprit is “leakage”, when a qubit slips out of the two states it is meant to occupy, a phenomenon the simulations left out and the tested circuits did not correct. And an 8% yield is low: on a large machine, the sieve will have to run fast and in parallel.

Fewer qubits per useful qubit: a preprint’s promise

The other bill in quantum computing is for qubits. Getting a single reliable “logical” qubit requires many imperfect physical ones that keep watch on each other. With the surface code, the most widely used method and the one Google runs on Willow, that ratio runs into the hundreds, even the thousands, at high levels of protection.

A preprint posted to arXiv on October 2 by 14 researchers from Google Quantum AI, Google DeepMind and MIT, including Oscar Higgott, Craig Gidney, Pushmeet Kohli and Hartmut Neven, takes another route. Instead of one huge chip, the processor would be split into small flat modules of about a hundred qubits, joined by a few fixed links along their edges. On that architecture, the authors build so-called “hyperbolic” codes, whose geometry packs more logical qubits into the same number of physical ones.

The numbers need careful reading. Simulations using two decoders, including DeepMind’s AlphaQubit neural network, show at least a tenfold cut in physical qubits compared with the surface code, even when links between modules are ten times noisier than operations on the chip. The “more than 30 times” highlighted by Quantum Computing Report is an extrapolation to larger systems, with a code encoding one logical qubit for every 16 physical ones. Nothing has been built: this is theory and simulation, not yet peer-reviewed.

What this changes, and what it doesn’t

Taken together, the two papers go after the two cost centres that make a useful quantum computer so enormous on paper: memory, with denser codes, and magic-state production, with a method that would take up a small slice of the chip rather than most of it. Flat modules also make an industrial case, since they keep the manufacturing advantages of planar chips and avoid long wire crossings on the chip.

But Willow is still a 105-qubit machine, and the experiment in Science uses about fifty of them to produce one state at a time. Google has announced no timeline, customers or revenue for its quantum business. The Quantum Insider puts it cautiously: the work does not establish that the resource problem has been solved at a practical scale. The next test is the one the authors themselves call for: running cultivation on a bigger chip, for longer, without leakage driving errors back up.