On October 15, 2026, Google Quantum AI announced experimental results for "magic state cultivation," a technique for producing the high-precision "magic states" that quantum computation requires, using its superconducting quantum processor Willow. The study, led by Emma Rosenfeld, Craig Gidney, and colleagues, was published in Science the same day. Compared with conventional state injection without cultivation, it reduced errors by roughly a factor of 40. A preprint of the paper was released in December 2025, so this announcement coincides with publication in a peer-reviewed journal. However, a closer look at the fraction of trials that yielded a high-precision state, and at the step of handing the generated state over to an actual computation, reveals both progress toward practical use and challenges that remain unresolved.
Cultivating the magic states behind quantum computation in a small code
In an error-corrected quantum computer, information is spread across many physical qubits and protected as a single "logical qubit." An error-correcting code, such as the surface code, defines how information is encoded and how errors are detected. Research on quantum memory with Willow so far has mainly aimed at preserving information without corrupting it.
However, to run arbitrary quantum computations while keeping information protected, the available set of operations must also be complete. "Clifford operations," which are easy to handle in codes such as the surface code, are not enough to construct arbitrary quantum computations. What is needed is a special quantum state used for "non-Clifford operations" such as the T gate. This is called a magic state, and it is prepared in advance and consumed partway through a computation. Because a used state cannot be reused, larger computations require a continuous supply. The introduction of the experimental paper also identifies the resources needed for this supply as a key research problem.
The leading conventional approach has been "magic state distillation," which extracts a higher-precision state from multiple lower-precision ones. But the operations used in distillation must themselves be protected from errors, which requires many physical qubits and a lot of processing time. A large area has to be set aside not only for the region where the quantum computation runs, but also for producing the necessary magic states.
Magic state cultivation, proposed in 2024 by Craig Gidney, Noah Shutty, and Cody Jones, refines a state held in a single logical qubit within a small code and then enlarges the code to protect it. Zero-level distillation, studied by Tomohiro Itogawa, Keisuke Fujii, and colleagues at the University of Osaka, which refines states at the physical-qubit stage, is another piece of prior work related to this idea. In this study, the team used part of Willow, which has 105 physical qubits, and began cultivation from a distance-3 color code. Here, "distance" is a measure of how many errors a code can withstand, not a count of qubits. Color codes have the advantage of making it easier to assemble the logical-state measurements that cultivation requires.
In the experiment, a noisy state is first injected into the code, and ancilla qubits are used to measure along the direction of the target magic state. Only trials in which the measurement result corresponds to the desired state and no problems turn up in other error checks are kept. This "postselection" removes unsuitable states and raises the precision of those that remain. The team also built in an operation that runs the circuit in reverse and additional checks to detect errors that arise during refinement. The key point is that the circuit was designed to detect not merely repeated measurements, but also errors contained in the measurements themselves.
What 99.99% fidelity and an 8% acceptance rate mean
When a state was injected without cultivation, the logical error probability was 4.4(2)×10⁻³. That is 0.44%, with a statistical uncertainty of about 0.02 percentage points. With cultivation, errors fell substantially, and the team evaluated an upper bound on the state's error at 1(1)×10⁻⁴. The abstract in Science reports that "fidelity," which expresses the degree of agreement with the ideal state, is at least 0.9999(1). This notation indicates a value of 99.99% accompanied by a statistical uncertainty of about 0.01 percentage points; it is not an exact, error-free value. Nor is it a figure for the success rate of an entire quantum computation. The roughly 40-fold error reduction and the 99.99% fidelity are evaluation results within a small color code, and they do not guarantee that the same precision will be maintained after moving to a surface code.
Based on Section II and Figure 3 and Section III and Figure 4 of the authors' public version by Rosenfeld et al., the experimental steps and results can be summarized as follows. The fidelity and acceptance rate are also given in the abstract in Science.
| Experimental step | Result | Conditions for reading the figure |
|---|---|---|
| State injection without cultivation | Error probability of 0.44%, uncertainty of about 0.02 percentage points | Baseline for comparison with the cultivated case |
| State preparation with cultivation and fidelity evaluation | Estimated lower bound on fidelity of 0.9999(1) | For the whole circuit including preparation and measurement; about 8% of trials accepted |
| Transition from distance-3 to distance-5 code | Features of the refined state confirmed in the destination code | Errors during idle time in the destination code limit precision |
The roughly 40-fold improvement is the result of comparing state injection with cultivated state preparation under specific evaluation conditions. It does not mean that errors across the whole chip fell to one-fortieth, nor that the number of required qubits fell to one-fortieth. The acceptance rate of about 8% also calls for caution. In this experiment, trials showing signs of error were discarded, including not only the state-generation step but also the additional cultivation circuits and error-correction checks used to examine precision. The 8% is therefore the acceptance rate for data that includes the evaluation circuits, and it cannot be directly compared with the yield of a future magic state supply device. To judge practicality, one has to consider not only the precision of the resulting state but also how many trials were discarded to achieve it.
Why the quantum state came out as a "physically impossible value"
In early cultivation tests, the research team ran into a problem: the quantum state inferred from measurement results was physically impossible. Picturing a qubit's state as a point inside the "Bloch sphere," there were cases where the inferred state fell outside the sphere. The device, of course, did not violate the laws of quantum mechanics. The problem lay in the assumptions of the method used to infer a quantum state from measurement results.
Ordinary "state tomography" measures identically prepared quantum states from different directions and combines the results to reconstruct the state. However, when postselection, which discards trials in which errors were detected, is combined with coherent noise, in which the phase drifts slowly, the set of accepted trials can change depending on the measurement direction. Combining measurement results selected under different conditions as components of a single state can lead to inferring a purer state than the real one. The paper's supplementary material shows that this problem can arise even when readout is ideal and the number of measurements is sufficiently large.
To address this, the team developed "kickback tomography." It exploits the fact that the cultivation circuit itself measures along the magic state's direction, and checks the prepared state with an additional cultivation circuit and error-correction circuit. Rather than combining measurements along different axes afterward, it evaluates agreement with the state of interest directly in the same circuit, so it avoids inconsistencies caused by phase noise.
The new measurement method also greatly reduces the number of measurements required. According to the paper, evaluating an error of about 10⁻⁴ with an uncertainty comparable to that error would require about 10⁸ measurements with ordinary tomography, versus about 10⁴ with kickback tomography as a guide. Measuring the direction of the target state directly reduces statistical scatter. However, this compares the number of measurements needed for precision evaluation; it does not mean that the speed of magic state generation or the total experiment time improves by the same proportion.
The 99.99% fidelity this time is backed not only by the technique for producing a high-precision state but also by the technique for measuring that precision without overestimating it. The result suggests that as the precision of logical qubits rises, the measurement methods used to evaluate physical qubits will also need to be revisited.
Idle-time errors remain beyond the "grafting"
Even a magic state refined within a small code loses precision if simply held, because logical errors occur while it waits. Protecting the state until it is used in an actual computation requires moving it into a larger code. The "grafting" that Google tested this time is an experiment to verify this connection.
The team extended a state refined in a distance-3 color code into a code that can connect to a distance-5 surface code. This confirmed on real hardware a division of roles in which the color code produces a high-precision state and hands it off to a quantum computer that uses the surface code. In Section III of the paper, the team also compared the results with simulations of a circuit containing 54 qubits and confirmed that the features of the refined state carry over to the destination.
However, when points close to the T state were evaluated after the code transition, the state's purity was almost the same as without cultivation. In both cases, precision was limited by idle-time errors occurring in the distance-5 destination. In other words, even though cultivation in a small code reduced errors, errors arising in later steps cancelled out the hard-won improvement.
Furthermore, a structure derived from the color code remains in the destination code. In this experiment it was handled with a decoding method called "Tesseract," and the step of switching to the matching-based decoding used in ordinary surface codes was not verified. Executing a T gate in real time using the refined magic state also remains a future task. Grafting has confirmed that magic states can be handed between different codes, but practical use will require keeping error rates low during and after the transition.
Resource costs and selection methods are the questions for practical use
The 2024 proposal for magic state cultivation estimated, through numerical evaluation assuming uniform depolarizing noise, that low logical error rates could be reached with roughly an order of magnitude less "qubits × error-correction rounds" than conventional methods. The possibility of reducing both the number of qubits and the processing time underpins expectations for cultivation. However, the Willow experiment did not measure this resource reduction.
For practical use, deciding which trials to accept among the generated states is also a challenge. The unreviewed paper "The practical cost of magic state cultivation," released on October 5, 2026 by Rohan Mehta, Mikhail Lukin, and colleagues, focuses on the selection methods used in conventional resource estimates. In experiments and simulations, the quantum state can be read out at the end and that result used to pick good trials. But performing that readout during an actual computation would destroy the very magic state that is about to be used. A practical supply device must therefore decide whether to accept a state using only the error-detection information obtainable while keeping the state intact.
The team proposed a method called "Caliper" for selecting states under this constraint. In numerical evaluations, depending on the code used and the target precision, it sometimes achieved efficiency close to conventional resource estimates, while in other cases a larger code or longer processing time was needed to reach the same low error rate. In other words, the practical constraint of having to judge quality without destroying the state could shape the final cost of supplying magic states.
Caliper's evaluation has limitations too. To simplify the calculation, the simulations used the Y state in place of the T state that is actually needed, and a rigorous evaluation combining the T state with this selection method remains a future task. This does not negate the cultivation demonstration on Willow; rather, the research clarifies what additional verification is needed to move from generating high-precision states in a small code to continuously supplying states usable in real quantum computation.
Google's research team also lists the move to larger codes and real-time T-gate execution as future tasks. What matters is not only generating high-precision magic states but also whether states can be selected without being destroyed and handed to computations while maintaining precision in larger codes. If these steps can be carried out end to end, the resource savings from magic state cultivation could be evaluated in terms of the number of qubits and processing time actually required for quantum computation.