Magic states play a crucial role in executing the functions necessary for effective and error-corrected quantum computing. The process of generating these states can consume a significant portion of a system’s total resources. According to a report from Google’s research team, cultivation acts as a filtration method: researchers input a noisy quantum state, perform synchronized measurements, and reject outcomes that show errors.
A previous preprint from the team indicates that the probability of logical errors during state injection stands at approximately 0.44%, while the upper limit for errors in cultivated states is around 0.01%. This high-fidelity benchmark involved two extra rounds of cultivation and three cycles of quantum error correction to validate the state. Cultivation enabled the preparation of a single logical qubit, with Willow housing 105 physical qubits.
The Threat to Cryptographic Keys
The significant danger to the transaction signatures of Bitcoin and Ethereum arises from Shor’s algorithm, which can solve the elliptic-curve discrete logarithm problem, enabling potential attackers to compute a private key from its corresponding public key.
Google’s resource study in March examined this issue within the secp256k1 curve, utilized for these signatures. The two circuit configurations examined require as many as 1,200 logical qubits and 90 million Toffoli gates, or alternatively, 1,450 logical qubits along with 70 million gates. Logical qubits are advanced units that ensure error correction, constructed from numerous physical qubits, while Toffoli gates are key computational operations that help assess processing time.
Under Google’s faster simulation, an attack would take roughly nine minutes post-public key exposure on a machine equipped with fewer than 500,000 physical qubits, assuming the use of superconducting hardware and advanced computation of the algorithm’s key-independent initial phase. These are theoretical resources and do not reflect actual capabilities. The Defiant reported on this study back in March.
This research already took into account the cultivation proposal to estimate the costs associated with magic-state production. The 40-fold improvement highlighted in Science pertains to state error measurements and does not indicate a 40-fold decrease in the qubit count or the processing time for breaking a key.
“This doesn’t immediately advance the timelines for Q-Day,” Pruden shared on X. “However, it does provide experimental validation for one of the core assumptions underlying those projections, thus enhancing their credibility.” Project Eleven is actively working on migration strategies for post-quantum technologies.
In its recent statement, Google emphasized its focus on generating usable quantum states rather than announcing a new capability for breaking encryption. Researchers have also shown the ability to transfer states between two forms of error correction: from a distance-3 color code to a distance-5 surface code. However, scaling these processes remains an incomplete task: “We still need to prove magic state cultivation at a larger scale to make it feasible for practical quantum computing,” remarked Google researchers Emma Rosenfeld and Craig Gidney.