The Pulse
Researchers Use AI to Find 564 New Magic-State Factories
A new arXiv paper reports 564 previously unreported magic-state factory classes found through symmetry-guided searches and language-model agents. The catalog includes protocols for producing T, CS and CCZ states, but the authors say further
AI.info Team · Written with AI ·
“Our searches yield 699 factory classes, including 564 new ones.”
Shubham P. Jain, Adam Wills and Shraddha Singh, authors of “Symmetry and AI-assisted discovery of magic-state factories”
The researchers posted their paper to arXiv on October 5, describing a search method that combines mathematical symmetry, language-model agents and deterministic checks to find new protocols for producing magic states. The term “factories” here means quantum circuits, not newly built hardware: each circuit distills noisy input states into fewer, higher-quality states used to carry out non-Clifford operations in fault-tolerant quantum computers.
564 classes beyond earlier catalogues
The paper reports 699 factory classes across distances three through nine, with 564 classified as new. The authors define a class by its input count, output count, distance and output gate, treating outputs related by certain CNOT and phase-gate transformations as equivalent. They call a class new if no published protocol specifies it and it falls outside the range of existing exhaustive classifications.
The catalog contains 493 distance-three classes, 88 at distance four, 69 at distance five and 42 at distance six; the remaining seven span distances seven through nine. The new entries range from 55 to 1,715 inputs, and 320 use 127 inputs or fewer. Their outputs include pure T states as well as entangled combinations of T, controlled-S (CS) and controlled-controlled-Z (CCZ) states.
Distance is the smallest number of faulty input states that can pass every check and still corrupt an output. The authors focus on distance three and above, beyond a previously exhaustively classified range that reached 54 inputs at distance three. They say extending that exhaustive search to the next input count would require an estimated 100 million core-hours, against a cost of the order of 100,000 core-hours for the existing classification.
Agents propose; solvers and verifiers check
The search begins with a binary-matrix representation that lets the researchers describe a factory both as a quantum error-correcting code and as a circuit. They use symmetry to narrow the possible error syndromes, then ask AI agents to suggest promising symmetry groups, syndrome sets—called “parents” in the paper—and code coordinates to remove in a search known as puncturing.
The agents work in repeated rounds. Proposers suggest candidates, deterministic software runs the specified searches, and an independent verifier checks each resulting circuit before it enters the catalogue; the merged catalogue is then reverified as a whole. The verifier derives the output gate and check parities from the circuit, tests the claimed distance, and checks that the declared outputs are genuinely present.
The authors say the agents were Anthropic Claude models throughout: they proposed parents, symmetry groups and search directions and, in later runs, pruned candidates as reviewers. They attribute the framework, search designs, solver, verifiers and acceptance criteria to their own work. That division puts the language models in a proposing role: a candidate did not count as a result until the independent checks passed.
Lower overhead scores still need an architecture test
Among the paper’s highlighted results, the pure-T [[63, 11, 3]] factory has an overhead exponent of 1.589, which the authors call the lowest they know for protocols with no more than 100 inputs. The [[850, 128, 6]] factory has an exponent of 1.057, their best known among explicit pure-T protocols with up to 1,000 inputs. A third, [[1715, 287, 6]], has an exponent below one at 0.998.
The exponent is a measure of how the input cost grows as a factory is repeatedly applied to reduce output error; lower is better within that comparison. It does not establish the total cost of running a factory in a quantum computer. The paper says its T-count measure covers synthesis cost for the output gates, not a factory’s full implementation cost.
Turning the catalog’s input counts and exponents into hardware savings still requires accounting for acceptance probabilities, leading error coefficients and the Clifford circuits that consume the outputs. The reported search also covers a specific class—postselected diagonal CSS protocols—and does not include catalytic or Hadamard-assisted protocols, which could reach different parameters. The researchers make their circuits, search engine, verifiers and campaign notes available as the basis for those comparisons.