When solving math problems, we can remove the draft lines after finding the answer. Regular computers also delete temporary results to free up memory. But with quantum computers, this is more complicated: if deleted incorrectly, the machine can ruin the answer.

This is an obstacle when designing quantum circuits. The machine must erase the temporary results to reuse the qubits, but still needs to be able to restore the computational steps that have been performed.

In a manuscript posted on arXiv on October 15, 2026, Andi Gu and three colleagues at Anthropic and Harvard University assigned Claude Mythos 5 eight quantum circuit design problems.

According to the research team, the seven new designs reduce both the number of qubits and the number of Toffoli gates compared to published options. The eighth problem leads to a new reversibility calculation.

Delete temporary results without losing answers

In quantum computers, qubits can be in a superposition state, combining multiple computational capabilities. Therefore, the machine cannot arbitrarily delete temporary results like a regular computer.

To reuse the extra qubits, the circuit must perform reverse calculations to return them to their original state without losing the answer. This technique is called uncompute.

You can imagine it like someone going through a maze: if you write down every turn, it will waste a lot of paper, but if you don't, you have to find a way to find your way back. Quantum circuits also have to choose between saving the computation history and finding a way to restore it.

Claude was assigned to write code that described the circuit. An automated evaluator examines the results, counts the number of qubits and Toffoli gates, then pays points for the model to continue improving.

In a prominent problem involving the addition of two points on an elliptic curve - a mathematical structure used in cryptography - Claude sought to infer the operation just performed from the remaining state, instead of saving the entire calculation history.

The original rules only work with small numbers, but fail when dealing with numbers that are 256 bits long. Claude continues to analyze algebraic relationships to find recovery rules. The team tests using simulation and uses Lean software to verify key mathematical propositions.

After 53 hours of searching, with a problem and some suggestions from humans, Claude created a family of designs: some circuits save qubits, some circuits reduce the number of gates.

Reduce the number of computing gates by 17 times

In the above problem, Claude's design uses 935 qubits and 4.01 million Toffoli gates. Luo and his colleagues' plan requires 838 qubits but uses up to 69.53 million gates.

Thus, Claude uses nearly 12% more qubits to reduce the number of Toffoli gates by about 17 times. Another plan from Schrottenloher requires only 1.9 million gates but uses up to 1,446 qubits.

The numbers show the trade-off between the amount of memory needed and the number of calculations that must be performed. This is the resource savings at the algorithm circuit level, not the results of running time measurements on actual quantum computers.

The team also improved the Reed-Solomon decoder, a tool that helps recover corrupted data in a quantum optimization algorithm.

Claude seeks to restore intermediate results from the current state, thereby reducing the amount of qubits that need to be spared. In 403 million simulations, about one in 10,000 required more than the 19-qubit allowance and could fail. Thanks to changing the algorithm and how to handle temporary results, this design reduces the number of Toffoli gates by about 12 times.

Not tested on quantum computers

The designs are tested using programs and simulations, not yet run on quantum hardware. Lean software only verifies a few key clauses, not covering the entire circuit. The draft has not yet undergone peer review.

Research shows that AI can participate in the search for more effective ways to design algorithms. In a context where qubits are scarce, the ability to roll back computational steps without having to save the entire history can lead to significant resource savings. However, the actual effectiveness still needs to be verified on quantum computers.

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