Designing more efficient quantum circuits with Claude

What it claims

Claude Mythos 5, working in a closed loop against an automated correctness-and-cost evaluator, produced circuits for eight quantum primitives (chemistry, optimization, quantum simulation, number theory, numerical computing). Each design used both fewer qubits and fewer gates than the best previously published construction. The page attributes the gains to new structural or mathematical insights rather than tuning of existing designs. Two examples are given:

• Point addition. It finds a new family of reversible modular-inversion circuits. One of these uses 12% more qubits but 17x fewer gates than the smallest previous design.
• DQI decoder. Its Reed–Solomon decoder for decoded quantum interferometry uses 12x fewer gates than Google's construction.

How it works

Setup. Each task is a plain-language brief. Point addition got one paragraph. The evaluator checks correctness, which works because each input has one definite, classically checkable output. It scores designs on qubits × gates. The brief requires several qualitatively different approaches developed in parallel. Human input was limited to the brief and occasional prompts to "think more broadly."

flowchart LR
  B[Plain-language brief] --> P[Parallel candidate designs]
  P --> E{Evaluator: correct?}
  E -- no --> P
  E -- yes --> S[Score qubits × gates]
  S --> P
  H[Occasional human 'broaden search' prompt] -.-> P

Divsteps inversion. A naive reversible version of divsteps must store the branch choice made at every iteration, which costs a lot of qubits. The process went like this:

1. Claude first tried guessed rules for decoding the branch from the current number pair. These worked on small cases but failed at 256 bits.
2. It then proved new algebraic identities about the iteration and derived an exact decoding rule.
3. It checked the rule in large-scale simulation and formalized it in Lean.

Decoding costs gates, so a tunable threshold between storing and decoding branch information yields a Pareto family of designs between the two extremes.

DQI decoder. The approach changed at three levels:

1. Method. It replaced the extended Euclidean algorithm with Berlekamp–Massey, which runs a fixed number of identical rounds. The previous design had to pad to worst-case rounds and execute every operation in every round.
2. Architecture. It reconstructs most temporary values from the circuit's current state instead of storing them.
3. Budget. A few exceptional values cannot be reconstructed. Reserving space for the worst case (35 rounds) would take 665 qubits. Claude wrote a fast simulator, ran 403 million sample decodings, and found that almost every run needs at most one saved value. The circuit therefore reserves 19 qubits.

The page says no single change would have been enough on its own.

Evidence

• Elliptic curve: the result came from one 53-hour run. The page compares this with the FeMoco gate-count reduction, about 50 trillion down to about 340 million Toffoli gates, which took many groups eight years.
• DQI: Google Quantum AI estimates put one OPI instance at about three months on the Frontier supercomputer versus roughly an hour with DQI on a future quantum computer. Most of that hour is Reed–Solomon decoding, the step that is now about 12x cheaper.
• The page does not give per-primitive numbers for the other six tasks. Those are only referenced to a figure and to the arXiv paper.

Limits

• Probabilistic decoder. About 1 run in 10,000 needs more than the one reserved slot and fails. The page says this is within the task's allowed error rate. Check that tolerance before reusing the circuit elsewhere.
• Cost metric. Qubits × gates is a proxy for runtime. The results also cover only primitives whose correctness is classically checkable per input.
• Not fully autonomous. Claude defaulted to conservative, well-known approaches and repeatedly re-checked results. Novel ideas needed the parallel-approaches requirement and human prompts to broaden the search.
• Scope. The work covers circuit design only. Error-correction codes, decoders and hardware control are not addressed; the page raises joint optimization of these only as a possibility.
• No artifacts. The page links no code or circuits. Details are deferred to the arXiv paper.