Quantum computing has a habit of announcing progress long before it announces a useful machine. This time the progress is real but narrow: Anthropic's Claude Mythos 5 has produced quantum circuits that, on some tasks, need roughly an order of magnitude fewer operations than the best published versions. The authors are careful to add that this does not put a working quantum computer any closer to your desk.
How the loop worked
The setup was less dramatic than the headline suggests, and more interesting for it. The model proposed a circuit. A program then checked whether the circuit was correct and calculated its computational cost. The model took that score, refined the design, and tried again. No human stepped in between iterations.
Over the project, Claude optimised eight basic computational procedures. They serve problems in chemistry, optimisation, simulation of quantum systems, number theory and numerical methods.
Elliptic curves and the cost of forgetting
The most eye-catching result concerns elliptic curves, the mathematical objects that underpin a good deal of modern cryptography. Working with them requires computing a modular inverse, and on a quantum machine that has to be done reversibly. Claude spent 53 hours on the problem.
Reversibility is the awkward part. A normal program can throw away intermediate values when it finishes with them. A quantum circuit has to be runnable backwards, so nothing can simply be deleted. The classical algorithm known as divsteps is a natural candidate, but earlier quantum versions had to store the full history of its conditional branches. That history costs extra qubits, the quantum counterparts of bits.
Claude found a way to reconstruct that history from the intermediate numbers instead of storing it. To do so it derived new algebraic identities and a formula for recovering the sequence of operations. The authors checked the result with numerical simulations, and the mathematical claim was also formalised in Lean, a system for verifying proofs.
The outcome is a trade-off rather than a free lunch. One new variant uses 12% more qubits than the most compact earlier version, but needs 17 times fewer quantum gates. Which side of that bargain is better depends on what a developer is short of, and now there is a menu to choose from.
A leaner decoder for optimisation
The second result concerns a decoder for Decoded Quantum Interferometry (DQI), an algorithm aimed at optimisation problems. The earlier design, from Google, relied on the extended Euclidean algorithm. Claude swapped it for Berlekamp-Massey decoding and also trimmed the amount of intermediate data that has to be kept.
The gate count fell by a factor of 12 compared with Google's previous construction.
The memory story is the more candid one. Reserving space for the worst case would take 665 qubits. The new circuit allocates 19. That is a gamble, and the authors document the odds. Based on 403 million simulations, roughly one run in 10,000 hits an exceptional case that needs more memory than was set aside, and the computation fails to finish. According to the authors, that failure rate sits within the error the problem can tolerate.
In other words, the circuit has been designed to be wrong occasionally, on purpose, in exchange for being dramatically smaller. Engineers will recognise the genre.
The FeMoco yardstick
To put the scale of possible savings in context, the report points to FeMoco, an iron-sulphur cluster inside the enzyme nitrogenase, which helps turn atmospheric nitrogen into ammonia. Estimating its ground-state energy on a quantum computer is a standard benchmark problem.
In 2017 the estimated cost was about 50 trillion Toffoli gates. After a series of algorithmic improvements from various research groups, the estimate dropped to 340 million, a reduction of about 150,000 times. The authors insist this should not be credited to Claude. It is the product of years of work by the wider community, and the model's contribution is a further step along a path others built.
What this does not show
The caveats are not buried, which is refreshing. There are three of them.
- Scope. The work covers the design of individual circuits. It does not touch the other parts of a fault-tolerant quantum computer, including error correction and control of the physical hardware.
- Verifiability. The method works best where an ordinary computer can efficiently check that a circuit is correct. Problems without a cheap checker are a harder fit for this loop.
- Timidity. Claude tended to be overly cautious and favoured familiar approaches. To get genuinely new solutions, the researchers had to require it to explore several different options in parallel.
That last point is worth a moment. The model that found new algebraic identities also needed to be told, more or less, to stop playing it safe.
A fair reading
The sober takeaway is that automated search with a strict referee is a credible way to squeeze gate counts, at least where correctness can be machine-checked. The result also changes some design trade-offs, such as spending a few more qubits to save a great many gates. It does not change the fact that nobody has yet built the machine on which these circuits would run.
One could say the qubits are cheaper on paper now. The hardware, as ever, still has to turn up.