In quantum computers, the information is contained in qubits that can work through vast numbers of different outcomes, which is not possible with classical computers. In quantum computers, the information is contained in qubits that can work through vast numbers of different outcomes, which is not possible with classical computers. The UK will not let quantum computing talent slip through its fingers and must learn lessons from US dominance of the AI race, the technology secretary has said, as the government announced a £1bn quantum funding pledge. Liz Kendall said the government hoped to retain homegrown quantum startups, engineers and researchers rather than lose them to competing countries, with the US stealing a march on its western rivals in AI. "I do look at what's happened on AI," said Kendall. "I do think we need to learn the lessons and make sure we give our brilliant scientists, spinouts and startups the ability to stay here and make it happen. And that requires a government that is bold and ambitious and confident in these technologies of the future."

The errors that quantum computers make are holding the technology back. Quantum computers won't be truly useful until they can correct their mistakes Quantum computers are already here, but they make far too many errors. This is arguably the biggest obstacle to the technology really becoming useful, but recent breakthroughs suggest a solution may be on the horizon. Errors creep into traditional computers too, but there are well-established techniques for correcting them. They rely on redundancy, where extra bits are used to detect when 0s incorrectly swap to 1s or vice versa.

Algorithms called phantom codes could help quantum computers run complex programs without errors, overcoming a big hurdle for making the technology more broadly useful. Early on, some physicists doubted that quantum computers would ever be useful because they expected these devices to be too prone to hard-to-correct errors. Today, several types of quantum computers exist and have already been used for scientific discovery and exploration. Yet, while progress has been made, researchers have not managed to fully curtail the error-making problem. Quantum computers have finally arrived, but will they ever be useful?

Quantum Algorithms (VQAs) have emerged to obtain possible quantum advantage. In particular, how to effectively incorporate hard constraints in VQAs remains a critical and open question.

Both of the techniques assume bitwise access to the oracle as a classical function.

Large language models (LLMs) can generate structured artifacts, but using them as dependable optimizers for scientific design requires a mechanism for iterative improvement under black-box evaluation. Here, we cast quantum circuit synthesis as a closed-loop, test-time optimization problem: an LLM proposes edits to a fixed-length gate list, and an external simulator evaluates the resulting state with the Meyer-Wallach (MW) global entanglement measure. We introduce a lightweight test-time learning recipe that can reuse prior high-performing candidates as an explicit memory trace, augments prompts with a score-difference feedback, and applies restart-from-the-best sampling to escape potential plateaus. Across fixed 20-qubit settings, the loop without feedback and restart-from-the-best improves random initial circuits over a range of gate budgets. To lift up this performance and success rate, we use the full learning strategy. For the 25-qubit, it mitigates a pronounced performance plateau when naive querying is used. Beyond raw scores, we analyze the structure of synthesized states and find that high MW solutions can correspond to stabilizer or graph-state-like constructions, but full connectivity is not guaranteed due to the metric property and prompt design. These results illustrate both the promise and the pitfalls of memory evaluator-guided LLM optimization for circuit synthesis, highlighting the critical role of prior human-made theoretical theorems to optimally design a custom tool in support of research.

Our code is available at https://github.com/martaskrt/qdeq.

In the following, we introduce GP, GP regression, and BO with an uncompressed notation.