Measurement-based quantum computation (MBQC) is a framework for quantum information processing in which a computational task is carried out through one-qubit measurements on a highly entangled resource state. Due to the indeterminacy of the outcomes of a quantum measurement, the random outcomes of these operations, if not corrected, yield a variational quantum channel family. Traditionally, this randomness is corrected through classical processing in order to ensure deterministic unitary computations. Recently, variational measurement-based quantum computation (VMBQC) has been introduced to exploit this measurement-induced randomness to gain an advantage in generative modeling. A limitation of this approach is that the corresponding channel model has twice as many parameters compared to the unitary model, scaling as $N \times D$, where $N$ is the number of logical qubits (width) and $D$ is the depth of the VMBQC model. This can often make optimization more difficult and may lead to poorly trainable models. In this paper, we present a restricted VMBQC model that extends the unitary setting to a channel-based one using only a single additional trainable parameter. We show, both numerically and algebraically, that this minimal extension is sufficient to generate probability distributions that cannot be learned by the corresponding unitary model.

A quantum computer capable of breaking the encryption that secures the internet now seems to be just around the corner. Stunning revelations from two research teams outline how it could happen, with one suggesting that the current largest quantum machine is already more than halfway towards the size needed. The two studies concern an encryption technique built around the elliptic curve discrete logarithm problem (ECDLP). The particulars of how this mathematical problem is solved made it a good candidate for encrypting data and led to its widespread adoption for securing lots of internet communication, including bank transactions, and nearly every major cryptocurrency, including bitcoin. It is extremely difficult for conventional computers to crack ECDLP-based encryption, but since the 1990s researchers have known that quantum computers wouldn't have the same trouble.

Classical Monte Carlo methods for pricing catastrophe insurance tail risk converge at order reciprocal root N, requiring large simulation budgets to resolve upper-tail percentiles of the loss distribution. This sample-sparsity problem can lead to AI models trained on impoverished tail data, producing poorly calibrated risk estimates where insolvency risk is greatest. Quantum Amplitude Estimation (QAE), following Montanaro, achieves convergence approaching order reciprocal N in oracle queries - a quadratic speedup that, at scale, would enable high-resolution tail estimation within practical budgets. We validate this advantage empirically using a Qiskit Aer simulator with genuine Grover amplification. A complete pipeline encodes fitted lognormal catastrophe distributions into quantum oracles via amplitude encoding, producing small readout probabilities that enable safe Grover amplification with up to k=16 iterations. Seven experiments on synthetic and real (NOAA Storm Events, 58,028 records) data yield three main findings: an oracle-model advantage, that strong classical baselines win when analytical access is available, and that discretisation, not estimation, is the current bottleneck.

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.