The Inference Report

Variational quantum algorithms (VQAs) optimize circuit angles through repeated quantum-device evaluations, often facing vanishing gradients and high optimization costs. We ask whether a large language model (LLM) can write these angles directly. Extending *weight-space programming* from classical networks to quantum circuits, we provide a frontier LLM (\gpt) with the problem, circuit, and gate conventions. Its angles are executed exactly as written, without returning losses, gradients, or accuracy feedback. Across 139 requests, we test handwritten-digit classification, VQE ground-state estimation for spin chains and H$_2$, and MaxCut QAOA, comparing against random weights, classical optimization, and optimization initialized with LLM weights on the same circuit. When parameters have interpretable structure, the LLM matches or approaches the optimizer: it achieves 95--100\% of the energy spectrum on every VQE problem, derives the exact H$_2$ ground state in closed form, finds optimal depth-one QAOA angles for every graph, and reaches 93--96\% accuracy on digits 3 versus 8 with 12--18 hand-written weights, outperforming an optimizer trained on the same ten examples. Its weights are also strong warm starts: optimization reaches its best value after a median of one evaluation rather than hundreds. Allowed to design circuits, the LLM chooses data-dependent rotation chains encoding pixel importance in all 30 cases (one qubit for binary tasks, one chain per qubit for ten classes), reaching 65\% accuracy across ten digits. Yet the approach fails in opaque weight spaces: accuracy drops to chance when fixed circuits exceed 30 weights, while optimization improves. It is also sensitive to gate conventions: 6 of 42 QAOA replies reverse mixing-angle signs and fail. We release all prompts, replies, and scores.

Entanglement is a crucial resource in quantum science and engineering, but detecting it in many-body states from experimentally accessible observables remains challenging. Here we introduce EntNet, an AI-driven framework to discover compact combinations of spin observables that accurately distinguish entangled from fully separable many-body mixed states in one-dimensional spin-$1/2$ chains governed by short-range Hamiltonians. We construct local-unitary-invariant representations of measurable Pauli correlators up to four-body order, sparsely select 16 candidate invariant feature channels, and learn their spatial structure using a Transformer architecture with rotary positional embeddings. Using only expectation values of these low-order observables, EntNet achieves $>98\%$ recall on certified entangled states with near-zero false-positive rates on separable states. Remarkably, it exhibits transferability across system sizes and distinct Hamiltonian families, including frustrated and disordered spin models, with minimal loss of accuracy. Beyond detection, EntNet provides physical insight into entanglement detection by revealing a selective spatial organization of pair correlations, while its finite-temperature decision boundary tracks the excitation gap of Jordan-Wigner quasiparticles. These results establish a transferable and physically interpretable framework for data-driven discovery of entanglement witnesses from local correlation functions.

The timeline by which quantum computers can solve breakthrough problems in science depends on improved quantum algorithms as much as on better hardware. Such algorithmic advances are typically achieved through many years of expert human collaboration. In mathematics and computer science, large language models have accelerated progress through automated discovery loops. However, quantum algorithms can only be evaluated by classical computers on restricted or small instances. Here we demonstrate automated discovery of quantum programs beyond these regimes including order-of-magnitude improvements on scientific applications. To achieve this, we build a quantum program library in the Lean theorem prover in which large language model agents synthesize novel programs against formal problem specifications and verify their correctness and cost. Agent teams collaborate, sharing results and knowledge through wikis and discussing ideas at organized conferences. Our results improve on prior baselines for parallel search (up to 1.4x), quantum arithmetic (290x), and simulations relevant to fusion, photochemistry and drug-metabolism by 11x, 8x and 2.5x respectively. Combining human and artificial intelligence at scale, under the rigor of mathematical proof, lets researchers design algorithms that today's classical and quantum computers cannot test, shortening the path to practical quantum computation.

Over the past few years, several quantum software stacks (QSS) have been developed in response to rapid hardware advances in quantum computing. A QSS includes a quantum programming language, an optimizing compiler that translates a quantum algorithm written in a high-level language into quantum gate instructions, a quantum simulator that emulates these instructions on a classical device, and a software controller that sends analog signals to a very expensive quantum hardware based on quantum circuits. In comparison to traditional compilers and architecture simulators, QSSes are difficult to tests due to the probabilistic nature of results, the lack of clear hardware specifications, and quantum programming complexity. This work devises a novel differential testing approach for QSSes, named QDIFF with three major innovations: (1) We generate input programs to be tested via semantics-preserving, source to source transformation to explore program variants. (2) We speed up differential testing by filtering out quantum circuits that are not worthwhile to execute on quantum hardware by analyzing static characteristics such as a circuit depth, 2 qubit gate operations, gate error rates, and T1 relaxation time. (3) We design an extensible equivalence checking mechanism via distribution comparison functions such as Kolmogorov Smirnov test and cross entropy

When a language model answers, we can usually only estimate why. We build a transformer in which every step is a Born measurement - attention $|\langle q|k\rangle|^4$ normalised over each row, a measured product in place of the feed-forward nonlinearity, and a Born readout. With its denominators held at their values for the input, each class probability is a polynomial in the word amplitudes, so its integrated-gradient evidence is computed by a finite quadrature with no quadrature error: the words' contributions sum to the class probability above its no-information share, to $10^{-11}$ or better. On e-SNLI natural language inference, with about 98k parameters outside the embedding, the model reaches $76.98 \pm 0.17$% test accuracy, level with a softmax transformer of the same size ($76.62 \pm 0.36$%). Deleting the word its evidence ranks first changes the answer in 45% of test pairs, out of the 53% any single deletion can change, against 32% for the softmax model explained the same way and 40% by its attention x gradient. Attention can look as much like the words annotators highlighted as the evidence does, yet accounts for the answer less well: deleting the word it ranks first changes the Born Transformer's answer in 32% of pairs. The same weights compile exactly to optoelectronic optics and to qubits, and a coherent attention layer becomes one circuit equal to the model (852 CNOTs on 23 qubits). On IBM's ibm_kingston, reading only the attention overlaps by Hadamard tests, the device gave the model's answers, also when a word was deleted. With calibration circuits as deep as the overlaps, each word's evidence with the device's attention row sums followed the exact evidence (correlations 0.997 and 0.932 on two pairs chosen in advance); where a pair's evidence is a small total of large opposite terms the earlier runs say it does not, and we say why.

Instantaneous quantum polynomial-time (IQP) Born machines are attractive quantum generative models, as certain IQP circuit families are conjectured to be hard to sample, yet they can be trained classically. Previously proposed conditional IQP Born machines make the parameters of the diagonal layer condition dependent. We introduce conditional IQP Born machines, in which the condition is encoded in the input state and a single IQP unitary is shared across conditions. Efficient sampling and amplitude-ratio evaluation for the reference state entering the diagonal layer suffice to obtain unbiased classical estimates of a conditional maximum mean discrepancy objective and its gradients. We show that input conditioning can represent conditional families that no diagonally conditioned IQP model with the same number of qubits can reproduce. For the sixteen-qubit Curie-Weiss spin model, a single conditional model captures the magnetization transition at held-out temperatures. Its mean total variation distance is six times lower than that of diagonal conditioning under the same protocol and comparable to that of classical generative models with up to seven times as many parameters. We also train conditional models classically with up to 2048 qubits, which reproduce the mean squared magnetization of the target away from the crossover. These results extend classically trained IQP Born machines to conditional generation.