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.
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.
Hybrid quantumclassical models are increasingly proposed for nancial prediction, but reported gains are rarely separated from the classical components around them. We study a hybrid quantum temporal convolutional network for daily cross-sectional ranking of 2000 Tokyo Stock Exchange equities under a protocol built to make the quantum contribution identiable: six conditions (circuit trained, frozen or absent, a parameter-matched classical surrogate, and the circuit alone, trained or frozen) through one code path; four walk-forward folds with ve seeds; bootstrap intervals, Deated Sharpe Ratios, backtest-overtting probabilities and family-wise error control; ve classical baselines including a gradient-boosted tree; and a locked holdout. On 500 out-of-sample days two one-sided tests place the trained-versus-frozen dierence inside 0.03 annualised Sharpe (p = 0.0055, minimum detectable eect 0.02): the circuit is equivalent to a frozen one, not merely indistinguishable from it. With the circuit as the head's only input the two are equivalent inside 0.25; against the network with no circuit the design resolves only 0.50. No condition is distinguishable from zero (best De-ated Sharpe Ratio 0.17). The holdout reproduces the ablation on a protable window, and 2000 US equities reproduce it where every condition loses money.
Parameterized instantaneous quantum polynomial-time (IQP) circuits generate distributions conjectured to be hard to sample classically. As reinforcement learning (RL) policies, their $2^n$ measurement outcomes are typically mapped to a smaller action space by a classical decoder. This aggregation can mitigate initialization concentration while making the policy classically simulable. We characterize this tradeoff through the decoder's Fourier--Pauli expansion. Under independent uniform initialization, we express policy variance as an exact sum over groups of nonconstant Pauli components with identical active-generator signatures. Each group contributes its squared aggregate coefficient times $2^{-r}$, where $r$ is the binary rank of its active generators. An inverse-polynomial aggregate coefficient with logarithmic rank prevents exponential policy concentration. Sparse Pauli expansions and contiguous action bins permit efficient classical additive estimation of action probabilities. We introduce a majority decoder combining protected low-weight components with exponentially large exact Fourier support, preserving initialization nonconcentration while excluding polynomial-size enumeration of the exact expansion. Numerical experiments corroborate the variance laws. In ten-qubit CartPole experiments, majority achieves higher returns than recursive parity and the tested local readouts, while higher-weight Pauli sectors contribute an increasing relative share of gradient magnitude during training. A complementary 21-qubit block-chain policy outperforms an extensive pool of fully connected classical neural networks in episode efficiency, even though its bounded-width structure permits efficient classical simulation. These results guide decoder design for quantum and quantum-inspired RL, distinguishing policy nonconcentration, learning performance, and classical simulability.
Hybrid quantum-classical models often report good accuracy on image tasks, but it is rarely clear whether the quantum part is responsible. This paper proposes QCA-DenseNet, a static American Sign Language (ASL) recognition pipeline in which an eight-qubit variational circuit acts as a channel-attention gate on DenseNet121 features. The quantum channel attention (QCA) gate has 17,464 parameters, 7.51 times fewer than a squeeze-and-excitation (SE) block. The pipeline is tested on 1,815 MU HandImages images by holding out one of five signers at a time, and a frozen-backbone ablation uses small parts of the Kaggle ASL Alphabet data. On unseen signers, QCA-DenseNet reaches 94.50% mean accuracy, above SE (93.72%) and within 0.28 points of the best model. A matched classical MLP and a model without attention perform about the same, and no difference is significant. QCA gives a much smaller attention gate without a detectable loss in accuracy, but no quantum advantage.
Hardware executions of the quantum approximate optimization algorithm (QAOA) are often validated by comparing the device's mean cost with a simulation, a check that can miss what matters for optimization. Under global depolarization, the mean normalized gap and the floor-corrected probability of every set of bitstrings, the optimum included, retain the same fraction of their noiseless improvement over uniform sampling. We test this prediction with depth-2, transferred-angle QAOA circuits for binary subproblems of an alternating-direction decomposition on the IBM Heron processor \texttt{ibm\_marrakesh}, with and without dynamical decoupling and twirling. At 12 qubits, the main-family circuits retained 29\% to 46\% of their mean-gap improvement but only 5\% to 15\% of their probability of the optimum, lower on at least nine of ten instances per run. Near-optimal bitstrings were lost about as much as the optimum, whereas the avoidance of poor bitstrings was retained best. In the first submission, a device-matched noise model reproduced the pattern but overestimated the retention of the optimum five- to eightfold. On a rugged planted family, the device found the optimum in 62\% of 768-shot blocks (noiseless: 98\%), within the range of local heuristics. Validations of optimization circuits should report retention of the optimum and of near-optimal sets.
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 Gemini 4 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 2.55x), 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.
How complex can the responses of a quantum process become as it runs longer with fixed internal memory? We measure this complexity by sequential response capacity, the depth of an adaptive tree of experiments whose acceptance probabilities separate possible processes by a prescribed gap. Each experiment uses a fresh complete run, and one fixed process must realize every response along a path. For any fixed common visible dimension of at least two and internal memory cap, we prove that capacity has order $K\log((K+1)/\gamma)$ for $K$ transitions per run and probability gap $0<\gamma\leq1$. Time-dependent single-qubit phase channels without internal memory already attain the fixed-gap $K\log K$ growth, realizing each path with zero-or-one response probabilities. Under the same tester permissions, classical stochastic processes that measure in a fixed basis at every transition have only linear capacity at fixed dimensions and gap. For phase sequences selected by a classical address stored inside the process, we then quantify how known independent Pauli noise changes this logarithmic enhancement. With ideal tester controls and weak residual phase noise after correction, we prove matching capacity bounds at a fixed small gap. At fixed address size and fixed positive residual noise, the logarithmic enhancement saturates once the phase-sequence length exceeds the inverse noise scale, and capacity then grows linearly with sequence length.
A fundamental question in physics is: When does classical behavior emerge from quantum systems? Bosonic Gaussian states provide a natural setting to explore this quantum-classical boundary, as they capture both the classical field behavior and the intrinsic quantum nature of light. Here, we address this problem from a learning-theoretic perspective by asking: When are bosonic Gaussian states classical to learn? That is, under what conditions (if any) can an n-mode bosonic Gaussian state be learned with as few samples, and with operations as simple, as are needed to learn a classical 2n-variate Gaussian distribution? We establish a smooth crossover in learnability governed by the state's thermal fluctuations: - Cold Gaussian states are non-classical to learn: When the covariance matrix satisfies $\Sigma\le(\frac12+O(\frac1n))I$, i.e. close to the vacuum covariance, tomography under single-copy (i.e., non-entangled) measurements fundamentally requires $\Omega(n^3)$ copies, strictly exceeding the sample complexity $\Theta(n^2)$ of learning classical Gaussian distributions. We show that this hardness persists even when few-copy entangled measurements are allowed. - Warm Gaussian states are classical to learn: When thermal fluctuations exceed the vacuum noise, parameterized by $\Sigma\ge(\frac12+\nu)I$ for any parameter $\nu>0$, we prove that single-copy tomography requires $N=\Theta\left(n^2\min(n,1+\nu^{-1})\right)$ copies. This bound is tight and is achieved by simple, non-adaptive, unentangled heterodyne measurements. Crucially, for $\nu=\Omega(1)$, the sample complexity drops to $\Theta(n^2)$, matching the classical case. Our results tightly characterize a quantum-to-classical crossover in the learnability of bosonic Gaussian states, reveal a novel connection between fundamental physics and statistical learning theory, and have implications for real-world sensing experiments.
Foundation models for ground states in spin-1/2 systems are a promising method for problems ranging from quantum chemistry to identifying new phase diagrams. Nearly all such models are currently pure-states that condition on the Hamiltonian's parameters, whose Monte Carlo samples give energy estimates according to the variational principle. In this contribution, we show that this representation is topologically obstructed. For any gapped Hamiltonian family whose ground-state bundle is non-trivial, every continuous normalized state-vector model has zero fidelity with the ground state at some parameter value in the Hamiltonian family. For that value, the energy is at least one spectral gap, $\Delta$, with an $O(\Delta)$ gap in an open-neighbourhood of that point. We show that this is a sufficient no-go also in the case of degenerate ground-state manifolds, time dynamics, and periodic systems with mixed space-time topology, demonstrating these obstructions on one- and two-qubit systems. We discuss how this causes a spike in the fidelity susceptibility, giving a numerical signature of a phase-transition where there is none. Finally, we show that operator-valued models canonically avoid these obstructions and preserve topological information, implying a structural necessity in representation for foundation neural quantum states.
Instantaneous Quantum Polynomial Circuit Born Machines (IQP-QCBMs) have been proposed as quantum generative models that combine a classically tractable training objective - based on the maximum mean discrepancy (MMD) - with a potential quantum advantage motivated by sampling-complexity arguments. While recent works have explored this model across various application domains, fundamental questions remain: does the model suffer from exponentially vanishing loss gradients, known as the barren plateau problem - a pervasive obstacle in quantum machine learning - and how do regimes of trainability relate to regimes of possible quantum advantage? Here, we address both questions analytically. To study trainability, we derive closed-form expressions for the variances of the partial derivatives of the MMD loss function and establish general upper and lower bounds. We explicitly characterize how trainability depends on the generator set and the spectrum of the chosen kernel, identifying regimes in which low Hamming-weight kernels avoid exponential gradient suppression under structured topologies. Regarding potential quantum advantage, we reformulate the anti-concentration property in terms of the same generator-set quantities that govern trainability, enabling a unified analysis. We show that sparse IQP architectures can produce classically intractable output distributions while simultaneously remaining trainable, at least at lower-weight frequencies. Our analytical results corroborate the numerical observations of prior work and provide principled guidelines for designing scalable IQP-QCBM architectures.
We present a unified quantum sensitivity sampling framework that streamlines coreset construction for many classical approximation problems, significantly speeding up clustering, regression, and low-rank approximation. We assume $n,d\geq\mathrm{poly}(k/\epsilon)$ and, for regression, $n\geq\mathrm{poly}(d)$: - $k$-median/$k$-means: For $n$ points in $\mathbb{R}^d$, we build an $\epsilon$-coreset of input points of size $\tilde O(k^{4/3}\epsilon^{-2})$ (resp. $\tilde O(k^{3/2}\epsilon^{-2})$) in time $\tilde O(\epsilon^{-1}n^{0.5}dk^{1.67})$ (resp. $\tilde O(\epsilon^{-1}n^{0.5}dk^{1.75})$). Our better $d$- and linear $1/\epsilon$-dependence improve on [Xue, Chen, Li and Jiang, ICML'23] for $d\geq\Omega(k^{7/3})$ (resp. $\Omega(k^{2.5})$). - $\ell_p$ regression: For $\min_x\|Ax-b\|_p$, $A\in\mathbb{R}^{n\times d}$, we build an $\epsilon$-coreset of size $\tilde O_p(d^{\max\{1,p/2\}}\epsilon^{-2})$ in time $\tilde O_p(n^{0.5}d^{1.5}\epsilon^{-1})$ for $p\leq 2$ and $\tilde O_p(n^{0.5}d^{p/4+1}(\epsilon^{-1}+d^{0.5}))$ for $p>2$, matching [Liu and Ji, ICML'26] for $p\leq 2$ and improving on the prior best quantum sampling approach [Apers and Gribling, SICOMP'26] for all $p>2$. - Low-rank approximation: We give the first quantum sublinear-time algorithm for Frobenius-norm rank-$k$ approximation of $A\in\mathbb{R}^{d\times n}$ free of data-dependent parameters, running in $\tilde O(n^{0.5}dk^{0.5}\epsilon^{-0.5})$ time with factored output (plus $\tilde O(nk^2\epsilon^{-2})$ to materialize them). We also give sublinear algorithms for kernel and tensor variants. - Lower bound: For generic sensitivity sampling with total sensitivity $S$, any quantum algorithm outputting an $\epsilon$-coreset of size $o(\sqrt{nS})$ needs $\Omega(\sqrt{nS})$ queries, so our query complexity is optimal up to $\mathrm{poly}(\epsilon^{-1},\log n)$ and VC-dimension factors.
We consider the problem of synthesizing Clifford quantum circuits for devices with all-to-all qubit connectivity. We approach this task as a reinforcement learning problem in which an agent learns to discover a sequence of elementary Clifford gates that reduces a given symplectic matrix representation of a Clifford circuit to the identity. This formulation permits a simple learning curriculum based on random walks from the identity. We introduce a novel neural network architecture that is equivariant to qubit relabelings of the symplectic matrix representation, and which is size-agnostic, allowing a single learned policy to be applied across different qubit counts without circuit splicing or network reparameterization. On six-qubit Clifford circuits, the largest regime for which optimal references are available, our agent finds circuits within one two-qubit gate of optimality in milliseconds per instance, and finds optimal circuits in 99.2% of instances within seconds per instance. After continued training on ten-qubit instances, the agent scales to unseen Clifford tableaus with up to thirty qubits, including targets generated from circuits with over a thousand Clifford gates, where it achieves lower average two-qubit gate counts than Qiskit's Aaronson-Gottesman and greedy Clifford synthesizers.
Quantum circuit Born machines (QCBMs) can learn distributions that are hard to sample from classically, but their value depends on generalizing from finite training data. Here, we study how hardware noise affects this generalization. We show that, for any noise process, the generalization gap of a QCBM trained with the maximum mean discrepancy is bounded by the complexity of the distributions the noisy model can reach. Scrambled local Pauli noise contracts this complexity but biases the model towards the uniform distribution, so residual noise acts as a regularizer whose optimal strength can be intermediate. We propose GENIE, a framework that realizes a chosen noise level with capped error mitigation and selects it during training from held-out data within a fixed execution budget, with provably bounded regret. In simulations on synthetic and census data, GENIE stays close to the best of four noise-control strategies, whereas every fixed noise level falls short in many settings.
When an image classifier decides, we can usually only estimate why. For quantum and all-optical classifiers that act linearly on amplitude-encoded pictures up to the measurement, with no trained classical network before or after them, each class's Born probability above its no-information share, $P_g - b_g$, splits exactly into contributions of the encoded amplitudes, shown as Born evidence maps (BEM). The split itself follows from known results on quadratic forms: with the transmitted light held fixed, it is what Integrated Gradients from a zero baseline and the Shapley value give. What we add is a way to measure it on the hardware that classifies, from class probabilities on a quantum chip or, in simulation, from camera frames on a lens bench, with no gradient circuit and no light sent backwards; a $g\times g$ map takes $1 + 2g^2$ runs. Deleting the 5% of pixels with the highest evidence drops accuracy from 73% to 9% (one seed), as occlusion and gradient $\times$ input do, while plain gradients remove much less. The classifiers share one architecture, a Fourier-plane mask followed by a brickwall circuit on qubits or by phase plates on a lens bench, read by a fixed Born headroom readout with no trained parameter; centring each picture on its own mean lets dark features count as much as bright ones. In simulation, four phase plates at one wavelength reach 72.3% on Caltech-10 colour photographs. On IBM's ibm_kingston, with the mask computed classically before approximate loading, 300 test pictures were classified at 37.7% against 10% chance (56.3% in exact simulation), and $2\times2$ maps of the filtered input of 30 test pictures drawn at random in advance, measured on the chip, agreed with the exact ones ($r = 0.88$; standard estimator 0.82). The maps also revealed a shortcut in the data; as the trim that removed it was chosen on test pictures, the Caltech-10 results are exploratory.
Quantum low-density parity-check codes promise low-overhead error correction, but high-performing constructions remain hard to find. Here we introduce structured concept evolution, in which a large language model (LLM) evolves construction programs and their internal search strategies by modifying the finite group, protograph shapes or entry-assignment rule. We search for codes with fewer than $600$ data qubits and check weight at most $12$, optimizing $kd^2/n$ or the circuit-level logical error rate. Our method improves on published lifted-product benchmarks in selected parameter regimes, with exactly certified distances for the leading results. Circuit-level optimization typically yields lower logical error rates than $kd^2/n$ optimization, often despite smaller code distances. With the same evolution framework and step budget, the best LLM outperforms all random-mutation and hill-climbing runs on both objectives. Our results point to LLM-driven program search as an approach to designing general quantum LDPC codes.
Trainable-frequency quantum models train the prefactors of their encoding gates so that the circuit's frequencies can move onto the target's. From the unit start of prior work, training rarely reaches a target more than one resolution step away. We show that the target-driven part of the prefactor gradient is a weighted sum of slopes of the overlap $\sin u/u$, where $u$ is the model-target frequency distance scaled by the window half-width. This gives each frequency a reach: under gradient flow, an isolated real frequency whose coefficient adapts optimally reaches its target from within half a step, for every target at least one step from zero frequency; with a fixed coefficient, a phase-dependent barrier can stop it. A ternary prefactor grid places a model frequency within half a step of every band frequency, with logarithmically many encoding gates. Single-frequency circuits trained with Adam and jointly trained amplitudes behave as predicted: inside the first side lobe, a frequency starts toward its target exactly when in phase with it in 98% of runs, and only 11 of 768 frequencies starting beyond the lobe reached their target. With several frequencies, the grid start raised successful fits on synthetic targets from 69% to 84% against the best random start. With many target frequencies, least squares on the fixed grid fits near-perfectly, but the circuit does not reach the coefficients; training the prefactors narrows this shortfall, but with 8 and 24 target frequencies, training the fixed grid ten times longer fitted better. On real series, training the frequencies improved held-out $R^2$ at equal budget by 0.010--0.045 on four of seven series, but a classical screen did not separate these from the others. A classical model with independently trainable frequencies shows the same dependence on the start; our results describe how to train such models, not an advantage of the circuit.
Many quantum software development kits provide a suite of circuit optimisation passes. These passes have been highly optimised and tested in isolation. However, the order in which they are applied is left to the user, or else defined in general-purpose default pass sequences. While general-purpose sequences miss opportunities for optimisation which are particular to individual circuits, designing pass sequences bespoke to particular circuits requires exceptional knowledge about quantum circuit design and optimisation. Here we propose and demonstrate training a reinforcement learning agent to compose optimisation-pass sequences. In particular the agent's action space consists of passes for two-qubit gate count reduction used in default PyTKET pass sequences. For the circuits in our diverse test set, the (mean, median) fraction of two-qubit gates removed by the agent is $(57.7\%, \ 56.7 \%)$, compared to $(41.8 \%, \ 50.0 \%)$ for the next best default pass sequence. In doing so our model demonstrates the ability to forgo reward to improve the final two-qubit gate count. Our approach clearly separates the problem of designing circuit optimisation passes from the problem of using them optimally in practice. We expect this separation of concerns to facilitate innovations in both areas.
The manifold hypothesis suggests that data lies on manifolds with smaller intrinsic dimension (ID) than their ambient dimension. However there is no empirical agreement on the estimates for ID from different estimators for realistic datasets. Thus it is important to test ID estimators (IDEs) with targeted stressors. In this work, we consider the role of anisotropy. To this end, we propose HomID, a collection of homogeneous spaces with anisotropic embedding, for benchmarking ID estimators. We observe that methods that perform well on standard benchmarks systematically degrade on HomID under identical resource allocation. We further observe that anisotropic distortion of such benchmarks also results in performance degradation. Finally, we demonstrate that controlled anisotropic distortions induce systematic shifts in the distributions on which these methods rely, providing a concrete mechanism for the resulting estimation errors in two particular IDEs. The code for the project is available at https://github.com/a-writes-code/homid
Choosing a quantum error-correcting code for a real device means scoring candidates with circuit-level simulations so slow that only a few hundred can be run. So every evaluation counts, and a search is judged by how many good codes it finds per paid evaluation. Quantum LDPC codes built from a few group elements protect many logical qubits, but good ones are rare in a huge space. We introduce GFlowQEC, to our knowledge the first generative flow network (GFlowNet) for quantum code design. It builds a code one group element at a time and learns to propose codes in proportion to a power of their score. We train it once on scores from earlier searches, freeze it, and let it propose lifted-product codes with 180 physical qubits, scored by their distances. Ranking ten of its draws per paid call, it finds more than twice as many new top-scoring codes (inequivalent to any it was trained on) as tuned parallel tempering, even when tempering starts from GFlowQEC's training codes. It finds more than three and a half times as many as a supervised screen ranking ten random candidates per call. When both rank a hundred, the screen beats GFlowQEC, and does best ranking GFlowQEC's draws. Soft Q-learning, which shares the GFlowNet's optimal policy, does as well at one noise bias and better at the other, so the gain does not depend on the GFlowNet's training loss. Trained proposers can make a budget of expensive evaluations go further when good codes are rare.