As IQP circuits produce remarkably low intermediate magic relative to phase-randomised states with the same sampling distributions, this renders IQP-based quantum generative models as promising candidates for resource-efficient demonstrations of quantum advantage on early fault-tolerant architectures.
Abstract
Quantum generative modelling casts sampling as a generative task: a parametrised quantum circuit is trained such that sampling reproduces a target probability distribution. Instantaneous Quantum Polynomial-time (IQP) circuits combine structural simplicity with complexity-theoretic evidence for quantum advantage. Yet their practical value depends not only on expressivity, but on how efficiently they consume genuinely quantum resources. We study this question through the lens of magic, or non-stabiliserness, as a resource for quantum generative modelling. We show that established fidelity- and geodesic-based notions of computational progress in a projective Hilbert space are ill-suited to generative models, since operational performance is determined by output probability distributions rather than quantum states themselves. We evaluate magic-consumption directly on the probability simplex, using changes in Jensen-Shannon divergence to quantify progress. Applying this framework to trained random {\gamma}-sparse IQP circuits shows signatures of efficient magic use, with the dominant contribution arising from two-qubit gates. As IQP circuits produce remarkably low intermediate magic relative to phase-randomised states with the same sampling distributions, this renders IQP-based quantum generative models as promising candidates for resource-efficient demonstrations of quantum advantage on early fault-tolerant architectures.
Extracting quantum information from a quantum state is a fundamental task of quantum computation, often requiring the estimation of many non-commuting observables under a finite measurement budget. For both near-term and early fault-tolerant settings, the measurement protocol must balance statistical efficiency against implementation resources such as circuit depth, connectivity, and entangling-gate count. Many existing strategies focus on two extremes: hardware-friendly product measurements with high sampling cost, and fully commuting measurements with deep circuits. Here we recast resource-constrained measurement design as a generative learning problem. We introduce FlowMeas, which uses a generative flow network to directly sample finite ensembles of shallow Clifford measurement circuits subject to a prescribed shot budget and hardware constraints. At zero entangling depth, FlowMeas learns qubit-wise commuting measurement schedules and already matches or improves leading product-measurement methods on nearly all molecular benchmarks. Allowing one or two entangling gate layers yields further reductions in energy estimation error of up to $27\%$ relative to the strongest state-independent product-measurement baseline. The learned policy can also be reused across related Hamiltonians, substantially accelerating retraining along a molecular potential-energy surface. We further obtain results for molecular Hamiltonians with up to 20 qubits and apply the framework to a compactly encoded 54-qubit interacting fermionic model, extending the demonstrated scale beyond prior molecular benchmarks. These results establish generative learning as a flexible and unified framework for quantum measurement design under practical resource constraints.
Jun Dai, O. Nahman-Lévesque, Guillaume Rabusseau et al.· 0 citations
The rapid commercialization of generative artificial intelligence (AI), along with the maturation of quantum technologies has raised a question: can quantum-powered neural networks become the next major shift in large language model (LLM) technology? This naturally leads to another misconception that quantum systems will replace classical LLMs. In this study, both architectures are compared in a contrastive manner in terms of mathematics. The data reveals that identical dynamics that help classical systems learn natural language distributions constrain its ability to use efficient sampling of quantum-mechanical spaces. Performing complexity-theoretic separations (i.e., the widely believed but unproven conjecture that BPP ⊆ BQP) and a 2025 preprint reporting experimental demonstrations of quantum advantage for generative tasks we conclude that quantum utility is unlikely to lie in tasks involving natural language processing under current architectures, but rather in certain computational subroutines. We then suggest a hybrid quantum-classical architecture as the best direction to take in the future, as it has the advantages of both paradigms. This is done by studying a case study that optimizes retrieval-augmented generation (RAG) pipelines with Grover's search algorithm.
Diljot Singh, O. J, S. G S· Frontiers in Artificial Inte...· 0 citations
The exponential parameter scaling of classical transformer models confronts severe physical and economic barriers. To sustain generative AI capabilities, alternative computational paradigms must be explored.
This paper projects the architecture and scaling laws of Quantum Generative AI Foundation Models by integrating Variational Quantum Algorithms (VQAs) with Fault-Tolerant Quantum Error Correction (QEC). We propose a hybrid quantum-classical framework utilizing isometric Tree Tensor Networks (TTNs) and a novel Quantum Self-Attention (QSA) subroutine, capable of compressing the latent space of a classical 10
11
-parameter Large Language Model (LLM) into a 10
6
parameter quantum neural network via amplitude encoding.
To circumvent Noise-Induced Barren Plateaus (NIBP), we map the training requirements onto a fault-tolerant regime. Assuming a surface code QEC overhead with a physical-to-logical qubit ratio of approximately 2,000:1, we establish the resource requirements for a VQA operating below the 10
−4
physical gate error threshold. Our numerical projections indicate an approximate 45% reduction in total energy expenditure for frontier model training and a per-query attention processing complexity of
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log
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The quantum framework fundamentally subverts the classical compute wall by substituting linear parameter scaling with logarithmic latent space compression, acknowledging that full attention matrix computation retains a dependency on measurement precision overheads.
R. Delhibabu· Frontiers of Computer Scienc...· 0 citations
A theoretical framework in Pauli-Liouville space is developed that provides a unified analytical treatment of the echo state property (ESP), nonlinear expressive power, and quantum resources and shows that the ESP is natively guaranteed by the Liouvillian spectral gap, decoupling it from quantum magic.
Quantum resource theory has sharpened our understanding of the intrinsic complexity of quantum systems, particularly their classical simulability. However, it remains unclear which quantum resource governs the classical learnability of quantum circuits, especially beyond the regime of efficient classical simulation. Here we close this knowledge gap by studying the expectation-value functions of families of tunable quantum circuits, with many applications in digital quantum simulation, quantum metrology, and quantum-system characterization. Specifically, we introduce a new resource measure, the dynamical stabilizer entropy (\DSE), which quantifies how broadly an expectation-value function is distributed across its frequency modes. By relating \DSE to operator stabilizer entropy, we establish a computational phase diagram that compares classical simulators with quantum-data-assisted classical surrogates. We first determine the \DSE-dependent learnability boundary of this diagram by deriving bounds on the sample complexity and runtime of classical surrogates, and by developing a \DSE-guided surrogate. We then complete the diagram by proving, under standard complexity-theoretic assumptions, the existence of circuit families that can be efficiently learned by this surrogate but cannot be efficiently emulated from their circuit descriptions alone. Numerical experiments on random and structured circuits with up to 80 qubits support the predicted \DSE-dependent computational landscape. These results establish a quantitative resource-theoretic framework for delineating the boundary between classical simulation and learning, motivate resource measures linking quantum resources to learnability, and guide the design of learning-based algorithms for scalable quantum systems beyond the reach of direct classical simulation.
Xin-Biao Wang, Yuxuan Du, Dacheng Tao· 0 citations
The scaling hypothesis assumes that increasing model parameters yields emergent reasoning capabilities. This position paper argues that applying this probabilistic paradigm to generic quantum circuit synthesis is a directional error. Unlike natural languages, quantum circuits require strict adherence to mathematical constraints that manifest a significant syntax-semantics gap. Training on unverified quantum programs means that models learn syntax but fail to capture the physical semantics of the Hilbert space. Since the valid subset of circuit designs decays exponentially with the number of qubits, post-hoc filtering is mathematically intractable. We propose a pivot from human-centric copilots to verifier-centric agents. We integrate hierarchical constraints, topological masks, and symbolic proxies directly into generation. Our analysis suggests that scale alone cannot bridge the validity gap. Verification-aware architectures offer a viable path for modular quantum program generation. These considerations point toward generation methods that encode task-specific rules of quantum information, rather than relying on imitation alone.
Jun-Jie Song, Yu Zhou, William J. Knottenbelt et al.· 0 citations
