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Quantum Interference Transformer (QIT): Emergent Sequence Intelligence from Amplitude Dynamics

Mihail Alexandru Stancescu

Published May 16, 2026• 0 citations
Publisher

Abstract

This working paper introduces the Quantum Interference Transformer (QIT), a sequence model in which token relationships are resolved by constructive and destructive interference in a parameterised quantum circuit, rather than by classical dot-product attention. We present QIT-0, a minimal PennyLane/PyTorch prototype. Tokens are encoded as rotation angles, cross-token correlations are seeded by a ring CNOT ladder, a learned strongly-entangling unitary acts as the attention operator, and Pauli-Z expectation values are decoded by a linear layer. On a 4-bit parity memorisation benchmark (16 inputs; 5 random seeds), QIT-0 (78 parameters) reaches 100% accuracy in 6.2 ± 1.7 epochs. Classical baselines with more parameters converge more slowly or fail within the epoch budget. Additional experiments include ablations, a first-token negative control, and related structured tasks. This is an independent technical report, not a peer-reviewed publication. We do not claim general quantum advantage for machine learning. Code: https://github.com/MihailStancescu/qit

DOI
10.5281/zenodo.21831268

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This working paper introduces the Quantum Interference Transformer (QIT), a sequence model in which token relationships are resolved by constructive and destructive interference in a parameterised quantum circuit, rather than by classical dot-product attention. We present QIT-0, a minimal PennyLane/PyTorch prototype. Tokens are encoded as rotation angles, cross-token correlations are seeded by a ring CNOT ladder, a learned strongly-entangling unitary acts as the attention operator, and Pauli-Z expectation values are decoded by a linear layer. On a 4-bit parity memorisation benchmark (16 inputs; 5 random seeds), QIT-0 (78 parameters) reaches 100% accuracy in 6.2 ± 1.7 epochs. Classical baselines with more parameters converge more slowly or fail within the epoch budget. Additional experiments include ablations, a first-token negative control, and related structured tasks. This is an independent technical report, not a peer-reviewed publication. We do not claim general quantum advantage for machine learning. Code: https://github.com/MihailStancescu/qit
GPT attention measures token compatibility through dot-product similarity. This mechanism is simple, effective, and memory-efficient. But it does not explicitly model whether strong token features should reinforce or suppress one another. We introduce Q-Interference, a fully classical quantum-inspired attention mechanism for autoregressive language modeling that augments each query and key feature with an amplitude and a learned phase. The resulting attention score is phase-aware which aligned phases contribute constructively while conflicting phases contribute destructively. Although Q-Interference yields a richer interaction rule than similarity alone, a naive implementation of Q-Interference requires a large token-pair-feature interaction tensor, making it memory-intensive and often impractical. To address this limitation, we propose an exact trigonometric factorization that computes the same score using two standard matrix multiplications avoiding materialization of the large intermediate tensor. Q-Interference fits directly into a Transformer block in GPT and leaves the remainder of the model architecture and next-token prediction objective unchanged. Experiments on public benchmark datasets and baseline models show that the proposed reformulation trains stably in a controlled GPT-style setting and provides a consistent memory advantage over naive phase-aware interference attention. These results support the specific contribution of this work: an exact memory-efficient reformulation that makes phase-aware interference attention practical within a standard GPT pipeline.
Quantum machine learning offers a compelling representational perspective: angle-encoded states inhabit Hilbert spaces in which periodic similarities and interactions can be expressed naturally. Realizing this perspective for visual recognition remains difficult, however, because present quantum neural networks are constrained by limited qubit counts, costly circuit simulation and measurement, noise, and unstable optimization on noisy intermediate-scale quantum devices. We investigate whether useful structural ideas from quantum models can instead be realized as scalable classical Transformer operations. We introduce QiT, a Quantum-inspired Transformer for vision tasks with three components: (i) angle-inspired encoding that maps image tokens to learned trigonometric Hilbert-space features analogous to quantum rotation-based state encoding; (ii) self-attention over these periodic features, inducing a classical cosine kernel approximated to quantum fidelity kernels; and (iii) gated multiplicative emulation, a trainable classical surrogate for interaction terms found in variational circuits. All components are differentiable tensor operations, so QiT claims neither quantum computation nor quantum speedup and retains the O(N2D)\mathcal{O}(N^2D)O(N2D) attention complexity of a standard Vision Transformer. Across image-classification benchmarks, QiT is competitive with a matched classical Transformer while avoiding the severe runtime cost observed for a small simulated quantum Transformer. QiT-B reaches 78.3\% ImageNet-1K top-1 accuracy with 45.7M parameters and 11.5 GFLOPs. These results position QiT as a scalable baseline for isolating and evaluating quantum-motivated inductive biases in visual recognition.
Progress in the realisation of reliable large-scale quantum computers has motivated research into the design of quantum machine learning models. We present Quixer: a novel quantum transformer model which utilises the Linear Combination of Unitaries and Quantum Singular Value Transform primitives as building blocks. Quixer operates by preparing a superposition of tokens and applying a trainable non-linear transformation to this mix. We present the first results for a quantum transformer model applied to a practical language modelling task, obtaining results competitive with an equivalent classical baseline. In addition, we include resource estimates for evaluating the model on quantum hardware, and provide an open-source implementation for classical simulation. We conclude by highlighting the generality of Quixer, showing that its parameterised components can be substituted with fixed structures to yield new classes of quantum transformers.
We propose a compact NISQ-compatible quantum transformer architecture for synthetic QNLP sequence modelling. The model preserves the autoregressive next-token interface of a classical transformer, but replaces attention and feed-forward sublayers with variational quantum encoder blocks, connector circuits, decoder blocks and a direct two-qubit measurement readout. Token contexts are angle-encoded into small quantum registers, processed by parallel variational heads and encoder integration circuits and conditioned through decoder ancillae to produce a distribution over a four-token vocabulary. We evaluate several architecture variants on deterministic and lexicographic grammar-generation tasks against a compact classical transformer baseline. The quantum models are trainable end-to-end and learn nontrivial grammar structure, including perfect deterministic generation in individual runs and high lexicographic validity in the strongest variant. The classical baseline remains more accurate and stable and the quantum models are sensitive to initialization. The contribution is therefore not a claim of quantum advantage, but a concrete architecture and evaluation of transformer-inspired QNLP sequence modelling under near-term quantum constraints.
We propose a variational quantum implementation of self-attention (QSA)-the core operation in transformers and large language models-which predicts future elements of a sequence by forming overlap-weighted combinations of past data. At variance with previous approaches, our QSA realizes the required nonlinearity through interference of state overlaps and a degree-kkk polynomial kernel, and estimates a loss based on Rényi-1/21/21/2 entropic functionals via two observables' expectation values, avoiding the decoding of amplitude-encoded predictions into classical probabilities. QSA also accommodates a constrained, trainable data-embedding tying state overlaps to data-level similarities. Its dominant end-to-end training complexity scales as O(μ−1k2Td)O\left(μ^{-1}k^2Td\right)O(μ−1k2Td), versus O(Tdk+1)O\left(T d^{k+1}\right)O(Tdk+1) of the fairest classical comparison, with μμμ a training signal; we show numerically that this allows a complexity advantage in the regime where sequence length TTT dominates the embedding size ddd. In simulations, our QSA-based quantum transformer learns sequence prediction on classical data and on many-body transverse-field Ising trajectories-establishing trainable attention as a practical primitive for quantum dynamical modeling.
Abstract A recurring weakness in quantum machine learning (QML) is that reported ‘quantum advantages’ are seldom tested against a capacity-matched classical control, leaving it unclear whether a gain comes from the quantum substrate or from the architectural change that accompanies it. Our primary contribution is methodological: a protocol for attributing such gains honestly—a capacity-matched classical bottleneck of identical parameter budget, transparent reporting of where quantum does not help, and validation on real quantum hardware—which we develop and apply through a concrete case study. That case study is Quantum Adaptive Self-Attention (QASA), a hybrid Transformer that replaces the value projection of a single encoder layer with a 36-parameter parameterized quantum circuit (PQC), keeping all other layers classical. Across nine synthetic benchmarks and the real-world ETTh1 dataset, QASA improves on a full-capacity classical Transformer for chaotic and trend-dominated signals. To ask whether this is a genuinely quantum effect, we introduce a control rarely applied in QML—a capacity-matched classical bottleneck with the same parameter budget—and find that it matches the PQC on the error metrics. The gain is therefore attributable to the low-rank value-projection bottleneck (an architectural parsimony principle), not to quantumness; adding further quantum layers only degrades performance and trainability. We accordingly position the quantum layer not as a source of accuracy advantage but as a competitive instantiation of this principle: its low-rank compression onto the signal’s intrinsic dimensionality is matched by a classical bottleneck, so the gain is architectural rather than quantum. The quantum layer’s distinguishing features are physical—a high circuit entanglement (Meyer–Wallach Q = 0.981 with only 27 CNOTs, which we report as a circuit-level property) and, most concretely, noisy intermediate-scale quantum deployability, which we verify by executing the trained model on a real IBM Quantum processor (one-step prediction within 7.5 % of noiseless simulation on the quantum-favored task and 25 % , with overlapping error bars, on a classical-favored control; no error mitigation). Relative to other quantum sequence models (quantum long short-term memory (QLSTM), QnnFormer), QASA is moreover the most resource-efficient of the three: it reaches competitive accuracy with the fewest quantum parameters (36 vs 90–128) and the strongest entanglement-per-gate ( Q = 0.981 with 27 CNOTs vs QLSTM’s 56), and retains trainable gradients that deeper circuits lose. We argue that capacity-matched baselines and honest reporting of where quantum does not help are prerequisites for credible quantum-machine-learning claims.