Jonathan Mei

Oliver Knitter, Sang Hyub Kim, Maximilian Wurzer et al.

We present an experimental study of energy-to-solution (ETS) of hybrid quantum-classical applications, enabled by direct instrumentation of power consumption of a Forte Enterprise trapped-ion quantum processor. We apply this methodology to a hybrid quantum-classical pipeline for quantum fine-tuning of foundational AI models, and validate the approach end-to-end on quantum hardware. Despite noise and limited qubit counts, the resulting models achieve accuracy competitive with and exceeding classical baselines such as logistic regression and support vector classifiers. Our results show that QPU energy consumption scales approximately linearly with qubit number for shallow circuits, while classical simulation exhibits exponential scaling, indicating a break-even for ETS around 34 qubits. The classification error improvement of the best quantum fine-tuned model over the best classical fine-tuned model considered in this study is around 24%. We further contextualize these findings with comparisons to tensor network methods. This work establishes energy-to-solution as a measurable and scalable metric for evaluating quantum applications and provides experimental evidence of favorable energy-accuracy trade-offs.

Sang Hyub Kim, Oliver Knitter, Jonathan Mei et al.

We study parity features as representations that can be evaluated entirely classically once the binary or quantized input representation and parity words are fixed, particularly when labels depend on higher-order feature interactions or when discrete inference interfaces support perturbation robustness. A parity feature is a signed product over selected bits of a binary input: once the participating bits are known, evaluation requires no quantum resources. Reaching a useful parity representation requires solving two challenges. When the input is parity-ready (a meaningful binary string), the challenge is basis discovery: selecting useful parity words from a combinatorial search space. Otherwise, the challenge is encoding: constructing a binary vector on which parity computation is meaningful. We use hybrid quantum-classical training pipelines to address these: learnable Pauli word selection for basis discovery, learned projection encodings for continuous embeddings, and sPQC-Parity for discrete inputs. On three native-binary parity tasks with 5-10 qubits, the learned parity basis improves mean accuracy by 23.9% to 41.7% over logistic-regression and support-vector baselines. A model comparison shows that the improvement comes primarily from discovering the right parity basis, rather than from quantum moment computation at inference. On five continuous text benchmarks, learned projection recovers much of the loss introduced by dimensionality reduction and fixed binarization, exceeding the full continuous baseline on CR, SST-2, and SST-5. On three encoding-limited discrete datasets, when compared with PCA-bin as the baseline, sPQC-Parity reaches 94.6% improvement on mushroom, 3.0% on splice, and matches PCA-bin on promoter. We also analyze inference robustness under binary or quantized inference, where rounding gives exact invariance below half the quantization step.

Dominic Widdows, Willie Aboumrad, Dohun Kim et al.

Language processing is at the heart of current developments in artificial intelligence, and quantum computers are becoming available at the same time. This has led to great interest in quantum natural language processing, and several early proposals and experiments. This paper surveys the state of this area, showing how NLP-related techniques have been used in quantum language processing. We examine the art of word embeddings and sequential models, proposing some avenues for future investigation and discussing the tradeoffs present in these directions. We also highlight some recent methods to compute attention in transformer models, and perform grammatical parsing. We also introduce a new quantum design for the basic task of text encoding (representing a string of characters in memory), which has not been addressed in detail before. Quantum theory has contributed toward quantifying uncertainty and explaining "What is intelligence?" In this context, we argue that "hallucinations" in modern artificial intelligence systems are a misunderstanding of the way facts are conceptualized: language can express many plausible hypotheses, of which only a few become actual.

Oliver Knitter, Jonathan Mei, Masako Yamada et al.

TorchQuantumDistributed (tqd) is a PyTorch-based [Paszke et al., 2019] library for accelerator-agnostic differentiable quantum state vector simulation at scale. This enables studying the behavior of learnable parameterized near-term and fault- tolerant quantum circuits with high qubit counts.

Alexander Moreno, Justin Xiao, Jonathan Mei

Structured Kernel Interpolation (SKI) (Wilson et al. 2015) helps scale Gaussian Processes (GPs) by approximating the kernel matrix via interpolation at inducing points, achieving linear computational complexity. However, it lacks rigorous theoretical error analysis. This paper bridges the gap: we prove error bounds for the SKI Gram matrix and examine the error's effect on hyperparameter estimation and posterior inference. We further provide a practical guide to selecting the number of inducing points under convolutional cubic interpolation: they should grow as $n^{d/3}$ for error control. Crucially, we identify two dimensionality regimes governing the trade-off between SKI Gram matrix spectral norm error and computational complexity. For $d \leq 3$, any error tolerance can achieve linear time for sufficiently large sample size. For $d > 3$, the error must increase with sample size to maintain linear time. Our analysis provides key insights into SKI's scalability-accuracy trade-offs, establishing precise conditions for achieving linear-time GP inference with controlled approximation error.

Jonathan Mei, Alexander Moreno, Luke Walters

Second order stochastic optimizers allow parameter update step size and direction to adapt to loss curvature, but have traditionally required too much memory and compute for deep learning. Recently, Shampoo [Gupta et al., 2018] introduced a Kronecker factored preconditioner to reduce these requirements: it is used for large deep models [Anil et al., 2020] and in production [Anil et al., 2022]. However, it takes inverse matrix roots of ill-conditioned matrices. This requires 64-bit precision, imposing strong hardware constraints. In this paper, we propose a novel factorization, Kronecker Approximation-Domination (KrAD). Using KrAD, we update a matrix that directly approximates the inverse empirical Fisher matrix (like full matrix AdaGrad), avoiding inversion and hence 64-bit precision. We then propose KrADagrad$^\star$, with similar computational costs to Shampoo and the same regret. Synthetic ill-conditioned experiments show improved performance over Shampoo for 32-bit precision, while for several real datasets we have comparable or better generalization.

Alexander Moreno, Jonathan Mei, Luke Walters

Toeplitz Neural Networks (TNNs) (Qin et. al. 2023) are a recent sequence model with impressive results. They require O(n log n) computational complexity and O(n) relative positional encoder (RPE) multi-layer perceptron (MLP) and decay bias calls. We aim to reduce both. We first note that the RPE is a non-SPD (symmetric positive definite) kernel and the Toeplitz matrices are pseudo-Gram matrices. Further 1) the learned kernels display spiky behavior near the main diagonals with otherwise smooth behavior; 2) the RPE MLP is slow. For bidirectional models, this motivates a sparse plus low-rank Toeplitz matrix decomposition. For the sparse component's action, we do a small 1D convolution. For the low rank component, we replace the RPE MLP with linear interpolation and use asymmetric Structured Kernel Interpolation (SKI) (Wilson et. al. 2015) for O(n) complexity: we provide rigorous error analysis. For causal models, "fast" causal masking (Katharopoulos et. al. 2020) negates SKI's benefits. Working in the frequency domain, we avoid an explicit decay bias. To enforce causality, we represent the kernel via the real part of its frequency response using the RPE and compute the imaginary part via a Hilbert transform. This maintains O(n log n) complexity but achieves an absolute speedup. Modeling the frequency response directly is also competitive for bidirectional training, using one fewer FFT. We set a speed state of the art on Long Range Arena (Tay et. al. 2020) with minimal score degradation.

Jonathan Mei, José M. F. Moura

A semi-parametric, non-linear regression model in the presence of latent variables is applied towards learning network graph structure. These latent variables can correspond to unmodeled phenomena or unmeasured agents in a complex system of interacting entities. This formulation jointly estimates non-linearities in the underlying data generation, the direct interactions between measured entities, and the indirect effects of unmeasured processes on the observed data. The learning is posed as regularized empirical risk minimization. Details of the algorithm for learning the model are outlined. Experiments demonstrate the performance of the learned model on real data.

Jonathan Mei, José M. F. Moura

Many applications donot have the benefit of the laws of physics to derive succinct descriptive models for observed data. In alternative, interdependencies among $N$ time series $\{ x_{nk}, k>0 \}_{n=1}^{N}$ are nowadays often captured by a graph or network $G$ that in practice may be very large. The network itself may change over time as well (i.e., as $G_k$). Tracking brute force the changes of time varying networks presents major challenges, including the associated computational problems. Further, a large set of networks may not lend itself to useful analysis. This paper approximates the time varying networks $\left\{G_k\right\}$ as weighted linear combinations of eigennetworks. The eigennetworks are fixed building blocks that are estimated by first learning the time series of graphs $G_k$ from the data $\{ x_{nk}, k>0 \}_{n=1}^{N}$, followed by a Principal Network Analysis procedure. The weights of the eigennetwork representation are eigenfeatures and the time varying networks $\left\{G_k\right\}$ describe a trajectory in eigennetwork space. These eigentrajectories should be smooth since the networks $G_k$ vary at a much slower rate than the data $x_{nk}$, except when structural network shifts occur reflecting potentially an abrupt change in the underlying application and sources of the data. Algorithms for learning the time series of graphs $\left\{G_k\right\}$, deriving the eigennetworks, eigenfeatures and eigentrajectories, and detecting changepoints are presented. Experiments on simulated data and with two real time series data (a voting record of the US senate and genetic expression data for the \textit{Drosophila Melanogaster} as it goes through its life cycle) demonstrate the performance of the learning and provide interesting interpretations of the eigennetworks.

Jonathan Mei, José M. F. Moura

A semi-parametric, non-linear regression model in the presence of latent variables is introduced. These latent variables can correspond to unmodeled phenomena or unmeasured agents in a complex networked system. This new formulation allows joint estimation of certain non-linearities in the system, the direct interactions between measured variables, and the effects of unmodeled elements on the observed system. The particular form of the model adopted is justified, and learning is posed as a regularized empirical risk minimization. This leads to classes of structured convex optimization problems with a "sparse plus low-rank" flavor. Relations between the proposed model and several common model paradigms, such as those of Robust Principal Component Analysis (PCA) and Vector Autoregression (VAR), are established. Particularly in the VAR setting, the low-rank contributions can come from broad trends exhibited in the time series. Details of the algorithm for learning the model are presented. Experiments demonstrate the performance of the model and the estimation algorithm on simulated and real data.

Jonathan Mei, José M. F. Moura

Many applications collect a large number of time series, for example, the financial data of companies quoted in a stock exchange, the health care data of all patients that visit the emergency room of a hospital, or the temperature sequences continuously measured by weather stations across the US. These data are often referred to as unstructured. A first task in its analytics is to derive a low dimensional representation, a graph or discrete manifold, that describes well the interrelations among the time series and their intrarelations across time. This paper presents a computationally tractable algorithm for estimating this graph that structures the data. The resulting graph is directed and weighted, possibly capturing causal relations, not just reciprocal correlations as in many existing approaches in the literature. A convergence analysis is carried out. The algorithm is demonstrated on random graph datasets and real network time series datasets, and its performance is compared to that of related methods. The adjacency matrices estimated with the new method are close to the true graph in the simulated data and consistent with prior physical knowledge in the real dataset tested.