Martin Roetteler

Natansh Mathur, Panagiotis Kl. Barkoutsos, Masako Yamada et al.

Training quantum neural networks (QNNs) on quantum hardware is currently bottlenecked by the cost of gradient estimation: standard parameter-shift methods require a number of circuit evaluations that grows quadratically with the number of trainable parameters, making hardware-based optimisation impractical beyond small system sizes. In this work, we introduce a training framework that reduces this cost to logarithmic in the number of qubits, making gradient-based QNN optimisation feasible on near-term hardware at increasing scales. Our framework combines three co-designed ingredients: (i) a structured, subspace-preserving Butterfly circuit architecture with $O(n \log n)$ parameters and logarithmic depth; (ii) a layer-wise training strategy that confines on-hardware optimisation to one small, well-structured layer at a time; and (iii) a parallelised parameter-shift rule that exploits the commuting structure within each Butterfly layer to extract all gradients in a constant number of circuit executions. Together these reduce the number of distinct circuit evaluations per optimisation step from $O(n^2)$ to $O(\log n)$. We validate the framework on clinical data imputation using the MIMIC-III electronic health record dataset, a demanding benchmark sensitive to optimisation instability and model variance. Hybrid classical-quantum models are trained directly on IonQ Forte Enterprise trapped-ion hardware at 16 qubits without performance degradation relative to ideal or noisy simulation and via tensor-network simulation at 32 qubits, with 32-qubit inference executed on hardware. The resulting models match or exceed strong classical neural baselines in downstream patient survival prediction while exhibiting reduced variance across runs, demonstrating that the proposed framework enables practical, scalable QNN training under realistic hardware constraints.

Daiwei Zhu, Miguel Angel Lopez-Ruiz, François-Henry Rouet et al.

Solving large-scale sparse linear systems is a challenging computational task due to the introduction of non-zero elements, or "fill-in." The Graph Partitioning Problem (GPP) arises naturally when minimizing fill-in and accelerating solvers. In this paper, we measure the end-to-end performance of a hybrid quantum-classical framework designed to accelerate Finite Element Analysis (FEA) by integrating a quantum solver for GPP into Synopsys/Ansys' LS-DYNA multiphysics simulation software. The quantum solver we use is based on Iterative-QAOA, a scalable, non-variational quantum approach for optimization. We focus on two specific classes of FEA problems, namely vibrational (eigenmode) analysis and transient simulation. We report numerical simulations on up to 150 qubits done on NVIDIA's CUDA-Q/cuTensorNet and implementation on IonQ's Forte quantum hardware. The potential impact on LS-DYNA workflows is quantified by measuring the wall-clock time-to-solution for complex problem instances, including vibrational analysis of large finite element models of a sedan car and a Rolls-Royce jet engine, as well as transient simulations of a drill and an impeller. We performed end-to-end performance measurements on meshes comprising up to 35 million elements. Measurements were conducted using LS-DYNA in distributed-memory mode via Message Passing Interface (MPI) on AWS and Synopsys compute clusters. Our findings indicate that with a quantum computer in the loop, amortized LS-DYNA wall-clock time can be improved by up to 15% for specific cases and by at least 7% for all models considered. These results highlight the significant potential of quantum computing to reduce time-to-solution for large-scale FEA simulations within the Noisy Intermediate-Scale Quantum (NISQ) era, offering an approach that is scalable and extendable into the fault-tolerant quantum computing regime.

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.

Carlos Flores-Garrigós, Anton Simen, Qi Zhang et al.

We present a quantum feature-selection framework based on a higher-order unconstrained binary optimization (HUBO) formulation that explicitly incorporates multivariate dependencies beyond standard quadratic encodings. In contrast to QUBO-based approaches, the proposed model includes one-, two-, and three-body interaction terms derived from mutual-information measures, enabling the objective function to capture feature relevance, pairwise redundancy, and higher-order statistical structure within a unified energy model. To suppress trivial all-selected solutions, we further include structured linear penalties that promote sparsity while preserving informative variables. The resulting HUBO instances are optimized with digitized counterdiabatic quantum optimization on IonQ Forte and compared against noiseless quantum simulation as well as two classical dimensionality-reduction baselines: SelectKBest based on mutual information and principal component analysis (PCA). We evaluate the proposed workflow on two benchmark classification datasets, namely the Gallstone dataset and the Spambase dataset, and analyze both predictive performance and selected-subset structure. The results show good qualitative agreement between hardware executions and noiseless simulations, supporting the feasibility of implementing higher-order feature-selection Hamiltonians on current trapped-ion processors. In addition, the quantum approach yields competitive classification performance while producing compact and informative feature subsets, highlighting the potential of higher-order quantum optimization for machine-learning preprocessing tasks.

Felix Tripier, Woo Chang Chung, Jacob Young et al.

We propose a fault-tolerant quantum computer architecture for trapped-ion devices, which we call the walking cat architecture. Our blueprint includes a compiler, a detailed description of all the quantum error-correction protocols, a micro-architecture, a sufficiently fast decoder, and thorough simulations. The backbone of the architecture is a cat factory, producing cat states distributed throughout the machine, which are consumed to perform logical operations. The walking cat architecture is based entirely on a modern quantum error-correction approach called low-density parity-check (LDPC) codes. We identify promising instances of the walking cat architecture, such as (1) a simple architecture based on a single LDPC code, (2) a fast architecture based on fast logical gates relying on a [[70, 6, 9]] code, equipped with Clifford-frame tracking for any 6-qubit Clifford gate, and (3) a dense architecture based on a [[102, 22, 9]]] code encoding 22 logical qubits per memory block. Our dense architecture provides a design with 110 logical qubits executing about one million T gates per day using only 2,514 physical qubits. We estimate that the quantum Hamiltonian simulation of a Heisenberg model on 100 sites can be executed within one month with 10,000 physical qubits, including all shots required to achieve chemical accuracy, suggesting that such a device could enter the regime of classically intractable physics simulations. Our design relies on hardware components that have been experimentally demonstrated on small devices. We emphasize simplicity over hypothetical performance to facilitate the practical realization of this machine. Based on this approach, we believe that a fault-tolerant quantum computer with hundreds of logical qubits capable of running millions of logical gates can be built in the near term, providing a platform to explore a broad range of applications.

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.

Daochen Wang, Aarthi Sundaram, Robin Kothari et al.

Reinforcement learning studies how an agent should interact with an environment to maximize its cumulative reward. A standard way to study this question abstractly is to ask how many samples an agent needs from the environment to learn an optimal policy for a $γ$-discounted Markov decision process (MDP). For such an MDP, we design quantum algorithms that approximate an optimal policy ($π^*$), the optimal value function ($v^*$), and the optimal $Q$-function ($q^*$), assuming the algorithms can access samples from the environment in quantum superposition. This assumption is justified whenever there exists a simulator for the environment; for example, if the environment is a video game or some other program. Our quantum algorithms, inspired by value iteration, achieve quadratic speedups over the best-possible classical sample complexities in the approximation accuracy ($ε$) and two main parameters of the MDP: the effective time horizon ($\frac{1}{1-γ}$) and the size of the action space ($A$). Moreover, we show that our quantum algorithm for computing $q^*$ is optimal by proving a matching quantum lower bound.

Alex Bocharov, Michael Freedman, Eshan Kemp et al.

A school of thought contends that human decision making exhibits quantum-like logic. While it is not known whether the brain may indeed be driven by actual quantum mechanisms, some researchers suggest that the decision logic is phenomenologically non-classical. This paper develops and implements an empirical framework to explore this view. We emulate binary decision-making using low width, low depth, parameterized quantum circuits. Here, entanglement serves as a resource for pattern analysis in the context of a simple bit-prediction game. We evaluate a hybrid quantum-assisted machine learning strategy where quantum processing is used to detect correlations in the bitstreams while parameter updates and class inference are performed by classical post-processing of measurement results. Simulation results indicate that a family of two-qubit variational circuits is sufficient to achieve the same bit-prediction accuracy as the best traditional classical solution such as neural nets or logistic autoregression. Thus, short of establishing a provable "quantum advantage" in this simple scenario, we give evidence that the classical predictability analysis of a human-generated bitstream can be achieved by small quantum models.

Markus Grassl, Brandon Langenberg, Martin Roetteler et al.

We present quantum circuits to implement an exhaustive key search for the Advanced Encryption Standard (AES) and analyze the quantum resources required to carry out such an attack. We consider the overall circuit size, the number of qubits, and the circuit depth as measures for the cost of the presented quantum algorithms. Throughout, we focus on Clifford$+T$ gates as the underlying fault-tolerant logical quantum gate set. In particular, for all three variants of AES (key size 128, 192, and 256 bit) that are standardized in FIPS-PUB 197, we establish precise bounds for the number of qubits and the number of elementary logical quantum gates that are needed to implement Grover's quantum algorithm to extract the key from a small number of AES plaintext-ciphertext pairs.

Martin Roetteler, Rainer Steinwandt

In a basic related-key attack against a block cipher, the adversary has access to encryptions under keys that differ from the target key by bit-flips. In this short note we show that for a quantum adversary such attacks are quite powerful: if the secret key is (i) uniquely determined by a small number of plaintext-ciphertext pairs, (ii) the block cipher can be evaluated efficiently, and (iii) a superposition of related keys can be queried, then the key can be extracted efficiently.

Andrew M. Childs, Robin Kothari, Maris Ozols et al.

We study the quantum query complexity of the Boolean hidden shift problem. Given oracle access to f(x+s) for a known Boolean function f, the task is to determine the n-bit string s. The quantum query complexity of this problem depends strongly on f. We demonstrate that the easiest instances of this problem correspond to bent functions, in the sense that an exact one-query algorithm exists if and only if the function is bent. We partially characterize the hardest instances, which include delta functions. Moreover, we show that the problem is easy for random functions, since two queries suffice. Our algorithm for random functions is based on performing the pretty good measurement on several copies of a certain state; its analysis relies on the Fourier transform. We also use this approach to improve the quantum rejection sampling approach to the Boolean hidden shift problem.