Agenda | PQAI 2025 - Edwardson School of Industrial Engineering - Purdue University

What kind of logic do people use to reason about natural events? What kind of probability theory best describes how people make inferences and decisions under uncertainty? I will review empirical evidence from a variety of domains that demonstrate the contextual nature of our reasoning and decision-making processes. This includes empirical examples from attitude surveys, membership judgments, categorization decisions, probability estimates, preferential choices, and risky decision-making. These findings are difficult to explain using classical logic and Bayesian probability theory. Although various heuristics have been proposed to account for these findings, they turn out to be ad hoc, unsystematic, and even inconsistent. Quantum probability is an alternative, and completely general, probability theory, which is based on different axioms that Bayesian probability. I will show that quantum probability theory provides a simple, systematic, and coherent way to understand the contextual nature of human reasoning.

Quantum algorithms are commonly used to solve unconstrained combinatorial optimization problems. While unconstrained problems map naturally into the algorithm, incorporating constraints typically requires penalizing constraint violations in the objective function. In this talk, we present techniques for incorporating constraints into quantum algorithms.

Quantum Artificial Intelligence (QAI) has emerged as a frontier discipline at the intersection of quantum computing and machine learning, with the potential to reshape the foundations of intelligent systems. This talk provides a perspective on several pioneering directions that collectively define a coherent research agenda for scalable and adaptive QAI. We begin with Quantum Reinforcement Learning (QRL), which introduced parameterized quantum circuits into sequential decision-making tasks and has since expanded into evolutionary, recurrent, and distributed variants. We then turn to Quantum Long Short-Term Memory (QLSTM) models, which extend quantum learning into temporal and sequential domains, enabling quantum-enhanced sequence modeling and federated learning applications. Building on these foundations, we present the concept of the Quantum Fast Weight Programmer (QFWP), a meta-learning framework that dynamically generates parameters and measurements for variational quantum circuits, paving the way for recursive and self-programming agents. Complementary to these advances, we highlight Differentiable Quantum Architecture Search (DiffQAS), which automates circuit design and contributes to the scalability of quantum neural networks. We conclude with a vision of QAI as a transformative force for the next technological epoch, outlining open challenges such as barren plateau mitigation, hybrid quantum-classical integration, and the development of distributed quantum architectures. Together, these contributions establish a foundation for QAI not only as a research field but as a paradigm for intelligent, self-improving quantum systems.

Quantum computing promises to transform how we solve optimization problems—but today’s devices alone cannot get us there. The most promising path forward lies in hybrid approaches that combine the strengths of classical algorithms with the emerging capabilities of quantum hardware, opening the door to scalable and high-performance solutions.

In this talk, I will present recent advances in quantum optimization that bring this vision to life. I will discuss how warm-starting the Quantum Approximate Optimization Algorithm (QAOA) with classical relaxations can dramatically improve performance, how hybrid pipelines leverage combinatorial and convex structure to achieve stronger approximations and noise resilience, and how benchmark families—such as strongly regular graphs and low-degree graphs—help us probe the boundary of quantum advantage. These results connect classical approximation algorithms, convex optimization, and quantum circuit design within a unified framework.

Looking ahead, I will outline a research vision for hybrid intelligence, where classical and quantum algorithms operate in synergy rather than competition—rethinking optimization for the next era of computing.

Over some 20 years we have developed a diagrammatic quantum formalism, sometimes referred to as quantum picturalism [1, 2]. We showed that this formalism enabled secondary school students to perform exceptionally well on an Oxford University post-grad quantum exam [3]. It was in fact John von Neumann himself who denounced `his own’ quantum formalism, that relies on Hilbert space. Alternatives had been proposed, including by von Neumann himself, but none play a role in quantum theory today. Quantum picturalism on the other hand, is not widespread in quantum industry. The same formalism has been used as the basis for interpretable AI [4], and even music [5].

[1] Bob Coecke and Aleks Kissinger (2017) Picturing Quantum Processes. Cambridge University Press.

[2] Bob Coecke and Stefano Gogioso (2022) Quantum in Pictures. Quantinuum.

[3] [4] [5]

This talk will explore ideas aimed at bridging the gap between today’s Noisy Intermediate-Scale Quantum (NISQ) era and the long-term goal of fully fault-tolerant quantum computing (FTQC). I will begin by introducing EFT-VQA, which proposes strategies for transitioning variational quantum algorithms (VQAs) into the early fault-tolerant (EFT) regime by leveraging partial error correction. Next, I will present DS-ZNE, which extends the widely used NISQ-era error mitigation technique of zero-noise extrapolation (ZNE) into fault-tolerant settings. Finally, if time permits, I will highlight how additional techniques developed for NISQ VQAs may continue to play a role in the EFT regime.

This talk gives an optimizer's perspective on what is known about the expected or potential utility of quantum computers for mathematical optimization. We will see that even if some of the existing research trends require empirical validation and have escaped rigorous theoretical characterization of potential advantage, other areas of quantum optimization are supported by well-established quantum subroutines, which open up many interesting possibilities in the era of fault-tolerant quantum computation, and possibly even before.

Computing the eigenvalues of a matrix is a fundamental task in numerical linear algebra and a building block of many classical and quantum machine learning algorithms. Kitaev's Quantum Phase Estimation (QPE) algorithm, when implemented on a quantum computer, enables the efficient solution of the eigenvalue problem for exponentially large matrices under specific conditions. This advancement has the potential to provide significant quantum advantages in fields like quantum chemistry and quantum machine learning. Recent research has focused on reducing the quantum resources needed for Kitaev's original protocol, leading to the development of “post-Kitaev” or early fault-tolerant QPE schemes. In this talk, I will present some of the recent progress made in this area. Specifically, I will first introduce the QMEGS algorithm, which enables the estimation of multiple dominant eigenvalues simultaneously using a single ancilla and shorter circuits. Next, I will discuss our recent work on estimating ground state degeneracy and learning topological properties using a quantum computer.

We present a quantum-compatible reformulation of Natural Policy Gradient (NPG) using deterministic, truncation-based estimators for both the policy gradient and Fisher information, enabling coherent evaluation with standard quantum environment and policy oracles. Leveraging quantum mean estimation and variance reduction within a classical–quantum double-loop scheme, the resulting Quantum NPG (QNPG) achieves a sample complexity of ˜O(ϵ−1.5) to reach an ϵ-optimal policy, improving upon the classical Ω(ϵ−2) lower bound for policy gradient methods. We outline the required assumptions (smooth score function, Fisher non-degeneracy, bounded compatible approximation error), highlight the exponentially decaying truncation bias, and sketch the convergence analysis that yields the overall complexity.

Reinforcement learning (RL) utilizing classical neural networks(NNs) has achieved substantial progress across numerous application domains. Nevertheless, classical RL faces significant challenges in training when applied to systems with high-dimensional action spaces, such as coordinated satellite networks. In these scenarios, the exponential increase in model parameters imposes heavy computational requirements, thereby constraining scalability and slowing convergence. Quantum reinforcement learning (QRL), which incorporates quantum neural networks (QNNs), provides a promising alternative by exploiting quantum mechanical properties, including superposition and entanglement. Through QNNs, multiple states can be compactly represented using a limited number of quantum bits (qubits), effectively reducing computational overhead. Due to these characteristics—namely, rapid convergence and enhanced scalability—QRL constitutes a suitable substitute for classical RL in coordinated satellite applications. Moreover, the proposed QRL framework mitigates the curse of dimensionality by efficiently leveraging qubit-based representations. In experimental environments characterized by high-dimensional action spaces, the proposed algorithm demonstrates superior training performance compared to conventional RL approaches.

The rapid growth of large language models (LLMs) has intensified the demand for efficient fine-tuning techniques under constrained computational and memory budgets. Parameter-efficient fine-tuning (PEFT) addresses this challenge, yet existing methods often sacrifice expressive capacity for reduced complexity. This paper introduces Quantum amplitude embedded (QAE) adaptation, a novel PEFT framework that leverages quantum-amplitude embedding to achieve logarithmic compression of activation vectors while preserving task-relevant information. By integrating parameterized quantum circuits (PQCs) as nonlinear transformation layers, QAE adaptation replaces conventional linear adapters in attention modules with compact quantum-inspired operators. This design provides high expressivity with significantly fewer trainable parameters. Experimental evaluations across benchmark tasks demonstrate that QAE achieves competitive or superior performance compared with state-of-the-art PEFT methods, which highlights its effectiveness for resource-constrained LLM adaptation.

We introduce CVQBoost, a novel classification algorithm that leverages early hardware implementing Quantum Computing Inc’s Entropy Quantum Computing (EQC) paradigm, Dirac-3 [Nguyen et. al. arXiv:2407.04512]. We apply CVQBoost to a fraud detection test case and benchmark its performance against XGBoost, a widely utilized ML method. Running on Dirac-3, CVQBoost demonstrates a significant runtime advantage over XGBoost, which we evaluate on high-performance hardware comprising up to 48 CPUs and four NVIDIA L4 GPUs using the RAPIDS AI framework. Our results show that CVQBoost maintains competitive accuracy (measured by AUC) while significantly reducing training time, particularly as dataset size and feature complexity increase. To assess scalability, we extend our study to large synthetic datasets ranging from 1M to 70M samples, demonstrating that CVQBoost on Dirac-3 is well-suited for large-scale classification tasks. These findings position CVQBoost as a promising alternative to gradient boosting methods, offering superior scalability and efficiency for high-dimensional ML applications such as fraud detection.

In this work, we characterize the Fourier structure of singlequbit, data-reuploading parameterized quantum circuits (PQCs). Each data-encoding rotation constrains the Bloch vector to a circle whose radius is fixed by the trainable blocks. We prove the Bloch Circle Projection Theorem: for a single layer, projecting this trajectory onto the measurement axis directly yields the circuit’s Fourier coefficients. This gives a concrete design rule: choose rotation axes non-collinear with the encoding axis to avoid degenerate projections. The same geometric argument extends to L-layer circuits; permitting layer-wise flexible rotation axes preserves full expressivity, even for targets with rich high-frequency content.

Anomaly detection plays a vital role in industrial quality control and manufacturing processes. Traditional machine learning methods often face challenges, especially in scenarios where training data is limited. In these circumstances, quantum machine learning (QML) has emerged as a promising approach to improve anomaly detection capabilities. This paper provides a comprehensive review of QML applications in industrial anomaly detection, with particular focus on image-based inspection systems, presenting our novel contributions. This paper classifies various types of anomalies encountered in industrial environments and provides a detailed review of classical and quantum anomaly detection approaches. In addition, we present the latest advances in quantum kernel methods in image-based anomaly detection. The analysis includes experimental results showing that quantum kernels outperform classical methods in certain industrial applications. For example, in shipment inspection, compared to an F1 score of 0.964 for SVM using an imbalanced dataset of 400 samples (300 normal, 100 anomalous), QSVM achieved an F1 score of 0.990 compared to 0.958 for ResNet (1132 normal), a 2.7% improvement in detection performance. We also discuss the implementation of quantum support vector machines (QSVM) with quantum kernels and their performance on quantum simulators and actual quantum hardware. Hardware validation reveals that quantum circuits with depths ≤32 maintain consistent performance between simulators and actual quantum devices, while circuits with depths >273 suffer significant degradation (AUC: 0.89→0.59) due to noise accumulation. These findings establish practical guidelines for deploying quantum machine learning in industrial settings and provide a roadmap for future quantum-enhanced manufacturing systems.

An exploration into D-Wave’s modern offerings, including a recent and successful AI-related project.

We are witnessing device- and software-wise advances in quantum computing (QC). Yet, cognitive and technical complexities in QC makes it difficult to interact with quantum devices, imposing tasks that users have not done previously. For example, they need to encode problems in a quantum way, explore different circuit optimization strategies, and consider uncertainty in measurement outcomes. Limited usability support, such as end-user interfaces, amplifies this difficulty. To bring seamless experiences in QC, we need to rethink how we design end-user interfaces as QC reshapes our way of computing. This innovation can only be successful through interdisciplinary collaborations among researchers around human-computer interaction (HCI) and QC. In this talk, therefore, I will introduce what HCI can offer to quantum computing with examples from recent research and outline potential venues for interdisciplinary research around HCI and QC.

Quantum algorithms for optimization have been a topic of intense investigation for decades due to their many potential applications to scientific computing, industrial engineering, and artificial intelligence. Despite this interest, there has been a limited number of quantum algorithms that exhibit large speedups over state-of-art classical methods, are applicable to general problems, and are based on concrete theoretical mechanisms. In this talk, I will give an overview of quantum algorithms research at JPMorganChase, and describe some recent efforts to identify and characterize such mechanisms. The primary focus will be on dynamical quantum algorithms for convex and non-convex optimization, and the potential for large provable speedups in both settings.

First-order methods are the workhorse of modern machine learning, but they are notoriously inefficient in non-convex landscapes, frequently becoming trapped by local minima and saddle points. These classical limitations make them a prime target for quantum acceleration. In this talk, I will first establish a fundamental connection between gradient flows (i.e., the continuous-time limit of gradient descent) and the evolution of a continuous-variable quantum system under a corresponding Hamiltonian. This mapping yields a new class of quantum algorithms that not only inherit the efficiency of gradient descent but also leverage quantum tunneling to escape saddle points and local minima. I will present results demonstrating this quantum advantage, including provable speedups and superior empirical performance in finding global solutions. Finally, I will briefly survey some recent advances in generalizing this quantum dynamical approach to higher-order optimization methods.

Abstract for David Stewart’s talk will be posted here.

The growing demand for solving large-scale, data-intensive linear and conic optimization problems, particularly in applications such as artificial intelligence and machine learning, has highlighted the limitations of classical interior point methods (IPMs). Despite their favorable polynomial-time convergence, conventional IPMs often suffer from high per-iteration computational costs, especially for dense problem instances. Recent advances in quantum computing, particularly quantum linear system solvers, offer promising avenues to accelerate the most computationally intensive steps of IPMs. However, practical challenges such as quantum error, hardware noise, and sensitivity to poorly conditioned systems remain significant obstacles. In response, a series of Quantum IPMs (QIPMs) have been developed to address these challenges, incorporating techniques such as feasibility maintenance, iterative refinement, and preconditioning. In this work, we review this line of research with a focus on our recent contributions, including a novel almost-exact QIPM framework. This hybrid quantum-classical approach constructs and solves the Newton system entirely on a quantum computer, while performing solution updates classically. Crucially, all matrix-vector operations are executed on quantum hardware, enabling the method to achieve an optimal worst-case scalability w.r.t dimension, surpassing the scalability of existing classical and quantum IPMs.

A series of recent studies has demonstrated that Quantum Amplitude Amplification (QAA), the generalization of Grover’s search algorithm, is capable of solving combinatorial optimization problems using oracle operations which apply phases proportional to all possible solutions. However, the algorithm’s success is highly sensitive to a free parameter choice which must be determined before running the quantum algorithm. In this study we demonstrate the feasibility of using regression neural network architectures to predict this parameter using only the weights and connections of a discrete objective function. We show that for both fixed length and varying length linear QUBO (quadratic unconstrained binary optimization) problems the neural network architectures can be trained to accurately predict the free parameter with sufficient error rates necessary for performing successful QAA.

The Variational Quantum Eigensolver (VQE) is a central method in quantum machine learning, with applications across disciplines such as finance, biostatistics, and related fields. Despite its impact, VQE suffers from limited scalability due to the exponential space complexity O(2N) required to store quantum states and compute expectation values, where N is the number of qubits. To address this, the Matrix Product State (MPS) VQE was developed, reducing storage complexity to O(nχ2), where χ is the bond dimension. However, the bond dimension typically grows with entangling operations such as CNOT or SWAP, leading to large memory demands in highly entangled circuits. The Tensor Ring (TR) VQE improves upon this by fixing the bond dimension and connecting the first and last qubits, thereby avoiding unbounded memory growth and enabling more complex circuits. Nevertheless, TR VQE still requires exponential space complexity O(2N) to evaluate expectation values, which restricts its scalability. In this work, we propose a space-efficient TR VQE method for combinatorial optimization. Our key contribution is a batched expectation value calculation that leverages MPS-style contraction to evaluate multiple Pauli terms simultaneously. This batching improves efficiency while reducing expectation evaluation space complexity to O(nχ4). Moreover, it increases only linear space complexity with respect to the number of Pauli terms, providing a scalable path toward practical quantum optimization.

Quantum algorithms are commonly used to solve unconstrained combinatorial optimization problems. While unconstrained problems map naturally into the algorithm, incorporating constraints typically requires penalizing constraint violations in the objective function. In this talk, we present techniques for incorporating constraints into quantum algorithms.

Simulating quantum systems is a foundational application in quantum computing, particularly in fields such as computational chemistry. We present our use of a scalable framework, the Quantum Economic Development Consortium (QED-C) Application-Oriented Benchmark Suite (QED-C), to evaluate the performance of quantum algorithms across various hardware platforms. A key focus is leveraging NVIDIA CUDA-Q, a powerful GPU-accelerated platform for quantum-classical hybrid programming, to benchmark Hamiltonian simulation, Quantum Fourier Transform (QFT), and Phase Estimation (PE). We simulate a range of physical systems within HamLib [12], including the transverse field Ising, Heisenberg, and Fermi-Hubbard models, as well as molecules such as H2 using Suzuki-Trotter evolution. Simulations were executed on NVIDIA GPUs, including the A100, H100, GH200, and GB200 systems, at Purdue University [7] and Lawrence Berkeley National Laboratory (LBNL) [8], as well as in collaboration with NVIDIA. CUDA-Q’s SpinOperator formalism enabled emulation of circuits for up to 38 qubits on the LBNL cluster, with performance up to 3× faster than real quantum hardware. Strong scaling behavior is observed up to 32 GPUs, with execution times for some simulations reduced by more than 90%. For example, execution times for simulating a 33-qubit TFIM dropped from 19 s (1 GPU) to 2 s (32 GPUs). Despite these gains, we observe classical HPC-like diminishing returns beyond 8 GPUs, due to inter-GPU communication bottlenecks. This impact is mitigated in the latest GB200 clusters that support extending the high-bandwidth NVLink GPU interconnect across multiple nodes. CUDA-Q proves especially effective for sampling-heavy workloads, offering near-linear scaling and improved parallel efficiency for PE and QFT. Our findings demonstrate that GPU-accelerated quantum Hamiltonian simulation with CUDA-Q provides a robust and high-throughput alternative to noisy intermediate-scale quantum (NISQ) devices, paving the way for future kernel-level optimizations and distributed quantum computing strategies.

Robust performance under distributional shifts and noisy inputs is critical for real world deployment of machine learning models. While Convolutional Neural Networks (CNNs) remain the foundation of vision models, they are notoriously sensitive to corruptions in the input data, such as sensor noise, partial occlusions, or bit level errors. Motivated by the growing interest in quantum machine learning, we investigate whether quantum inspired architectural inductive biases can confer greater resilience to such perturbations. We conduct a systematic evaluation of three neural architectures Classical CNN, Quantum Convolutional Neural Network (QCNN), and Quantum Multi Head Attention (QMHA) on the CIFAR 10 dataset under a diverse set of corruption regimes. Specifically, we test inference time robustness against Gaussian noise, salt and pepper corruption, Fourier masking, stripe noise, block masking, and bit flip noise, without any retraining or augmentation. Our results demonstrate that while CNNs degrade significantly under most corruptions, quantum inspired architectures, particularly QMHA, exhibit improved robustness in multiple scenarios. These findings highlight the potential of quantum informed designs in developing resilient vision models and suggest promising directions for future hybrid quantum classical architectures in real world deployment settings.

We explore the encoding Quadratic Integer Optimization (QIP) problems into Quadratic Unconstrained Integer Optimization (QUIO) formulations with a target integer basis. These formulations are suitable for solving on quantum computers based on qudits, which natively extend the integer representation of their qubit-based counterparts. For qubit-based computers, the usual framework for representing discrete optimization problems is the Quadratic Unconstrained Binary Optimization (QUBO) formulation. Decision variables can, for QUBOs, assume only binary values, while for QUIOs, they can represent integer values from zero up to a machine-dependent maximum. One advantage of working with a larger domain of decision variables is that it enables QIP problems to be cast as QUIO formulations. As our results highlight, these formulations use fewer decision variables than, for example, Quadratic Unconstrained Binary Optimization (QUBO)-based formulations. We selected various candidate problems to empirically verify our reformulations: Quadratic Facility Location Problem, Quadratic Inventory Management Problem, Quadratic Vehicle Routing Problem, and Quadratic Knapsack Problem. Problem instances for these problems are diverse in data distribution and size and are reformulated into QUBO and QUIO. We compare these formulations, characterizing them using metrics associated with solution performance. Moreover, using qubit- and qudit-based entropy quantum machines, we compared the performance of the resulting formulations for instances amenable to these architectures. Our primary goal is to conduct computational experiments to verify the impacts of each encoding type on these problems, aiming to find insights that could potentially generalize to similar optimization problems. Moreover, we also indicate guidelines to accelerate the encoding process, ensuring that the potential quantum advantage using qudit quantum computers is not lost during the classical pre-processing and during problem reformulation. Finally, we provide open-source software to perform the reformulations and communicate them with qudit-based entropy quantum devices, allowing others to map and solve QIP problems using QUIO reformulations.

Systems of linear equations are ubiquitous across science, engineering, machine learning, and even finance. While classical methods can be prohibitively slow for large-scale problems, quantum linear systems algorithms offer the potential for exponential speedup in certain parameter regimes. However, a significant gap persists between this theoretical promise and practical implementation, as the advantages are often obscured by the substantial quantum resources and high sensitivity to noise inherent in current quantum hardware. One way to bridge this gap is through the use of Iterative Refinement, a classical post-processing scheme that can exponentially improve the accuracy to which a linear system of equations can be solved using low-precision arithmetic. In the context of quantum linear systems algorithms, such as the HHL algorithm proposed by Harrow, Hassidim, and Loyd, Iterative Refinement can greatly reduce the quantum resources required to calculate an accurate solution in terms of tomography cost, circuit volume, and fault-tolerant overhead. Here, we compute and benchmark highly precise solutions to linear systems of equations of up to eight variables by running HHL with Iterative Refinement on NISQ quantum computers. We also present our open-source implementation, emphasizing that our circuit is not tailored to specific problem instances, as most available implementations are.

Discovering unconventional optical designs via machine-learning promises to advance on-chip circuitry, imaging, sensing, energy, and quantum information technology. In this talk, we discuss photonic design approaches and emerging material platforms for showcasing machine-learning-assisted topology optimization for optical metasurface designs with applications in thermophotovoltaics, reflective optics, quantum photonic circuitry and lightsail technology. We demonstrate the effectiveness of autoencoders for compressing the vast design space of metasurfaces into a smaller search space. By employing global optimization via adjoint methods or quantum annealing, one can find the optimal metasurface designs within the smaller space constructed by the autoencoder. We also report on the quantum-assisted machine learning framework, named bVAE-QUBO, that is a generic framework that compresses an arbitrary continuous optimization problem into an Ising-model formalism for quantum sampling. When compared to other global optimization techniques, bVAE-QUBO has the potential for quantum speedups and achieving higher quality designs than traditional adjoint optimization methods. The techniques employed in this work extend well beyond the metasurface optimization space and into other inverse design problems. We also apply machine learning approaches to advance quantum measurements and superresolution imaging.