Contributed Session: Quantum Applications

Paper ID: 44

Authors: Nahid Binandeh Dehaghani, Ban Tran, Rafal Wisniewski, Susan Mengel and A. Pedro Aguiar

Title: Quantum-Inspired Tensor Networks for Approximating PDE Flow Maps

Abstract: We investigate quantum-inspired tensor networks (QTNs) for approximating flow maps of hydrodynamic partial differential equations (PDEs). Motivated by the effective lowrank structure that emerges after tensorization of discretized transport and diffusion dynamics, we encode PDE states as matrix product states (MPS) and represent the evolution operator as a structured low-rank matrix product operator (MPO) in tensor-train form (e.g., arising from finite-difference discretizations assembled in MPO form). The MPO is applied directly in MPS form, and rank growth is controlled via canonicalization and SVD-based truncation after each step. We provide theoretical context through standard matrix product properties, including exact MPS representability bounds, local optimality of SVD truncation, and a Lipschitz-type multi-step error propagation estimate. Experiments on one- and twodimensional linear advection–diffusion and nonlinear viscous Burgers equations demonstrate accurate short-horizon prediction, favorable scaling in smooth diffusive regimes, and error growth in nonlinear multi-step predictions.

Paper ID: 68

Authors: Maria Gabriela Jordão Oliveira, Karl Michael Ziems and Nina Glaser

Title: Quantum Krylov subspace methods: when numerical precision meets noise

Abstract: Current quantum devices are limited by noise, short coherence times, and restricted qubit counts. However, the quantum computing community anticipates the upcoming availability of early fault-tolerant hardware, offering more qubits and greater noise resilience. Consequently, algorithms tailored to these new devices are necessary to explore the advantages of quantum computing in the near term. Quantum Krylov methods, which are extensions of classical algebraic techniques to the quantum realm, are prime candidates for this new generation of devices. However, the ill-conditioned nature of the generalized eigenvalue problem on the Krylov basis generated using quantum devices is pointed out in the literature as a major drawback and a possible obstacle to achieving practical quantum advantage. In this context, we investigate whether this ill-conditioning is truly a fundamental limitation of quantum Krylov algorithms. We analyze the impact of both numerical and statistical errors, considering realistic sampling noise models and modern regularization techniques used to stabilize the problem. Furthermore, we propose a diagnostic strategy to assess the reliability of the computed solutions without requiring a priori knowledge of the exact solution. Our results suggest that ill-conditioning may be less prohibitive than previously thought when noise and modern regularization techniques are taken into account, providing new insights into the practical viability of these methods.

Paper ID: 97

Authors: Sina Zeytinoglu

Title: Efficient State Preparation using Quantum Signal Processing

Abstract: The preparation of nonclassical states of bosonic modes is a central task for quantum sensing, communication, and error-corrected quantum information processing. However, designing explicit protocols for such state-preparation problems remains challenging. The dominant approach relies on quantum optimal control, where classical simulations are used to numerically optimize control fields. While powerful, this strategy scales poorly with Hilbert-space dimension and typically produces control sequences that are difficult to interpret or generalize. In this talk we introduce a new paradigm for quantum control based on Quantum Signal Processing (QSP). Originally developed as a central primitive for quantum algorithms, QSP also has a deep connection to composite pulse sequences. Leveraging this connection, we show that these algorithmic ideas naturally translate into analytically tractable control protocols for bosonic cavity systems. We first apply this methodology to Generalized Parity Measurements (GPMs) in superconducting cavity QED. The resulting QSP protocols implement arbitrary GPMs in constant time with respect to both the system size and the measurement modulus, while also admitting simple analytical approximations. In realistic architectures, they enable the preparation of multi-component cat states with photon numbers approaching 400 photons and fidelities exceeding 90% [1], far surpassing the scale of cat states realized in current experiments [2]. Beyond measurement-based preparation, we introduce a new theoretical framework for micromaser control using quantum singular value transformations (QSVT) [3]. In this setting, a high-Q microwave cavity interacts sequentially with a stream of atoms, through Jaynes-Cummings interactions. We show that QSP-structured control of the atomic stream enables the engineering of any nonclassical steady-state photon-number distribution that approximates the steady state of a Markovian birth-and-death process [4]. To our knowledge, QSVT has not previously been applied in the micromaser setting, opening a new interface between quantum algorithms and cavity-QED control. Finally, we discuss how emerging experimental capabilities—including optically accessible microwave cavities and transportable neutral-atom platforms—provide a realistic route for implementing these protocols in next-generation cavity QED and other hybrid quantum systems. Together, these results demonstrate how algorithmic primitives from quantum computing can be repurposed to design scalable and interpretable quantum control protocols for near-term quantum technologies.

[1] S. Zeytinoglu, arXiv:2409.05186, accepted to Physical Review Research (2026)

[2] J. C. Curtis et al., Phys. Rev. A 103, 023705 (2021)

[3] S. Lloyd et al., arXiv:2104.01410

[4] A. Kizilirmak, C. Ballestero, O. Mustecaplioglu, S. Zeytinoglu (in preparation)”