arXiv subjects

Adelina Bärligea

Publications and source records attributed to Adelina Bärligea.

8 recordsLinked to original sources

arXiv2026

Lie-Algebraic Classical Simulation of Bosonic Systems Beyond Gaussian Dynamics

Classical simulability is ultimately determined by both the dynamics of a quantum system and the observables being evaluated. Lie-algebraic simulation exploits the latter to make exact polynomial-time classical simulations by propagating observables through low-dimensional invariant operator spaces. However, its conventional formulation in terms of polynomial-dimensional dynamical Lie algebras does not directly accommodate bosonic systems as their algebras are neither compact nor semisimple. In this contribution, we overcome this limitation, making bosonic systems accessible to the Lie-algebraic programme of exact polynomial-time classical simulation. We prove that expectation values, fixed-order correlation functions, including multi-time correlators and out-of-time-ordered correlators, and gradients are efficiently computable whenever their operator modules have polynomial dimension. This recovers Gaussian quantum optics and extends it to non-Gaussian input states, while identifying exact polynomial regimes of interacting non-Gaussian dynamics including bounded-photon Kerr and pair-hopping Hamiltonians and nilpotent polynomial phase dynamics. We show that unlike in the finite-dimensional spin and fermionic setting treated previously, a finite-dimensional bosonic generator algebra alone does not guarantee finite observable dynamics. We further derive a controlled perturbative hierarchy for squeezing beyond exact sector confinement and confirm the predicted error orders numerically. We also evaluate operator spreading on interacting chains of up to $400$ modes and connect a topological doublon band with flux-reversed edge motion. These results provide a unified formalism for classifying, discovering, and systematically approximating tractable bosonic quantum dynamics with classical polynomial-time simulation.

quant-ph↗

arXiv2026

Enabling Lie-Algebraic Classical Simulation beyond Free Fermions

Efficient classical simulation has matured to a critical component of the quantum computing stack, driving hardware validation, algorithm design, benchmarking, and the study of structured quantum dynamics. Lie-algebraic simulation ($\mathfrak{g}$-sim) offers a compelling approach: it represents Heisenberg-picture dynamics in the adjoint space whose dimension is set by the dynamical Lie algebra (DLA) governing the circuit, enabling efficient simulation of expectation values whenever the DLA grows only polynomially with system size. Despite this promise, existing applications of $\mathfrak{g}$-sim have been confined to free-fermionic settings. It has therefore remained unclear if the method can be applied to other structured circuit families, especially when their generators have large Pauli expansions, and hence whether Lie-algebraic simulability presents a genuinely broader paradigm than free fermions. In this work, we resolve this question by identifying additional non-trivial families of polynomial-dimensional DLAs and introducing symmetry-adapted bases that make the required adjoint-space preprocessing tractable. In particular, we develop an explicit Pauli orbit representation for permutation-equivariant dynamics, enabling efficient processing of cubic-dimensional algebras despite exponential Pauli support, and a modified generalized Gell--Mann representation for bounded Hamming-weight ($U(1)$-equivariant) dynamics, yielding polynomial simulation costs on fixed excitation sectors. Together with streamlined routines for free-fermionic algebras, these constructions significantly broaden the practical scope of $\mathfrak{g}$-sim as a unifying simulation tool for structured quantum circuits. Numerical benchmarks confirm favorable preprocessing scaling and validate large-scale proof-of-concept simulations beyond the reach of state-vector simulation.

quant-ph↗

arXiv2026

PauliEngine: High-Performant Symbolic Arithmetic for Quantum Operations

Quantum computation is inherently hybrid, and fast classical manipulation of qubit operators is necessary to ensure scalability in quantum software. We introduce PauliEngine, a high-performance C++ framework that provides efficient primitives for Pauli string multiplication, commutators, symbolic phase tracking, and structural transformations. Built on a binary symplectic representation and optimized bit-wise operations, PauliEngine supports both numerical and symbolic coefficients and is accessible through a Python interface. Runtime benchmarks demonstrate substantial speedups over state-of-the-art implementations. PauliEngine provides a scalable backend for operator-based quantum software tools and simulations.

quant-ph↗

arXiv2025

Scalability Challenges in Variational Quantum Optimization under Stochastic Noise

With rapid advances in quantum hardware, a central question is whether quantum devices with or without full error correction can outperform classical computers on practically relevant problems. Variational Quantum Algorithms (VQAs) have gained significant attention as promising candidates in this pursuit, particularly for combinatorial optimization problems. While reports of their challenges and limitations continue to accumulate, many studies remain optimistic based on small-scale, idealized testing setups, leaving doubt about the scalability of VQAs for large-scale problems. We systematically investigate this scaling behavior by analyzing how classical optimizers minimize variational quantum loss functions for random QUBO instances in the presence of uncertainty, modeled as effective Gaussian noise. We find that the critical noise threshold for successful optimization decreases rapidly as system size grows. This decline exceeds what can be explained solely by shrinking loss variance, confirming deeper, fundamental limitations in the loss landscapes of VQAs beyond barren plateaus. Translating these thresholds into required measurement shots reveals that achieving sufficient precision in the evaluated loss values quickly becomes impractical, even for moderately-sized problems. Our findings demonstrate serious scalability challenges for VQAs in optimization stemming from mere uncertainty, indicating potential barriers to achieving practical quantum advantage with current hybrid approaches.

quant-ph↗

arXiv2025

Creating Automated Quantum-Assisted Solutions for Optimization Problems

When trying to use quantum-enhanced methods for optimization problems, the sheer number of options inhibits its adoption by industrial end users. Expert knowledge is required for the formulation and encoding of the use case, the selection and adaptation of the algorithm, and the identification of a suitable quantum computing backend. Navigating the decision tree spanned by these options is a difficult task and supporting integrated tools are still missing. We propose the QuaST decision tree, a framework that allows to explore, automate and systematically evaluate solution paths. It helps end users to transfer research to their application area, and researchers to gather experience with real-world use cases. Our setup is modular, highly structured and flexible enough to include any kind of preparation, pre-processing and post-processing steps. We develop the guiding principles for the design of the ambitious framework and discuss its implementation. The QuaST decision tree includes multiple complete top-down paths from an application to its fully hybrid quantum solution.

quant-ph↗

arXiv2025

Solving Combinatorial Optimization Problems with a Block Encoding Quantum Optimizer

In the pursuit of achieving near-term quantum advantage for combinatorial optimization problems, the Quantum Approximate Optimization Algorithm (QAOA) and the Variational Quantum Eigensolver (VQE) are the primary methods of interest, but their practical effectiveness remains uncertain. Therefore, there is a persistent need to develop and evaluate alternative variational quantum algorithms. This study presents an investigation of the Block ENcoding Quantum Optimizer (BENQO), a hybrid quantum solver that uses block encoding to represent the cost function. BENQO is designed to be universally applicable across discrete optimization problems. Beyond Maximum Cut, we evaluate BENQO's performance in the context of the Traveling Salesperson Problem, which is of greater practical relevance. Our findings confirm that BENQO performs significantly better than QAOA and competes with VQE across a variety of performance metrics. We conclude that BENQO is a promising novel hybrid quantum-classical algorithm that should be further investigated and optimized to realize its full potential.

quant-ph↗

arXiv2024

Challenges for Reinforcement Learning in Quantum Circuit Design

Quantum computing (QC) in the current NISQ era is still limited in size and precision. Hybrid applications mitigating those shortcomings are prevalent to gain early insight and advantages. Hybrid quantum machine learning (QML) comprises both the application of QC to improve machine learning (ML) and ML to improve QC architectures. This work considers the latter, leveraging reinforcement learning (RL) to improve quantum circuit design (QCD), which we formalize by a set of generic objectives. Furthermore, we propose qcd-gym, a concrete framework formalized as a Markov decision process, to enable learning policies capable of controlling a universal set of continuously parameterized quantum gates. Finally, we provide benchmark comparisons to assess the shortcomings and strengths of current state-of-the-art RL algorithms.

quant-ph↗

arXiv2024

A Generalized Variable Projection Algorithm for Least Squares Problems in Atmospheric Remote Sensing

This paper presents a solution for efficiently and accurately solving separable least squares problems with multiple datasets. These problems involve determining linear parameters that are specific to each dataset while ensuring that the nonlinear parameters remain consistent across all datasets. A well-established approach for solving such problems is the variable projection algorithm introduced by Golub and LeVeque, which effectively reduces a separable problem to its nonlinear component. However, this algorithm assumes that the datasets have equal sizes and identical auxiliary model parameters. This article is motivated by a real-world remote sensing application where these assumptions do not apply. Consequently, we propose a generalized algorithm that extends the original theory to overcome these limitations. The new algorithm has been implemented and tested using both synthetic and real satellite data for atmospheric carbon dioxide retrievals. It has also been compared to conventional state-of-the-art solvers, and its advantages are thoroughly discussed. The experimental results demonstrate that the proposed algorithm significantly outperforms all other methods in terms of computation time, while maintaining comparable accuracy and stability. Hence, this novel method can have a positive impact on future applications in remote sensing and could be valuable for other scientific fitting problems with similar properties.

math.NA↗