arXiv subjects

Dieter Jaksch

Publications and source records attributed to Dieter Jaksch.

At least 19 recordsLinked to original sources

arXiv2026

A priori Assessment of Tensor-Network Encoding for Isotropic Turbulent Flows

Tensor networks (TNs), originally developed for simulating many-body quantum systems, provide a systematic framework for approximating high-dimensional fields. This is achieved by factorizing the field into interconnected tensors with small bond dimensions, thereby restricting the correlations captured across field bipartitions. Belonging to the family of TNs, the matrix product state (MPS) ansatz is utilized here as a reduced-order modeling framework to construct truncated representations of isotropic turbulent flow data. Two direct numerical simulation (DNS) datasets are considered: the hydrodynamic field of an incompressible three-dimensional flow, and a conserved Fickian scalar in a similar flow. Each field is encoded as an MPS through a sequence of singular value decompositions (SVDs) in which small singular values are discarded. The truncated representation is contracted back to the full grid, and the resulting reconstructed field is compared against DNS. An interleaved ordering of the spatial tensor indices of the transport variables is applied prior to decomposition in order to localize the dominant inter-tensor correlations. Velocity reconstructions achieve $99.8\%$ fidelity using only $5\%$ of the original DNS memory, while the scalar field reaches the same fidelity at $15\%$ memory usage. A wide range of lower- and higher-order statistics, including velocity gradients, dissipation, and structure functions, are systematically examined. At these compression levels, the total kinetic energy and the scalar energy are both recovered within $0.2\%$ relative error, while the mean dissipation and mean scalar dissipation remain within approximately $10\%$ of the DNS generated values. These findings support the suitability of MPS for scalable reduced-order analysis of complex turbulent datasets and motivate further exploration of TN-based methods in computational turbulence.

physics.flu-dyn↗

arXiv2026

Efficient Treatment of Non-Linearity in Quantum Computational Fluid Dynamics Using Hybrid Tensor Networks

Nonlinear terms present a fundamental challenge for quantum computational fluid dynamics, as their implementation on inherently linear quantum hardware typically requires resource-intensive workarounds that limit scalability to large-scale simulations. We present a hybrid quantum-classical tensor network algorithm that addresses this bottleneck by combining variational time-stepping with quantum tensor programming to efficiently compile operators and time-dependent fields into quantum circuits. Within a probabilistic framework, we replace prior state-based nonlinear implementations with tensor-based block encodings, stabilizing success probabilities that otherwise decay exponentially with system size. Benchmarking on turbulent flow fields demonstrates that the algorithm maintains high success probabilities and moderate measurement overhead across increasing Reynolds numbers and grid resolutions. Compared to fully classical tensor network solvers, our hybrid approach yields substantial reductions in both memory footprint and computational cost, establishing a scalable pathway toward practical quantum advantage in scale-resolving CFD simulations.

quant-ph↗

arXiv2026

Iterative tensor network transformations for element-wise evaluation of elementary and filtering functions

Tensor networks are powerful formats for compressing large-scale data. However, their application to general data processing has been limited by the difficulty of performing nonlinear operations. Here, we introduce iterative tensor network transformations (ITNTs), a general algorithmic framework for the element-wise evaluation of elementary and nonlinear filtering functions on data encoded as tensor trains (TTs), a class of tensor networks. Our approach operates entirely in the compressed domain, enabling efficient computation on exponentially large datasets while maintaining a controlled computational cost. We demonstrate its power in two key areas: (I) evaluating highly nonlinear elementary and filtering functions on a 3D reactive flow field, enabling high-fidelity reaction rate computation and region filtering, and (II) finding extrema in complex optimization problems, such as solving Max-SAT instances on spaces up to $2^{70}$ configurations. These results establish ITNT as a foundational tool that provides tensor network methods with the capability for general-purpose data science and large-scale optimization.

cs.LG↗

arXiv2026

Time evolution of nonlinear dynamics on a quantum processor

From fluid flow and transport to collective dynamics, numerical simulation of nonlinear partial differential equations underpins modern scientific computing. Extending this capability to quantum computers remains a longstanding challenge because nonlinear and non-Hermitian evolution is fundamentally incompatible with conventional Hamiltonian-based quantum simulation. Here we experimentally realize the time evolution of nonlinear fluid dynamics on a quantum processor using a hybrid variational framework for the viscous and inviscid Burgers equations. Our approach directly encodes the nonlinear dynamics into a variational optimization procedure, avoiding the enlarged linear embeddings and truncation overhead associated with Carleman linearization-based quantum algorithms. We further demonstrate convection-dominated dynamics corresponding to Reynolds numbers of order $10^2$. We encode the governing evolution into parametrized quantum circuits and iteratively reconstruct the time-dependent field through quantum-classical optimization. By introducing a zero-noise extrapolation method without additional circuit-folding overhead, we accurately execute deep error-circuits with entangling-gate counts beyond those typical of Hadamard test circuits. We accurately reconstruct the time evolution across multiple timesteps despite hardware noise and finite device coherence. Our results constitute, to our knowledge, the first experimental realization of nonlinear time propagation on a quantum processor, extending quantum simulation beyond predominantly linear settings and establishing a route toward quantum computation for nonlinear continuum dynamics.

quant-ph↗

arXiv2026

Symplectic Optimization on Bosonic Gaussian States

Computing bosonic Gaussian ground states via variational optimization is challenging because the covariance matrices must satisfy the uncertainty principle, rendering constrained or Riemannian optimization costly, delicate, and thus difficult to scale, particularly in large and inhomogeneous systems. We introduce a symplectic optimization framework that addresses this challenge by parameterizing covariance matrices directly as positive-definite symplectic matrices using unit-triangular factorizations. This approach enforces all physical constraints exactly, yielding a globally unconstrained variational formulation of the bosonic ground-state problem. The unconstrained structure also naturally supports solution reuse across nearby Hamiltonians: warm-starting from previously optimized covariance matrices substantially reduces the number of optimization steps required for convergence in families of related configurations, as encountered in crystal lattices, molecular systems, and fluids. We demonstrate the method on weakly dipole-coupled lattices, recovering ground-state energies, covariance matrices, and spectral gaps accurately. The framework further provides a foundation for large-scale approximate treatments of weakly non-quadratic interactions and offers potential scaling advantages through tensor-network enhancements.

quant-ph↗

arXiv2026

How Hard Is Quantum Advantage? A Cloud Microphysics Stress Test for Variational Quantum Models

Quantum machine learning (QML) could have the potential to leverage advantages of quantum over classical computing but still lacks strong evidence of actual improvements and scalability, partly due to phenomena such as barren plateaus. In this paper, we employ a hybrid quantum neural network (QNN) on a dataset on cloud microphysics, containing processes for phase transitions of water in the atmosphere and its related temperature changes, which are highly relevant for accurate climate predictions and projections. To reach optimal performance of our QNNs, we employ a rich and trainable frequency spectrum together with expressivity enhancing classical postprocessing. We find that our QNNs strongly benefit from extensive hyperparameter optimization and thereby demonstrate the feasibility of applying QNNs to complex physical systems. At the same time, the QNNs are outperformed by classical baselines in the form of simple fully-connected neural networks. We discuss identified bottlenecks of this class of quantum models to learn the full complexity of the cloud microphysics dataset to show that there is a need to further understand and improve variational quantum models for machine learning such that they might fill the gap where classical models fail or are inefficient.

quant-ph↗

arXiv2026

Optimizing Symmetry Informed Probabilistic Error Cancellation

We show that combining quantum error detection (QED) with probabilistic error cancellation (PEC) gives more accurate and lower-variance estimates than PEC alone, provided that the symmetry measurements required for QED are carefully chosen. Because noisy symmetry measurements can negate the benefits of the PEC+QED approach, we cast the selection of measurement configurations as a classical optimization problem that systematically suppresses the impact of noise. Applying optimized PEC+QED to GHZ-state output distributions and to simulating the time-dynamics of a generalized superfast encoded Fermi-Hubbard model, we find consistent improvements over PEC. For GHZ states, the optimization over symmetry measurement configurations is essential for achieving an advantage. For the Fermi-Hubbard model, PEC+QED improves observable estimation on a $2 \times 2$ lattice and for larger systems the mitigation overheads can be reduced by measuring only subsets of stabilizers. Our results demonstrate the importance of circuit-specific tailoring of QEM techniques and that fault-tolerant design principles may already provide value for near-term devices.

quant-ph↗

arXiv2026

Resource-Efficient Quantum Optimization via Higher-Order Encoding

Quantum approaches to combinatorial optimization problems (COPs) are often limited by the resource demands of Quadratic Unconstrained Binary Optimization (QUBO) encodings, which enlarge circuits through penalty terms and increase qubit and gate counts. We show that Higher-Order Unconstrained Binary Optimization (HUBO) enables a more resource-efficient formulation. Our method systematically constructs HUBO Hamiltonians and, compared to a QUBO formulation in benchmarks on Gate Assignment (GAP), Maximum k-Colorable Subgraph (MkCS), and Integer Programming (IP) problems, significantly reduces qubit requirements and decreases total CNOT gate counts by at least 89.6% for all tested instances. These results highlight HUBO as a practical alternative for quantum optimization on near-term devices. To promote adoption, we release an open-source Python library that automates HUBO model construction, extends beyond the examples presented in this work, and broadens access to resource-efficient quantum optimization.

quant-ph↗

arXiv2026

Quantum computation at the edge of chaos

A key challenge in classical machine learning is to mitigate overparameterization by selecting sparse solutions. We translate this concept to the quantum domain, introducing quantum sparsity as a principle based on minimizing quantum information shared across multiple parties. This allows us to address fundamental issues in quantum data processing and convergence issues such as the barren plateau problem in Variational Quantum Algorithm (VQA). We propose a practical implementation of this principle using the topological Entanglement Entropy (TEE) as a cost function regularizer. A non-negative TEE is associated with states with a sparse structure in a suitable basis, while a negative TEE signals untrainable chaos. The regularizer, therefore, guides the optimization along the critical edge of chaos that separates these regimes. We link the TEE to structural complexity by analyzing quantum states encoding functions of tunable smoothness, deriving a quantum Nyquist-Shannon sampling theorem that bounds the resource requirements and error propagation in VQA. Numerically, our TEE regularizer demonstrates significantly improved convergence and precision for complex data encoding and ground-state search tasks. This work establishes quantum sparsity as a design principle for robust and efficient VQAs.

quant-ph↗

arXiv2026

Efficient mapping of multi-constraint satisfaction problems to Rydberg platforms

We present a hardware-native gadget framework for solving constraint satisfaction problems on Rydberg quantum computing architectures. Our approach introduces a compact $xor_1$ gadget that enforces exactly-one constraints, ubiquitous in combinatorial optimization, directly through geometric embedding and blockade interactions. A key advantage of the $xor_1$ gadget is its fixed, problem-size-independent detuning requirements: enforcing constraints through blockade interactions eliminates the need for large penalty terms, thereby substantially reducing the detuning range compared to Quadratic Unconstrained Binary Optimization (QUBO) formulations and improving experimental feasibility. By tailoring the construction to the geometric connectivity of Rydberg atom arrays, the framework bypasses the all-to-all physical couplings often assumed in logical encodings. This enables embeddings compatible with planar layouts and avoids highly connected arrangements. We develop scalable implementations that reduce atom count and connectivity overhead while avoiding extensive classical preprocessing, making them compatible with near-term neutral-atom hardware. As illustrations, we apply our framework to the gate-assignment and $N$-queens problems, highlighting its practicality, resource efficiency, and hardware compatibility. In these examples, we observe reductions in detuning range of up to $99\%$ and savings in atom count and connectivity overhead of up to $54\%$ compared to the QUBO method. These results establish a route toward implementing large-scale combinatorial optimization on Rydberg platforms beyond the limits of existing encodings.

quant-ph↗

arXiv2026

Quantum-Inspired Simulation of 2D Turbulent Rayleigh-Bénard Convection

Turbulent thermal convection governs heat transport in systems ranging from stellar interiors to industrial heat exchangers. Two-dimensional Rayleigh-Bénard convection serves as a paradigm for these flows, reproducing key features such as thin boundary layers, large-scale circulation, and sustained plume dynamics. While Matrix Product State (MPS) methods have demonstrated significant compression of isothermal turbulent fields, their application to buoyancy-driven flows with active thermal coupling has remained unexplored. We apply MPS to two-dimensional Rayleigh-Bénard convection with dynamical simulations up to $\mathrm{Ra} = 10^{10}$. An a priori decomposition of DNS snapshots up to $\mathrm{Ra} = 10^{11}$ shows that the bond dimension $χ$ required to represent the flow fields grows without saturation, in contrast to the plateauing of $χ$ reported for velocity fields in isothermal 2D turbulence. Crucially, however, dynamical simulations solving the governing equations directly in the compressed MPS format at fixed $χ$ show that the $χ$ required to recover statistical observables, such as the Nusselt number, scales significantly more favorably with $\mathrm{Ra}$ than the a priori complexity suggests. At $\mathrm{Ra} = 10^{10}$, a relative error of $1.8\%$ in the mean Nusselt number is achieved with a nearly 9-fold reduction in degrees of freedom, using a $χ$ comparable to that required at $\mathrm{Ra} = 10^{9}$. Spectral analysis confirms the progressive recovery of spatial and temporal scales with increasing $χ$. These findings establish MPS as a scalable tool for simulating thermally driven turbulence, suggesting the method may remain viable for investigations of the ultimate regime at substantially higher $\mathrm{Ra}$.

physics.flu-dyn↗

arXiv2025

Matrix Product State Simulation of Reacting Shear Flows

Direct numerical simulation (DNS) of turbulent reactive flows has been the subject of significant research interest for several decades. Accurate prediction of the effects of turbulence on the rate of reactant conversion, and the subsequent influence of chemistry on hydrodynamics remain a challenge in combustion modeling. The key issue in DNS is to account for the wide range of temporal and spatial physical scales that are caused by complex interactions of turbulence and chemistry. In this work, a new computational methodology is developed that is shown to provide a viable alternative to DNS. The framework is the matrix product state (MPS), a form of tensor network (TN) as used in computational many body physics. The MPS is a well-established ansatz for efficiently representing many types of quantum states in condensed matter systems, allowing for an exponential compression of the required memory compared to exact diagonalization methods. Due to the success of MPS in quantum physics, the ansatz has been adapted to problems outside its historical domain, notably computational fluid dynamics. Here, the MPS is used for computational simulation of a shear flow under non-reacting and nonpremixed chemically reacting conditions. Reductions of 30% in memory are demonstrated for all transport variables, accompanied by excellent agreements with DNS. The anastaz accurately captures all pertinent flow physics such as reduced mixing due to exothermicity & compressibility, and the formation of eddy shocklets at high Mach numbers. A priori analysis of DNS data at higher Reynolds numbers shows compressions as large as 99.99% for some of the transport variables. This level of compression is encouraging and promotes the use of MPS for simulations of complex turbulent combustion systems.

physics.flu-dyn↗

arXiv2025

Tensor-Programmable Quantum Circuits for Solving Differential Equations

We present a quantum solver for partial differential equations based on a flexible matrix product operator representation. Utilizing mid-circuit measurements and a state-dependent norm correction, this scheme overcomes the restriction of unitary operators. Hence, it allows for the direct implementation of a broad class of differential equations governing the dynamics of classical and quantum systems. The capabilities of the framework are demonstrated for linear and non-linear partial differential equations using the example of the linearized Euler equations with absorbing boundaries and the nonlinear Burgers' equation. For a turbulence data set, we demonstrate potential advantages of the quantum tensor scheme over its classical counterparts.

quant-ph↗

arXiv2025

A Quantum Information Perspective on Many-Body Dispersive Forces

Despite its ubiquity, the quantum many-body properties of dispersion remain poorly understood. Here, we investigate the entanglement distribution in assemblies of quantum Drude oscillators, minimal models for dispersion-bound systems. We establish an analytic relationship between entanglement and correlation energy and show how entanglement monogamy determines whether many-body corrections to the pair potential are attractive, repulsive, or zero. These findings, demonstrated in trimers and extended lattices, apply in more general chemical environments where dispersion coexists with other cohesive forces.

quant-ph↗

arXiv2025

Towards Variational Quantum Algorithms for generalized linear and nonlinear transport phenomena

This article proposes a Variational Quantum Algorithm to solve linear and nonlinear thermofluid dynamic transport equations. The hybrid classical-quantum framework is applied to problems governed by the heat, wave, and Burgers' equation in combination with different engineering boundary conditions. Topics covered include the encoding of band matrices, as in the consideration of non-constant material properties and upwind-biased first- and higher-order approximations, widely used in engineering Computational Fluid Dynamics, by the use of a mask function. Verification examples demonstrate high predictive agreement with classical methods. Furthermore, the scalability analysis shows a polylog scaling of the number of quantum gates with the number of qubits. Remaining challenges refer to the implicit construction of upwind schemes and the identification of an appropriate parameterization strategy of the quantum ansatz.

quant-ph↗

arXiv2025

Quantum-Inspired Tensor-Network Fractional-Step Method for Incompressible Flow in Curvilinear Coordinates

We introduce an algorithmic framework based on tensor networks for computing fluid flows around immersed objects in curvilinear coordinates. We show that the tensor network simulations can be carried out solely using highly compressed tensor representations of the flow fields and the differential operators and discuss the numerical implementation of the tensor operations required for computing fluid flows in detail. The applicability of our method is demonstrated by applying it to the paradigm example of steady and transient flows around stationary and rotating cylinders. We find excellent quantitative agreement in comparison to finite difference simulations for Strouhal numbers, forces and velocity fields. The properties of our approach are discussed in terms of reduced order models. We estimate the memory saving and potential runtime advantages in comparison to standard finite difference simulations. We find accurate results with errors of less than 0.3% for flow-field compressions by a factor of up to 20 and differential operators compressed by factors of up to 1000 compared to sparse matrix representations. We provide strong numerical evidence that the runtime scaling advantages of the tensor network approach with system size will provide substantial resource savings when simulating larger systems. Finally, we note that, like other tensor network-based fluid flow simulations, our algorithmic framework is directly portable to a quantum computer leading to further scaling advantages.

physics.flu-dyn↗

arXiv2025

Dynamical quantum phase transitions on random networks

We investigate two types of dynamical quantum phase transitions (DQPTs) in the transverse field Ising model on ensembles of Erdős-Rényi networks of size $N$. These networks consist of vertices connected randomly with probability $p$ ($0<p\leq 1$). Using analytical derivations and numerical techniques, we compare the characteristics of the transitions for $p<1$ against the fully connected network ($p=1$). We analytically show that the overlap between the wave function after a quench and the wave function of the fully connected network after the same quench deviates by at most $\mathcal{O}(N^{-1/2})$. For a DQPT defined by an order parameter, the critical point remains unchanged for all $p$. For a DQPT defined by the rate function of the Loschmidt echo, we find that the rate function deviates from the $p=1$ limit near vanishing points of the overlap with the initial state, while the critical point remains independent for all $p$. Our analysis suggests that this divergence arises from persistent non-trivial global many-body correlations absent in the $p=1$ limit.

quant-ph↗

arXiv2025

Quantum many-body attractors

Complex dynamics when occurring autonomously, i.e. without external driving, is usually associated with everyday length scales and classical physics, e.g. living organisms. This dynamics is \emph{not} quantum coherent. Quantum coherent dynamics is, by contrast, assumed to be either simple periodic oscillation in particular when autonomous, e.g. spin precession, or random quantum fluctuations. Combining autonomous complex and quantum coherent dynamics on microscopic length-scales could allow for novel coherent quantum machines working without external time-dependent driving. Motivated by this, here we provide an exact theoretical condition for a system to display complex quantum coherent dynamics on both microscopic and macroscopic length scales that we call a \emph{dynamical quantum algebraic thread} (D-QAT). Due to D-QATs our autonomous quantum coherent dynamics is robust to realistic imperfections (including low-doped disorder) and present for generic initial states, allowing for potential realisations in experiments. We give an example of a \emph{spin lace} model structurally similar to magnetic azurite and certain recently experimentally realized large single-molecular magnets with long coherence times. Our work opens the possibility for many potential applications including ultra-dense storage and manipulation of quantum memories, creating \emph{giant} quantum coherent qubits, or microscopic quantum mechanism perform complicated motion.

quant-ph↗