arXiv subjects

Martin Kiffner

Publications and source records attributed to Martin Kiffner.

At least 19 recordsLinked to original sources

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

Operator Learning for efficient Quantum Computation

An efficient implementation of quantum algorithms is often hindered by the lack of efficient primitives for operators and state preparation. This limits both the ability of near-term quantum hardware to simulate complex problems and the potential of fault-tolerant algorithms to achieve practical quantum advantage. To address this, we propose a full-stack variational framework that transforms arbitrary operators to compact quantum circuits. The resulting variational circuits can be tailored to the connectivity and long-range interaction of the target hardware. The learning process employs backpropagation together with a cost function that efficiently optimizes unitary operators and non-unitary -- dense or sparse -- operators using only a single ancilla qubit for block encoding. Additionally, we introduce a regularization term that reduces the approximation error. The approach is validated for both quantum mechanical and engineering applications. In the former case, we learn propagators that arise in native quantum problems -- such as quantum simulation and quantum chemistry -- and achieve improved resource scaling in comparison to standard Suzuki-Trotter expansions. In the latter case, we demonstrate the approach's ability to implement the second-order central finite difference approximation of the Laplace operator -- relevant for solving partial differential equations -- while improving upon current error metrics. The final example deals with learning a dense, non-unitary operator that arises in the analysis of inviscid potential flow around an airfoil. This universality of the framework opens the door for solving general problems beyond prototypical engineering and quantum applications.

quant-ph↗

arXiv2025

Quantum Bayesian Optimization for the Automatic Tuning of Lorenz-96 as a Surrogate Climate Model

In this work, we propose a hybrid quantum-inspired heuristic for automatically tuning the Lorenz-96 model -- a simple proxy to describe atmospheric dynamics, yet exhibiting chaotic behavior. Building on the history matching framework by Lguensat et al. (2023), we fully automate the tuning process with a new convergence criterion and propose replacing classical Gaussian process emulators with quantum counterparts. We benchmark three quantum kernel architectures, distinguished by their quantum feature map circuits. A dimensionality argument implies, in principle, an increased expressivity of the quantum kernels over their classical competitors. For each kernel type, we perform an extensive hyperparameter optimization of our tuning algorithm. We confirm the validity of a quantum-inspired approach based on statevector simulation by numerically demonstrating the superiority of two studied quantum kernels over the canonical classical RBF kernel. Finally, we discuss the pathway towards real quantum hardware, mainly driven by a transition to shot-based simulations and evaluating quantum kernels via randomized measurements, which can mitigate the effect of gate errors. The very low qubit requirements and moderate circuit depths, together with a minimal number of trainable circuit parameters, make our method particularly NISQ-friendly.

quant-ph↗

arXiv2024

Tensor Train Multiplication

We present the Tensor Train Multiplication (TTM) algorithm for the elementwise multiplication of two tensor trains with bond dimension $\chi$. The computational complexity and memory requirements of the TTM algorithm scale as $\chi^3$ and $\chi^2$, respectively. This represents a significant improvement compared with the conventional approach, where the computational complexity scales as $\chi^4$ and memory requirements scale as $\chi^3$.We benchmark the TTM algorithm using flows obtained from artificial turbulence generation and numerically demonstrate its improved runtime and memory scaling compared with the conventional approach. The TTM algorithm paves the way towards GPU accelerated tensor network simulations of computational fluid dynamics problems with large bond dimensions due to its dramatic improvement in memory scaling.

physics.comp-ph↗

arXiv2024

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↗

arXiv2024

Solving lattice gauge theories using the quantum Krylov algorithm and qubitization

Computing vacuum states of lattice gauge theories (LGTs) containing fermionic degrees of freedom can present significant challenges for classical computation using Monte-Carlo methods. Quantum algorithms may offer a pathway towards more scalable computation of groundstate properties of LGTs. However, a comprehensive understanding of the quantum computational resources required for such a problem is thus far lacking. In this work, we investigate using the quantum subspace expansion (QSE) algorithm to compute the groundstate of the Schwinger model, an archetypal LGT describing quantum electrodynamics in one spatial dimension. We perform numerical simulations, including the effect of measurement noise, to extrapolate the resources required for the QSE algorithm to achieve a desired accuracy for a range of system sizes. Using this, we present a full analysis of the resources required to compute LGT vacuum states using a quantum algorithm using qubitization within a fault tolerant framework. We develop of a novel method for performing qubitization of a LGT Hamiltonian based on a 'linear combination of unitaries' (LCU) approach. The cost of the corresponding block encoding operation scales as $\tilde{O}(N)$ with system size $N$. Including the corresponding prefactors, our method reduces the gate cost by multiple orders of magnitude when compared to previous LCU methods for the QSE algorithm, which scales as $\tilde{O}(N^2)$ when applied to the Schwinger model. While the qubit and single circuit T-gate cost resulting from our resource analysis is appealing to early fault-tolerant implementation, we find that the number of shots required to avoid numerical instability within the QSE procedure must be significantly reduced in order to improve the feasibility of the methodology we consider and discuss how this might be achieved.

quant-ph↗

arXiv2024

Partitioned Quantum Subspace Expansion

We present an iterative generalisation of the quantum subspace expansion algorithm used with a Krylov basis. The iterative construction connects a sequence of subspaces via their lowest energy states. Diagonalising a Hamiltonian in a given Krylov subspace requires the same quantum resources in both the single step and sequential cases. We propose a variance-based criterion for determining a good iterative sequence and provide numerical evidence that these good sequences display improved numerical stability over a single step in the presence of finite sampling noise. Implementing the generalisation requires additional classical processing with a polynomial overhead in the subspace dimension. By exchanging quantum circuit depth for additional measurements the quantum subspace expansion algorithm appears to be an approach suited to near term or early error-corrected quantum hardware. Our work suggests that the numerical instability limiting the accuracy of this approach can be substantially alleviated in a parameter-free way.

quant-ph↗

arXiv2023

Tensor network reduced order models for wall-bounded flows

We introduce a widely applicable tensor network-based framework for developing reduced order models describing wall-bounded fluid flows. As a paradigmatic example, we consider the incompressible Navier-Stokes equations and the lid-driven cavity in two spatial dimensions. We benchmark our solution against published reference data for low Reynolds numbers and find excellent agreement. In addition, we investigate the short-time dynamics of the flow at high Reynolds numbers for the lid driven and doubly-driven cavities. We represent the velocity components by matrix product states and find that the bond dimension grows logarithmically with simulation time. The tensor network algorithm requires at most a few percent of the number of variables parameterizing the solution obtained by direct numerical simulation, and approximately improves the runtime by an order of magnitude compared to direct numerical simulation on similar hardware. Our approach is readily transferable to other flows, and paves the way towards quantum computational fluid dynamics in complex geometries.

physics.flu-dyn↗

arXiv2022

A Quantum Inspired Approach to Exploit Turbulence Structures

Understanding turbulence is the key to our comprehension of many natural and technological flow processes. At the heart of this phenomenon lies its intricate multi-scale nature, describing the coupling between different-sized eddies in space and time. Here we introduce a new paradigm for analyzing the structure of turbulent flows by quantifying correlations between different length scales using methods inspired from quantum many-body physics. We present results for interscale correlations of two paradigmatic flow examples, and use these insights along with tensor network theory to design a structure-resolving algorithm for simulating turbulent flows. With this algorithm, we find that the incompressible Navier-Stokes equations can be accurately solved within a computational space reduced by over an order of magnitude compared to direct numerical simulation. Our quantum-inspired approach provides a pathway towards conducting computational fluid dynamics on quantum computers.

physics.flu-dyn↗

arXiv2022

Coarse grained intermolecular interactions on quantum processors

Variational quantum algorithms (VQAs) are increasingly being applied in simulations of strongly-bound (covalently bonded) systems using full molecular orbital basis representations. The application of quantum computers to the weakly-bound intermolecular and non-covalently bonded regime however has remained largely unexplored. In this work, we develop a coarse-grained representation of the electronic response that is ideally suited for determining the ground state of weakly interacting molecules using a VQA. We require qubit numbers that grow linearly with the number of molecules and derive scaling behaviour for the number of circuits and measurements required, which compare favourably to traditional variational quantum eigensolver methods. We demonstrate our method on IBM superconducting quantum processors and show its capability to resolve the dispersion energy as a function of separation for a pair of non-polar molecules - thereby establishing a means by which quantum computers can model Van der Waals interactions directly from zero-point quantum fluctuations. Within this coarse-grained approximation, we conclude that current-generation quantum hardware is capable of probing energies in this weakly bound but nevertheless chemically ubiquitous and biologically important regime. Finally, we perform experiments on simulated and real quantum computers for systems of three, four and five oscillators as well as oscillators with anharmonic onsite binding potentials; the consequences of the latter are unexamined in large systems using classical computational methods but can be incorporated here with low computational overhead.

quant-ph↗

arXiv2022

Quantum Self-Supervised Learning

The resurgence of self-supervised learning, whereby a deep learning model generates its own supervisory signal from the data, promises a scalable way to tackle the dramatically increasing size of real-world data sets without human annotation. However, the staggering computational complexity of these methods is such that for state-of-the-art performance, classical hardware requirements represent a significant bottleneck to further progress. Here we take the first steps to understanding whether quantum neural networks could meet the demand for more powerful architectures and test its effectiveness in proof-of-principle hybrid experiments. Interestingly, we observe a numerical advantage for the learning of visual representations using small-scale quantum neural networks over equivalently structured classical networks, even when the quantum circuits are sampled with only 100 shots. Furthermore, we apply our best quantum model to classify unseen images on the ibmq\_paris quantum computer and find that current noisy devices can already achieve equal accuracy to the equivalent classical model on downstream tasks.

quant-ph↗

arXiv2020

Directional THz generation in hot Rb vapor excited to a Rydberg state

We optically excite $^{85}$Rb atoms in a heated vapor cell to a low-lying Rydberg state 10D$_{5/2}$ and observe directional terahertz (THz) beams at 3.3 THz and 7.8 THz. These THz fields are generated by amplified spontaneous emission from the 10D$_{5/2}$ state to the 11P$_{3/2}$ and 8F$_{7/2}$ states, respectively. In addition, we observe ultraviolet (UV) light produced by four-wave mixing of optical pump lasers and the 3.3 THz field. We characterize the generated THz power over the detuning and power of pump lasers, and identify experimental conditions favoring THz and UV generation, respectively. Our scheme paves a new pathway towards generating high-power narrow-band THz radiation.

physics.atom-ph↗

arXiv2020

Minimum Hardware Requirements for Hybrid Quantum-Classical DMFT

We numerically emulate noisy intermediate-scale quantum (NISQ) devices and determine the minimal hardware requirements for two-site hybrid quantum-classical dynamical mean-field theory (DMFT). We develop a circuit recompilation algorithm which significantly reduces the number of quantum gates of the DMFT algorithm and find that the quantum-classical algorithm converges if the two-qubit gate fidelities are larger than 99%. The converged results agree with the exact solution within 10%, and perfect agreement within noise-induced error margins can be obtained for two-qubit gate fidelities exceeding 99.9%. By comparison, the quantum-classical algorithm without circuit recompilation requires a two-qubit gate fidelity of at least 99.999% to achieve perfect agreement with the exact solution. We thus find quantum-classical DMFT calculations can be run on the next generation of NISQ devices if combined with the recompilation techniques developed in this work.

quant-ph↗

arXiv2020

Characterizing the phase diagram of finite-size dipolar Bose-Hubbard systems

We use state-of-the-art density matrix renormalization group calculations in the canonical ensemble to determine the phase diagram of the dipolar Bose-Hubbard model on a finite cylinder. We consider several observables that are accessible in typical optical lattice setups and assess how well these quantities perform as order parameters. We find that, especially for small systems, the occupation imbalance is less susceptible to boundary effects than the structure factor in uncovering the presence of a periodic density modulation. By analysing the non-local correlations, we find that the appearance of supersolid order is very sensitive to boundary effects, which may render it difficult to observe in quantum gas lattice experiments with a few tens of particles. Finally, we show how density measurements readily obtainable on a quantum gas microscope allow distinguishing between superfluid and solid phases using unsupervised machine-learning techniques.

cond-mat.quant-gas↗

arXiv2019

Variational quantum algorithms for nonlinear problems

We show that nonlinear problems including nonlinear partial differential equations can be efficiently solved by variational quantum computing. We achieve this by utilizing multiple copies of variational quantum states to treat nonlinearities efficiently and by introducing tensor networks as a programming paradigm. The key concepts of the algorithm are demonstrated for the nonlinear Schrödinger equation as a canonical example. We numerically show that the variational quantum ansatz can be exponentially more efficient than matrix product states and present experimental proof-of-principle results obtained on an IBM Q device.

quant-ph↗

arXiv2019

Ultrafast creation of overlapping Rydberg electrons in an atomic BEC and Mott-insulator lattice

An array of ultracold atoms in an optical lattice (Mott insulator) excited to a state where single electron wave-functions spatially overlap would represent a new and ideal platform to simulate exotic electronic many-body phenomena in the condensed phase. However, this highly excited non-equilibrium system is expected to be so short-lived that it has eluded observation so far. Here, we demonstrate the first step toward its realization by exciting high-lying electronic (Rydberg) states of the atomic Mott insulator with a coherent ultrashort laser pulse. Beyond a threshold principal quantum number where Rydberg orbitals of neighboring lattice sites overlap with each other, the atoms efficiently undergo spontaneous Penning ionization resulting in a drastic change of ion-counting statistics, sharp increase of avalanche ionization and the formation of an ultracold plasma. These observations signal the actual creation of exotic electronic states with overlapping wave functions, which is further confirmed by a significant difference in ionization dynamics between a Bose-Einstein condensate and a Mott insulator.

physics.atom-ph↗

arXiv2019

Collimated UV light generation by two-photon excitation to a Rydberg state in Rb vapor

We use two continuous-wave (CW) laser beams of 780 nm and 515 nm to optically drive $^{85}$Rb atoms in a heated vapor cell to a low-lying Rydberg state 10D$_{5/2}$. We observe a collimated ultraviolet (UV) beam at 311 nm, corresponding to the transition frequency from the 11P$_{3/2}$ state to the 5S$_{1/2}$ state. This indicates the presence of a coherent four-wave mixing process, built up by two input laser fields as well as a terahertz (THz) radiation of 3.28 THz that is generated by amplified spontaneous emission between the 10D$_{5/2}$ and the 11P$_{3/2}$ states. We characterize the 311 nm UV light generation and its dependence on various physical parameters. This scheme could open up a new possibility for generating narrow-band THz waves as well as deep UV radiation.

physics.atom-ph↗

arXiv2019

Mott polaritons in cavity-coupled quantum materials

We show that strong electron-electron interactions in cavity-coupled quantum materials can enable collectively enhanced light-matter interactions with ultrastrong effective coupling strengths. As a paradigmatic example we consider a Fermi-Hubbard model coupled to a single-mode cavity and find that resonant electron-cavity interactions result in the formation of a quasi-continuum of polariton branches. The vacuum Rabi splitting of the two outermost branches is collectively enhanced and scales with $g_{\text{eff}}\propto\sqrt{2L}$, where $L$ is the number of electronic sites, and the maximal achievable value for $g_{\text{eff}}$ is determined by the volume of the unit cell of the crystal. We find that $g_{\text{eff}}$ for existing quantum materials can by far exceed the width of the first excited Hubbard band. This effect can be experimentally observed via measurements of the optical conductivity and does not require ultra-strong coupling on the single-electron level. Quantum correlations in the electronic ground state as well as the microscopic nature of the light-matter interaction enhance the collective light-matter interaction compared to an ensemble of independent two-level atoms interacting with a cavity mode.

cond-mat.str-el↗