arXiv subjects

Jakob S. Kottmann

Publications and source records attributed to Jakob S. Kottmann.

At least 19 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

Shallow Quantum Circuits for Deep Chemistry via Valence Bond Embeddings

Quantum chemistry is one of the major potential applications in quantum computation. Currently there is a considerable focus on relatively small active spaces as a consequence of hardware noise and exponential bottlenecks in simulations. In the long run, there will be an increasing demand in reliable approximations for larger systems -- both, as initial states for projective algorithms like the quantum phase estimation or for the evaluation of dynamical properties. While numerous approaches to select active spaces and extrapolate basis set accuracy exist, there is currently no consistent approach that results in a single quantum circuit for the total system. In this work, we combine hybrid Fermionic-Bosonic encodings with the structured approach of Quantum Valence Bond Theory to directly construct quantum circuits for comparably large molecular systems. With this approach we are able to push simulability barrier of variational quantum eigensolvers towards chemically relevant systems and demonstrate circuit designs that outperform active space counterparts and achieve good approximations with respect to the exact solutions.

quant-ph↗

arXiv2026

Consistent Initial States with Constant Circuit Depth for Quantum Computational Chemistry

Variational quantum eigensolvers have been extensively studied, yet there are still no methods that offer black-box applicability with consistent performance. Separable pair approximations promise to be candidates for such methods: they compile to shallow constant-depth quantum circuits with linear gate count and parameter dependence and circumvent most bottlenecks of variational quantum algorithms through their classical simulability. At the same time, they seamlessly integrate into prominent more general circuit designs and subspace strategies. So far, their capability as a consistent method has only been indicated and demonstrations have been restricted to manually designed model systems. In this work, we extensively evaluate the consistency of SPA states for hydrogen chains, alkanes, and small molecules within an orbital-optimized VQE framework. Our benchmarks demonstrate consistent approximations with classical complexity comparable to Hartree-Fock. Our open-source implementation within the Tequila framework allows convenient use of the algorithms as a standalone method or as a subpart of more extensive procedures. Our results underpin the potential of SPA circuits as scalable, chemically motivated low-depth circuits with various applications and validate their usage as a chemically consistent method.

physics.chem-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

Unitaria: Quantum Linear Algebra via Block Encodings

We introduce Unitaria, a Python library that brings the simplicity of classical linear algebra toolkits such as NumPy and SciPy to the implementation of quantum algorithms based on block encodings, a general-purpose abstraction in which a matrix is embedded as a sub-block of a larger unitary operator. Their implementation has so far required deep knowledge of low-level circuit construction, which Unitaria aims to eliminate. The library provides a composable, array-like interface through which users can define block encodings of matrices and vectors, combine them through standard operations such as addition, multiplication, tensor products, and the Quantum Singular Value Transformation, and extract the resulting quantum circuits automatically. A key feature is a matrix-arithmetic evaluation path in which every operation can be computed directly on encoded vectors and matrices without dependence on ancilla qubits or circuit simulation. This enables correctness verification and classical simulation that scale well beyond what state vector simulation permits and also allows resource estimation, including gate counts, qubit counts, and normalization constants, without executing any circuit. Together, these capabilities allow researchers to develop, verify, and analyze quantum linear algebra algorithms today, ahead of the availability of error-corrected hardware. Unitaria is open source and available at https://github.com/tequilahub/unitaria.

quant-ph↗

arXiv2026

A Transferable Machine Learning Approach to Predict Optimized Orbitals for Electronic Structure Problems

Variational quantum eigensolver ansätze hold considerable promise for ground-state energy calculations on near-term quantum hardware, yet most promising ansatz designs currently strongly depend on how well the molecular orbital basis captures the electronic correlation of the system. Computing optimized orbital coefficients via classical routines is computationally expensive and must be performed independently for each molecular geometry -- a bottleneck that limits scalability across chemical space. We present a graph neural network framework that predicts optimized orbital coefficients directly from molecular geometry and pair-wise bonding structure. Trained on hydrogenic systems of modest size ($H_4$ and $H_6$) across tens of thousands of geometries, our model transfers to larger, unseen systems ($H_8$, $H_{10}$ and $H_{12}$) without retraining -- demonstrating strong out-of-distribution generalization with respect to system size. When evaluating on structured and random configurations, and comparing against energies obtained with full classical optimization, our model reaches mean absolute energy errors $\mathcal{O}(10^2)$ and $\mathcal{O}(10)$ milli-Hartrees, respectively. Beyond energy estimation, the predicted orbitals serve as high-quality warm-start initializations that substantially reduce optimizer iterations to ground-state energy convergence. These results establish graph neural networks as an effective and scalable strategy for accelerating orbital optimization in hybrid quantum-classical workflows, directly reducing the classical pre-processing overhead that currently limits the practical deployment of variational quantum eigensolver on near-term quantum hardware.

quant-ph↗

arXiv2026

Swap Network Augmented Ansätze on Arbitrary Connectivity

Efficient parametrizations of quantum states are essential for trainable hybrid classical-quantum algorithms. A key challenge in their design consists in adapting to the available qubit connectivity of the quantum processor, which limits the capacity to generate correlations between distant qubits in a resource-efficient and trainable manner. In this work we first introduce an algorithm that optimizes qubit routing for arbitrary connectivity graphs, resulting in a swap network that enables direct interactions between any pair of qubits. We then propose a co-design of circuit layers and qubit routing by embedding the derived swap networks within layered, connectivity-aware ansätze. This construction significantly improves the trainability of the ansatz, leading to enhanced performance with reduced resources. We showcase these improvements through ground-state simulations of strongly correlated systems, including spin-glass and molecular electronic structure models. Across exemplified connectivities, the swap-enhanced ansatz consistently achieves lower energy errors using fewer entangling gates, shallower circuits, and fewer parameters than standard layered-structured baselines. Our results indicate that swap network augmented ansätze provide enhanced trainability and resource-efficient design to capture complex correlations on devices with constrained qubit connectivity.

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

The advent of fully variational quantum eigensolvers using a hybrid multiresolution approach

In electronic structure theory, variational methods offer a valuable paradigm for approximating electronic ground states. However, for historical reasons, this principle is mostly restricted to model chemistries in pre-defined fixed basis sets. Especially in quantum computation, these model chemistries are far from an accurate description of the initial electronic Hamiltonian. This work demonstrates a \textit{fully} variational approach to the electronic structure problem by optimizing the orbitals that represent the second-quantized Hamiltonian, alongside a quantum circuit that generates the many-electron wavefunction. To this end, the orbitals are represented within an adaptive multi-wavelet format, guaranteeing numerical precision. We then present explicit numerical protocols and highlight the quantum circuit's role in determining the optimal orbital basis.

quant-ph↗

arXiv2025

A Transferable Machine Learning Approach to Predict Quantum Circuit Parameters for Electronic Structure Problems

The individual optimization of quantum circuit parameters is currently one of the main practical bottlenecks in variational quantum eigensolvers for electronic systems. To this end, several machine learning approaches have been proposed to mitigate the problem. However, such method predominantly aims at training and predicting parameters tailored to individual molecules: either a specific structure, or several structures of the same molecule with varying bond lengths. This work explores machine learning based modeling strategies to include transferability between different molecules. We use a well investigated quantum circuit design and apply it to model properties of hydrogenic systems where we show parameter prediction that is systematically transferable to instances significantly larger than the training instances.

quant-ph↗

arXiv2025

State Specific Measurement Protocols for the Variational Quantum Eigensolver

A central roadblock in the realization of variational quantum eigensolvers on quantum hardware is the high overhead associated with measurement repetitions, which hampers the computation of complex problems, such as the simulation of mid- and large-sized molecules. In this work, we propose a novel measurement protocol which relies on computing an approximation of the Hamiltonian expectation value. The method involves measuring cheap grouped operators directly and estimating the residual elements through iterative measurements of new grouped operators in different bases, with the process being truncated at a certain stage. The measured elements comprehend the operators defined by the Hard-Core Bosonic approximation, which encode electron-pair annihilation and creation operators. These can be easily decomposed into three self-commuting groups which can be measured simultaneously. Applied to molecular systems, the method achieves a reduction of 30% to 80% in the number of measurement and gates depth in the measuring circuits compared to state-of-the-art methods. This provides a scalable and cheap measurement protocol, advancing the application of variational approaches for simulating physical systems.

quant-ph↗

arXiv2024

A Hybrid Qubit Encoding: Splitting Fock Space into Fermionic and Bosonic Subspaces

Efficient encoding of electronic operators into qubits is essential for quantum chemistry simulations. The majority of methods map single electron states to qubits, effectively handling electron interactions. Alternatively, pairs of electrons can be represented as quasi-particles and encoded into qubits, significantly simplifying calculations. This work presents a hybrid encoding that allows splitting the Fock space into Fermionic and Bosonic subspaces. By leveraging the strengths of both approaches, we provide a flexible framework for optimizing quantum simulations based on molecular characteristics and hardware constraints.

quant-ph↗

arXiv2024

Reducing Entanglement With Physically-Inspired Fermion-To-Qubit Mappings

In ab-initio electronic structure simulations, fermion-to-qubit mappings represent the initial encoding step of the fermionic problem into qubits. This work introduces a physically-inspired method for constructing mappings that significantly simplify entanglement requirements when simulating states of interest. The presence of electronic excitations drives the construction of our mappings, reducing correlations for target states in the qubit space. To benchmark our method, we simulate ground states of small molecules and observe an enhanced performance when compared to classical and quantum variational approaches from prior research employing conventional mappings. In particular, on the quantum side, our mappings require a reduced number of entangling layers to achieve accuracy for $LiH$, $H_2$, $(H_2)_2$, the $H_4$ stretching and benzene's π system using the RY hardware efficient ansatz. In addition, our mappings also provide an enhanced ground state simulation performance in the density matrix renormalization group algorithm for the $N_2$ molecule.

quant-ph↗

arXiv2024

A Quantum Algorithmic Approach to Multiconfigurational Valence Bond Theory: Insights from Interpretable Circuit Design

Efficient ways to prepare fermionic ground states on quantum computers are in high demand and different techniques have been developed over the last years. Despite having a vast set of methods, it is still unclear which method performs well for which system. In this work, we combine interpretable circuit designs with an effective basis approach in order to optimize a multiconfigurational valence bond wavefunction. Based on selected model systems, we show how this leads to explainable performance. We demonstrate that the developed methodology outperforms related methods in terms of the size of the effective basis as well as individual quantum resources for the involved circuits.

quant-ph↗

arXiv2024

Mutual information-assisted Adaptive Variational Quantum Eigensolver

Adaptive construction of ansatz circuits offers a promising route towards applicable variational quantum eigensolvers on near-term quantum hardware. Those algorithms aim to build up optimal circuits for a certain problem and ansatz circuits are adaptively constructed by selecting and adding entanglers from a predefined pool. In this work, we propose a way to construct entangler pools with reduced size by leveraging classical algorithms. Our method uses mutual information between the qubits in classically approximated ground state to rank and screen the entanglers. The density matrix renormalization group method is employed for classical precomputation in this work. We corroborate our method numerically on small molecules. Our numerical experiments show that a reduced entangler pool with a small portion of the original entangler pool can achieve same numerical accuracy. We believe that our method paves a new way for adaptive construction of ansatz circuits for variational quantum algorithms.

quant-ph↗

arXiv2024

Comparing Classical and Quantum Ground State Preparation Heuristics

One promising field of quantum computation is the simulation of quantum systems, and specifically, the task of ground state energy estimation (GSEE). Ground state preparation (GSP) is a crucial component in GSEE algorithms, and classical methods like Hartree-Fock state preparation are commonly used. However, the efficiency of such classical methods diminishes exponentially with increasing system size in certain cases. In this study, we investigated whether in those cases quantum heuristic GSP methods could improve the overlap values compared to Hartree-Fock. Moreover, we carefully studied the performance gain for GSEE algorithms by exploring the trade-off between the overlap improvement and the associated resource cost in terms of T-gates of the GSP algorithm. Our findings indicate that quantum heuristic GSP can accelerate GSEE tasks, already for computationally affordable strongly-correlated systems of intermediate size. These results suggest that quantum heuristic GSP has the potential to significantly reduce the runtime requirements of GSEE algorithms, thereby enhancing their suitability for implementation on quantum hardware.

quant-ph↗

arXiv2023

Molecular Quantum Circuit Design: A Graph-Based Approach

Science is rich in abstract concepts that capture complex processes in astonishingly simple ways. A prominent example is the reduction of molecules to simple graphs. This work introduces a design principle for parametrized quantum circuits based on chemical graphs, providing a way forward in three major obstacles in quantum circuit design for molecular systems: Operator ordering, parameter initialization and initial state preparation. It allows physical interpretation of each individual component and provides an heuristic to qualitatively estimate the difficulty of preparing ground states for individual instances of molecules.

quant-ph↗

arXiv2023

Partitioning Quantum Chemistry Simulations with Clifford Circuits

Current quantum computing hardware is restricted by the availability of only few, noisy qubits which limits the investigation of larger, more complex molecules in quantum chemistry calculations on quantum computers in the near-term. In this work, we investigate the limits of their classical and near-classical treatment while staying within the framework of quantum circuits and the variational quantum eigensolver. To this end, we consider naive and physically motivated, classically efficient product ansatz for the parametrized wavefunction adapting the separable pair ansatz form. We combine it with post-treatment to account for interactions between subsystems originating from this ansatz. The classical treatment is given by another quantum circuit that has support between the enforced subsystems and is folded into the Hamiltonian. To avoid an exponential increase in the number of Hamiltonian terms, the entangling operations are constructed from purely Clifford or near-Clifford circuits. While Clifford circuits can be simulated efficiently classically, they are not universal. In order to account for missing expressibility, near-Clifford circuits with only few, selected non-Clifford gates are employed. The exact circuit structure to achieve this objective is molecule-dependent and is constructed using simulated annealing and genetic algorithms. We demonstrate our approach on a set of molecules of interest and investigate the extent of our methodology's reach. Empirical validation of our approach using numerical simulations shows a reduction of the qubit count of up to a 50\% at a similar accuracy as compared to the separable-pair ansatz.

quant-ph↗