arXiv subjects

Jakob Günther

Publications and source records attributed to Jakob Günther.

7 recordsLinked to original sources

arXiv2026

Sublinear-depth Quantum Simulation of Electrons with Atomic Orbitals

Discretizing electronic degrees of freedom into atomic orbitals is the default choice to accurately model electrons in molecules in a compact and flexible way. We consider the task of simulating such electronic structure models on a quantum computer for $N$ orbitals, keeping the number of orbitals per atom constant. Atomic orbitals give rise to Hamiltonians with potentially up to $\mathcal{O}(N^4)$ terms and little structure, which made it challenging to match the complexity of methods based on plane waves and real-space grids. In this work, we show that a Trotter step for atomic orbitals can be implemented in depth $\mathcal{O}(\mathrm{polylog}(N))$ without ancillas by combining a rigorous treatment of orbital localization, a hierarchical Hamiltonian decomposition based on the Fast Multipole Method, and shallow quantum Fourier arithmetic circuits. By bounding the Trotter error, we obtain sublinear simulation depth, and our total gate count $N^{5/3 + o(1)}$ matches the best scaling known for any basis.

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arXiv2026

phase2: Full-State Vector Simulation of Quantum Time Evolution at Scale

Classical simulation of quantum computers is essential for designing and benchmarking quantum algorithms. Here we present phase2, a full-state-vector simulator optimised for sequences of many-qubit Pauli rotations on distributed CPU and GPU clusters. Exploiting the common-suffix structure of Pauli-rotation circuits, the implementation reduces inter-node communication and achieves two orders of magnitude speedup for grouped rotations. We demonstrate weak and strong scaling to 40 qubits across 512 NVIDIA H100 GPUs using 32 TB of distributed memory. Applying the simulator to Hamiltonian time evolution of ruthenium-ligand active spaces up to 40 qubits, we find that the empirical Trotter error lies more than two orders of magnitude below the rigorous analytic upper bound for every active space in which the fit converged (up to 32 qubits). Practical circuit depths and simulation costs are therefore substantially smaller than the conservative estimates suggest.

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arXiv2026

Phase estimation with partially randomized time evolution

Quantum phase estimation combined with Hamiltonian simulation is the most promising algorithmic framework to computing ground state energies on quantum computers. Its main computational overhead derives from the Hamiltonian simulation subroutine. In this paper we use randomization to speed up product formulas, one of the standard approaches to Hamiltonian simulation. We propose new partially randomized Hamiltonian simulation methods in which some terms are kept deterministically and others are randomly sampled. We perform a detailed resource estimate for single-ancilla phase estimation using partially randomized product formulas for benchmark systems in quantum chemistry and obtain orders-of-magnitude improvements compared to other simulations based on product formulas. When applied to the hydrogen chain, we have numerical evidence that our methods exhibit asymptotic scaling with the system size that is competitive with the best known qubitization approaches.

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arXiv2025

How to use quantum computers for biomolecular free energies

Free energy calculations are at the heart of physics-based analyses of biochemical processes. They allow us to quantify molecular recognition mechanisms, which determine a wide range of biological phenomena from how cells send and receive signals to how pharmaceutical compounds can be used to treat diseases. Quantitative and predictive free energy calculations require computational models that accurately capture both the varied and intricate electronic interactions between molecules as well as the entropic contributions from motions of these molecules and their aqueous environment. However, accurate quantum-mechanical energies and forces can only be obtained for small atomistic models, not for large biomacromolecules. Here, we demonstrate how to consistently link accurate quantum-mechanical data obtained for substructures to the overall potential energy of biomolecular complexes by machine learning in an integrated algorithm. We do so using a two-fold quantum embedding strategy where the innermost quantum cores are treated at a very high level of accuracy. We demonstrate the viability of this approach for the molecular recognition of a ruthenium-based anticancer drug by its protein target, applying traditional quantum chemical methods. As such methods scale unfavorable with system size, we analyze requirements for quantum computers to provide highly accurate energies that impact the resulting free energies. Once the requirements are met, our computational pipeline FreeQuantum is able to make efficient use of the quantum computed energies, thereby enabling quantum computing enhanced modeling of biochemical processes. This approach combines the exponential speedups of quantum computers for simulating interacting electrons with modern classical simulation techniques that incorporate machine learning to model large molecules.

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arXiv2025

High ground state overlap via quantum embedding methods

Quantum computers can accurately compute ground state energies using phase estimation, but this requires a guiding state that has significant overlap with the true ground state. For large molecules and extended materials, it becomes difficult to find guiding states with good ground state overlap for growing molecule sizes. Additionally, the required number of qubits and quantum gates may become prohibitively large. One approach for dealing with these challenges is to use a quantum embedding method, which allows a reduction to one or multiple smaller quantum cores embedded in a larger quantum region. In such situations it is unclear how the embedding method affects the hardness of constructing good guiding states. In this work, we therefore investigate the preparation of guiding states in the context of quantum embedding methods. We extend previous work on quantum impurity problems, a framework in which we can rigorously analyze the embedding of a subset of orbitals. While there exist results for optimal active orbital space selection in terms of energy minimization, we rigorously demonstrate how the same principles can be used to define selected orbital spaces for state preparation in terms of the overlap with the ground state. Moreover, we perform numerical studies of molecular systems relevant to biochemistry, one field in which quantum embedding methods are required due to the large size of biomacromolecules such as proteins and nucleic acids. We investigate two different embedding strategies which can exhibit qualitatively different orbital entanglement. In all cases we demonstrate that the easy-to-obtain mean-field state will have a sufficiently high overlap with the target state to perform quantum phase estimation.

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arXiv2024

More quantum chemistry with fewer qubits

Quantum computation is one of the most promising new paradigms for the simulation of physical systems composed of electrons and atomic nuclei, with applications in chemistry, solid-state physics, materials science, and molecular biology. This requires a truncated representation of the electronic structure Hamiltonian using a finite number of orbitals. While it is, in principle, obvious how to improve on the representation by including more orbitals, this is usually unfeasible in practice (e.g., because of the limited number of qubits available) and severely compromises the accuracy of the obtained results. Here, we propose a quantum algorithm that improves on the representation of the physical problem by virtue of second-order perturbation theory. In particular, our quantum algorithm evaluates the second-order energy correction through a series of time-evolution steps under the unperturbed Hamiltonian. An important application is to go beyond the active-space approximation, allowing to include corrections of virtual orbitals, known as multireference perturbation theory. Here, we exploit that the unperturbed Hamiltonian is diagonal for virtual orbitals and show that the number of qubits is independent of the number of virtual orbitals. This gives rise to more accurate energy estimates without increasing the number of qubits. Moreover, we demonstrate numerically for realistic chemical systems that the total runtime has highly favorable scaling in the number of virtual orbitals compared to previous work. Numerical calculations confirm the necessity of the multireference perturbation theory energy corrections to reach accurate ground state energy estimates. Our perturbation theory quantum algorithm can also be applied to symmetry-adapted perturbation theory. As such, we demonstrate that perturbation theory can help to reduce the quantum hardware requirements for quantum chemistry.

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arXiv2021

A state-averaged orbital-optimized hybrid quantum-classical algorithm for a democratic description of ground and excited states

In the Noisy Intermediate-Scale Quantum (NISQ) era, solving the electronic structure problem from chemistry is considered as the "killer application" for near-term quantum devices. In spite of the success of variational hybrid quantum/classical algorithms in providing accurate energy profiles for small molecules, careful considerations are still required for the description of complicated features of potential energy surfaces. Because the current quantum resources are very limited, it is common to focus on a restricted part of the Hilbert space (determined by the set of active orbitals). While physically motivated, this approximation can severely impact the description of these complicated features. A perfect example is that of conical intersections (i.e. a singular point of degeneracy between electronic states), which are of primary importance to understand many prominent reactions. Designing active spaces so that the improved accuracy from a quantum computer is not rendered useless is key to finding useful applications of these promising devices within the field of chemistry. To answer this issue, we introduce a NISQ-friendly method called "State-Averaged Orbital-Optimized Variational Quantum Eigensolver" (SA-OO-VQE) which combines two algorithms: (1) a state-averaged orbital-optimizer, and (2) a state-averaged VQE. To demonstrate the success of the method, we classically simulate it on a minimal Schiff base model (namely the formaldimine molecule CH2NH) relevant also for the photoisomerization in rhodopsin -- a crucial step in the process of vision mediated by the presence of a conical intersection. We show that merging both algorithms fulfil the necessary condition to describe the molecule's conical intersection, i.e. the ability to treat degenerate (or quasi-degenerate) states on the same footing.

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