arXiv subjects

Andreas Sturm

Publications and source records attributed to Andreas Sturm.

7 recordsLinked to original sources

arXiv2026

TARE: Block Encoding Linear Combinations of Pauli Strings Without Ancilla State Preparation

Quantum algorithms based on Quantum Signal Processing (QSP) offer the potential for speedups across a broad range of applications, with block encodings serving as the central input model. In this framework, non-unitary matrices are embedded into larger unitary operators, and the cost of constructing these encodings often dominates the overall gate complexity. In this work, we introduce Tag-and-Restore Encoding (TARE), a block-encoding method for linear combinations of Pauli strings. In this method coefficient magnitudes are absorbed into a unitary built from a set of mutually anti-commuting Pauli strings acting on the system register. These Pauli strings are then mapped to the target Pauli strings through appropriate transformations, yielding a block encoding of the target operator. The ancilla register size scales logarithmically with the number of Pauli strings and can be extended to larger registers providing a width/depth tradeoff. We evaluate TARE through numerical simulations of the transverse-field Ising model, the Jordan-Wigner image of a fermionic star Hamiltonian, and random Pauli-string operators. Compared with standard Linear Combination of Unitaries (LCU), TARE substantially reduces the T-gate count while improving circuit depth in several cases. These results suggest that TARE can provide resource-efficient block encodings for a wide range of relevant systems.

quant-ph↗

arXiv2025

Efficient and Explicit Block Encoding of Finite Difference Discretizations of the Laplacian

The data input model is a fundamental component of every quantum algorithm, as its efficiency is crucial for achieving potential speed-ups over classical methods. For quantum linear algebra tasks that utilize quantum eigenvalue or singular value transformations, block encoding is the established technique for accessing matrix data. A key application of this is solving partial differential equations, where the Laplacian operator and its finite difference discretization serve as foundational examples. In this paper, we present an efficient and explicit block encoding method that enhances existing approaches in key aspects. We detail the construction of the quantum algorithm and illustrate how it leverages the unique structure of finite difference discretizations. Furthermore, we analytically derive the scaling of the sub-normalization factor and of the success probability of the block encoding with respect to the problem dimension, the grid width of the finite difference grid and the regularity of the exact solution, and we give resource estimates.

quant-ph↗

arXiv2024

Variational Quantum Algorithms for Differential Equations on a Noisy Quantum Computer

The role of differential equations (DEs) in science and engineering is of paramount importance, as they provide the mathematical framework for a multitude of natural phenomena. Since quantum computers promise significant advantages over classical computers, quantum algorithms for the solution of DEs have received a lot of attention. Particularly interesting are algorithms that offer advantages in the current noisy intermediate scale quantum (NISQ) era, characterized by small and error-prone systems. We consider a framework of variational quantum algorithms, quantum circuit learning (QCL), in conjunction with derivation methods, in particular the parameter shift rule, to solve DEs. As these algorithms were specifically designed for NISQ computers, we analyze their applicability on NISQ devices by implementing QCL on an IBM quantum computer. Our analysis of QCL without the parameter shift rule shows that we can successfully learn different functions with three-qubit circuits. However, the hardware errors accumulate with increasing number of qubits and thus only a fraction of the qubits available on the current quantum systems can be effectively used. We further show that it is possible to determine derivatives of the learned functions using the parameter shift rule on the IBM hardware. The parameter shift rule results in higher errors which limits its execution to low-order derivatives. Despite these limitations, we solve a first-order DE on the IBM quantum computer. We further explore the advantages of using multiple qubits in QCL by learning different functions simultaneously and demonstrate the solution of a coupled differential equation on a simulator.

quant-ph↗

arXiv2024

Unlocking Quantum Optimization: A Use Case Study on NISQ Systems

The major advances in quantum computing over the last few decades have sparked great interest in applying it to solve the most challenging computational problems in a wide variety of areas. One of the most pronounced domains here are optimization problems and a number of algorithmic approaches have been proposed for their solution. For the current noisy intermediate-scale quantum (NISQ) computers the quantum approximate optimization algorithm (QAOA), the variational quantum eigensolver (VQE), and quantum annealing (QA) are the central algorithms for this problem class. The two former can be executed on digital gate-model quantum computers, whereas the latter requires a quantum annealer. Across all hardware architectures and manufactures, the quantum computers available today share the property of being too error-prone to reliably execute involved quantum circuits as they typically arise from quantum optimization algorithms. In order to characterize the limits of existing quantum computers, many component and system level benchmarks have been proposed. However, owing to the complex nature of the errors in quantum systems these benchmark fail to provide predictive power beyond simple quantum circuits and small examples. Application oriented benchmarks have been proposed to remedy this problem, but both, results from real quantum systems as well as use cases beyond constructed academic examples, remain very rare. This paper addresses precisely this gap by considering two industrial relevant use cases: one in the realm of optimizing charging schedules for electric vehicles, the other concerned with the optimization of truck routes. Our central contribution are systematic series of examples derived from these uses cases that we execute on different processors of the gate-based quantum computers of IBM as well as on the quantum annealer of D-Wave.

quant-ph↗

arXiv2023

Theory and Implementation of the Quantum Approximate Optimization Algorithm: A Comprehensible Introduction and Case Study Using Qiskit and IBM Quantum Computers

The present tutorial aims to provide a comprehensible and easily accessible introduction into the theory and implementation of the famous Quantum Approximate Optimization Algorithm (QAOA). We lay our focus on practical aspects and step-by-step guide through the realization of a proof of concept quantum application based on a real-world use case. In every step we first explain the underlying theory and subsequently provide the implementation using IBM's Qiskit. In this way we provide a thorough understanding of the mathematical modelling and the (quantum) algorithms as well as the equally important knowledge how to properly write the code implementing those theoretical concepts. As another central aspect of this tutorial we provide extensive experiments on the 27 qubits state-of-the-art quantum computer ibmq_ehningen. From the discussion of these experiments we gain an overview on the current status of quantum computers and deduce which problem sizes can meaningfully be executed on today's hardware.

quant-ph↗

arXiv2021

Laser-equipped gas reaction chamber for probing environmentally sensitive materials at near atomic scale

Numerous metallurgical and materials science applications depend on quantitative atomic-scale characterizations of environmentally-sensitive materials and their transient states. Studying the effect upon materials subjected to thermochemical treatments in specific gaseous atmospheres is of central importance for specifically studying a material's resistance to certain oxidative or hydrogen environments. It is also important for investigating catalytic materials, direct reduction of an oxide, particular surface science reactions or nanoparticle fabrication routes. This manuscript realizes such experiments upon a thermochemical reaction chamber called the Reacthub and allows for transferring treated materials under cryogenic & ultrahigh vacuum workflow conditions for characterisation by either atom probe or scanning Xe+/electron microscopies. Two examples are discussed in the present study. One protocol was in the deuterium gas charging (25 kPa D2 at 200 °C) of a high-manganese twinning-induced-plasticity steel and characterization of the ingress and trapping of hydrogen at various features (grain boundaries in particular) in efforts to relate this to the steel's hydrogen embrittlement susceptibility. Deuterium was successfully detected after gas charging but most contrast originated from the complex ion FeOD+ signal and the feature may be an artefact. The second example considered the direct deuterium reduction (5 kPa D2 at 700 °C) of a single crystal wuestite sample, demonstrating that under a standard thermochemical treatment causes rapid reduction upon the nanoscale. Further studies are required for complete confidence about these phenomena, but these experiments successfully demonstrate that how an ex-situ thermochemical treatment can be realised that captures environmentally-sensitive transient states that can be analysed by atomic-scale by atom probe microscope.

cond-mat.mtrl-sci↗

arXiv2018

The Laplace project: an integrated suite for correlative atom probe tomography and electron microscopy under cryogenic and UHV conditions

We present sample transfer instrumentation and integrated protocols for the preparation and correlative characterization of environmentally-sensitive materials by both atom probe tomography and electron microscopy. Ultra-high vacuum cryogenic suitcases allow specimen transfer between preparation, processing and several imaging platforms without exposure to atmospheric contamination. For expedient transfers, we installed a fast-docking station equipped with a cryogenic pump upon three systems; two atom probes, a scanning electron microscope / Xe-plasma focused ion beam and a N$_2$-atmosphere glovebox. We also installed a plasma FIB with a solid-state cooling stage to reduce beam damage and contamination, through reducing chemical activity and with the cryogenic components as passive cryogenic traps. We demonstrate the efficacy of the new laboratory protocols by the successful preparation and transfer of two highly contamination- and temperature-sensitive samples - water and ice. Analysing pure magnesium atom probe data, we show that surface oxidation can be effectively suppressed using an entirely cryogenic protocol (during specimen preparation and during transfer). Starting with the cryogenically-cooled plasma FIB, we also prepared and transferred frozen ice samples while avoiding significant melting or sublimation, suggesting that we may be able to measure the nanostructure of other normally-liquid or soft materials. Isolated cryogenic protocols within the N$_2$ glove box demonstrate the absence of ice condensation suggesting that environmental control can commence from fabrication until atom probe analysis.

cond-mat.mtrl-sci↗