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René Zander

Publications and source records attributed to René Zander.

13 recordsLinked to original sources
arXiv2026

Block-encodings as programming abstractions: The Eclipse Qrisp BlockEncoding Interface

Block-encoding is a foundational technique in modern quantum algorithms, enabling the implementation of non-unitary operations by embedding them into larger unitary matrices. While theoretically powerful and essential for advanced protocols like Quantum Singular Value Transformation (QSVT) and Quantum Signal Processing (QSP), the generation of compilable implementations of block-encodings poses a formidable challenge. This work presents the BlockEncoding interface within the Eclipse Qrisp framework, establishing block-encodings as a high-level programming abstraction accessible to a broad scientific audience. Serving as both a technical framework introduction and a hands-on tutorial, this paper explicitly details key underlying concepts abstracted away by the interface, such as block-encoding construction and qubitization, and their practical integration into methods like the Childs-Kothari-Somma (CKS) algorithm. We outline the interface's software architecture, encompassing constructors, core utilities, arithmetic composition, and algorithmic applications such as matrix inversion, polynomial filtering, and Hamiltonian simulation. Through code examples, we demonstrate how this interface simplifies both the practical realization of advanced quantum algorithms and their associated resource estimation.

quant-ph↗
arXiv2026

Quantum Computing for Query Containment of Conjunctive Queries

We address the problem of checking query containment, a foundational problem in database research. Although extensively studied in theory research, optimization opportunities arising from query containment are not fully leveraged in commercial database systems, due to the high computational complexity and sometimes even undecidability of the underlying decision problem. In this article, we present the first approach to applying quantum computing to the query containment problem for conjunctive queries under set semantics. We propose a novel formulation as an optimization problem that can be solved on gate-based quantum hardware, and in some cases directly maps to quantum annealers. We formally prove this formulation to be correct and present a prototype implementation which we evaluate using simulator software as well as quantum devices. Our experiments successfully demonstrate that our approach is sound and scales within the current limitations of quantum hardware. In doing so, we show that quantum optimization can effectively address this problem. Thereby, we contribute a new computational perspective on the query containment problem.

cs.DB↗
arXiv2025

Double-bracket quantum algorithms for quantum imaginary-time evolution

Efficiently preparing approximate ground-states of large, strongly correlated systems on quantum hardware is challenging and yet nature is innately adept at this. This has motivated the study of thermodynamically inspired approaches to ground-state preparation that aim to replicate cooling processes via imaginary-time evolution. However, synthesizing quantum circuits that efficiently implement imaginary-time evolution is itself difficult, with prior proposals generally adopting heuristic variational approaches or using deep block encodings. Here, we use the insight that quantum imaginary-time evolution is a solution of Brockett's double-bracket flow and synthesize circuits that implement double-bracket flows coherently on the quantum computer. We prove that our Double-Bracket Quantum Imaginary-Time Evolution (DB-QITE) algorithm inherits the cooling guarantees of imaginary-time evolution. Concretely, each step is guaranteed to i) decrease the energy of an initial approximate ground-state by an amount proportion to the energy fluctuations of the initial state and ii) increase the fidelity with the ground-state. We provide gate counts for DB-QITE through numerical simulations in Qrisp which demonstrate scenarios where DB-QITE outperforms quantum phase estimation. Thus DB-QITE provides a means to systematically improve the approximation of a ground-state using shallow circuits.

quant-ph↗
arXiv2025

Role of Riemannian geometry in double-bracket quantum imaginary-time evolution

Double-bracket quantum imaginary-time evolution (DB-QITE) is a quantum algorithm which coherently implements steps in the Riemannian steepest-descent direction for the energy cost function. DB-QITE is derived from Brockett's double-bracket flow which exhibits saddle points where gradients vanish. In this work, we perform numerical simulations of DB-QITE and describe signatures of transitioning through the vicinity of such saddle points. We provide an explicit gate count analysis using quantum compilation programmed in Qrisp.

quant-ph↗
arXiv2025

A parameter study for LLL and BKZ with application to shortest vector problems

In this work, we study the solution of shortest vector problems (SVPs) arising in terms of learning with error problems (LWEs). LWEs are linear systems of equations over a modular ring, where a perturbation vector is added to the right-hand side. This type of problem is of great interest, since LWEs have to be solved in order to be able to break lattice-based cryptosystems as the Module-Lattice-Based Key-Encapsulation Mechanism published by NIST in 2024. Due to this fact, several classical and quantum-based algorithms have been studied to solve SVPs. Two well-known algorithms that can be used to simplify a given SVP are the Lenstra-Lenstra-Lovász (LLL) algorithm and the Block Korkine-Zolotarev (BKZ) algorithm. LLL and BKZ construct bases that can be used to compute or approximate solutions of the SVP. We study the performance of both algorithms for SVPs with different sizes and modular rings. Thereby, application of LLL or BKZ to a given SVP is considered to be successful if they produce bases containing a solution vector of the SVP.

cs.CR↗
arXiv2024

Quantum Backtracking in Qrisp Applied to Sudoku Problems

The quantum backtracking algorithm proposed by Ashley Montanaro raised considerable interest, as it provides a quantum speed-up for a large class of classical optimization algorithms. It does not suffer from Barren-Plateaus and transfers well into the fault-tolerant era, as it requires only a limited number of arbitrary angle gates. Despite its potential, the algorithm has seen limited implementation efforts, presumably due to its abstract formulation. In this work, we provide a detailed instruction on implementing the quantum step operator for arbitrary backtracking instances. For a single controlled diffuser of a binary backtracking tree with depth n, our implementation requires only $6n+14$ CX gates. We detail the process of constructing accept and reject oracles for Sudoku problems using our interface to quantum backtracking. The presented code is written using Qrisp, a high-level quantum programming language, making it executable on most current physical backends and simulators. Subsequently, we perform several simulator based experiments and demonstrate solving 4x4 Sudoku instances with up to 9 empty fields. This is, to the best of our knowledge, the first instance of a compilable implementation of this generality, marking a significant and exciting step forward in quantum software engineering.

quant-ph↗
arXiv2024

Solving the Product Breakdown Structure Problem with constrained QAOA

Constrained optimization problems, where not all possible variable assignments are feasible solutions, comprise numerous practically relevant optimization problems such as the Traveling Salesman Problem (TSP), or portfolio optimization. Established methods such as quantum annealing or vanilla QAOA usually transform the problem statement into a QUBO (Quadratic Unconstrained Binary Optimization) form, where the constraints are enforced by auxiliary terms in the QUBO objective. Consequently, such approaches fail to utilize the additional structure provided by the constraints. In this paper, we present a method for solving the industry relevant Product Breakdown Structure problem. Our solution is based on constrained QAOA, which by construction never explores the part of the Hilbert space that represents solutions forbidden by the problem constraints. The size of the search space is thereby reduced significantly. We experimentally show that this approach has not only a very favorable scaling behavior, but also appears to suppress the negative effects of Barren Plateaus.

quant-ph↗
arXiv2024

Qrisp: A Framework for Compilable High-Level Programming of Gate-Based Quantum Computers

While significant progress has been made on the hardware side of quantum computing, support for high-level quantum programming abstractions remains underdeveloped compared to classical programming languages. In this article, we introduce Qrisp, a framework designed to bridge several gaps between high-level programming paradigms in state-of-the-art software engineering and the physical reality of today's quantum hardware. The framework aims to provide a systematic approach to quantum algorithm development such that they can be effortlessly implemented, maintained and improved. We propose a number of programming abstractions that are inspired by classical paradigms, yet consistently focus on the particular needs of a quantum developer. Unlike many other high-level language approaches, Qrisp's standout feature is its ability to compile programs to the circuit level, making them executable on most existing physical backends. The introduced abstractions enable the Qrisp compiler to leverage algorithm structure for increased compilation efficiency. Finally, we present a set of code examples, including an implementation of Shor's factoring algorithm. For the latter, the resulting circuit shows significantly reduced quantum resource requirements, strongly supporting the claim that systematic quantum algorithm development can give quantitative benefits.

quant-ph↗
arXiv2024

Benchmarking Multipartite Entanglement Generation with Graph States

As quantum computing technology slowly matures and the number of available qubits on a QPU gradually increases, interest in assessing the capabilities of quantum computing hardware in a scalable manner is growing. One of the key properties for quantum computing is the ability to generate multipartite entangled states. In this paper, aspects of benchmarking entanglement generation capabilities of noisy intermediate-scale quantum (NISQ) devices are discussed based on the preparation of graph states and the verification of entanglement in the prepared states. Thereby, we use entanglement witnesses that are specifically suited for a scalable experiment design. This choice of entanglement witnesses can detect A) bipartite entanglement and B) genuine multipartite entanglement for graph states with constant two measurement settings if the prepared graph state is based on a 2-colorable graph, e.g., a square grid graph or one of its subgraphs. With this, we experimentally verify that a fully bipartite entangled state can be prepared on a 127-qubit IBM Quantum superconducting QPU, and genuine multipartite entanglement can be detected for states of up to 23 qubits with quantum readout error mitigation.

quant-ph↗
arXiv2020

How one can repair non-integrable Kahan discretizations

Kahan discretization is applicable to any system of ordinary differential equations on $\mathbb R^n$ with a quadratic vector field, $\dot{x}=f(x)=Q(x)+Bx+c$, and produces a birational map $x\mapsto \widetilde{x}$ according to the formula $(\widetilde{x}-x)/ε=Q(x,\widetilde{x})+B(x+\widetilde{x})/2+c$, where $Q(x,\widetilde{x})$ is the symmetric bilinear form corresponding to the quadratic form $Q(x)$. When applied to integrable systems, Kahan discretization preserves integrability much more frequently than one would expect a priori, however not always. We show that in some cases where the original recipe fails to preserve integrability, one can adjust coefficients of the Kahan discretization to ensure its integrability.

nlin.SI↗
arXiv2016

A combinatorial approach to integrals of Kahan-Hirota-Kimura discretizations

We consider an Ansatz for the study of the existence of formal integrals of motion for Kahan-Hirota-Kimura discretizations. In this context, we give a combinatorial proof of the formula of Celledoni-McLachlan-Owren-Quispel for an integral of motion of the discretization in the case of cubic Hamiltonian systems on symplectic vector spaces and Poisson vector spaces with constant Poisson structure.

nlin.SI↗