# Research#

Below, we present a collection of scientific papers and articles that have either contributed to the development of Qrisp or highlight its applications and advantages in the field of quantum computing. These citations provide a foundation for understanding the theoretical underpinnings and practical implications of Qrisp. We encourage researchers, developers, and enthusiasts to explore these resources to gain a deeper insight into the capabilities and potential of Qrisp.

## Research from within the Qrisp community#

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Abstract

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.

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Abstract

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.

**Quantum Backtracking in Qrisp Applied to Sudoku Problems**

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Abstract

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.

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Abstract

Uncomputation is an essential part of reversible computing and plays a vital role in quantum computing. Using this technique, memory resources can be safely deallocated without performing a nonreversible deletion process. For the case of quantum computing, several algorithms depend on this as they require disentangled states in the course of their execution. Thus, uncomputation is not only about resource management, but is also required from an algorithmic point of view. However, synthesizing uncomputation circuits is tedious and can be automated. In this paper, we describe the interface for automated generation of uncomputation circuits in our Qrisp framework. Our algorithm for synthesizing uncomputation circuits in Qrisp is based on an improved version of “Unqomp”, a solution presented by Paradis et. al. Our paper also presents some improvements to the original algorithm, in order to make it suitable for the needs of a high-level programming framework. Qrisp itself is a fully compilable, high-level programming language/framework for gate-based quantum computers, which abstracts from many of the underlying hardware details. Qrisp’s goal is to support a high-level programming paradigm as known from classical software development.