Noisy intermediate-scale quantum (NISQ) devices are restricted by their limited number of qubits and their short decoherence times. An approach addressing these problems is quantum circuit cutting. It decomposes the execution of a large quantum circuit into the execution of multiple smaller quantum circuits with additional classical postprocessing. Since these smaller quantum circuits require fewer qubits and gates, they are more suitable for NISQ devices. To investigate the effect of quantum circuit cutting in a quantum algorithm targeting NISQ devices, we design two experiments using the quantum approximate optimization algorithm (QAOA) for the Maximum Cut (MaxCut) problem and conduct them on state-of-the-art superconducting devices. Our first experiment studies the influence of circuit cutting on the objective function of QAOA, and the second evaluates the quality of results obtained by the whole algorithm with circuit cutting. The results show that circuit cutting can reduce the effects of noise in QAOA, and therefore, the algorithm yields better solutions on NISQ devices.

Due to low numbers of qubits and their error-proneness, Noisy Intermediate-Scale Quantum (NISQ) computers impose constraints on the size of quantum algorithms they can successfully execute. State-of-the-art research introduces various techniques addressing these limitations by utilizing known or inexpensively generated approximations, solutions, or models as a starting point to approach a task instead of starting from scratch. These so-called warm-starting techniques aim to reduce quantum resource consumption, thus facilitating the design of algorithms suiting the capabilities of NISQ computers. In this work, we collect and analyze scientific literature on warm-starting techniques in the quantum computing domain. In particular, we (i) create a systematic map of state-of-the-art research on warm-starting techniques using established guidelines for systematic mapping studies, (ii) identify relevant properties of such techniques, and (iii) based on these properties classify the techniques identified in the literature in an extensible classification scheme. Our results provide insights into the research field and aim to help quantum software engineers to categorize warm-starting techniques and apply them in practice. Moreover, our contributions may serve as a starting point for further research on the warm-starting topic since they provide an overview of existing work and facilitate the identification of research gaps.

The Boolean satisfiability problem (SAT), in particular 3SAT with its bounded clause size, is a well-studied problem since a wide range of decision problems can be reduced to it. The Quantum Approximate Optimization Algorithm (QAOA) is a promising candidate for solving 3SAT for Noisy Intermediate-Scale Quantum devices in the near future due to its simple quantum ansatz. However, although QAOA generally exhibits a high approximation ratio, there are 3SAT problem instances where the algorithm’s success probability when obtaining a satisfying variable assignment from the approximated solution drops sharply compared to the approximation ratio. To address this problem, in this paper, we present variants of the algorithm that are inspired by the amplitude amplification algorithm to improve the success probability for 3SAT. For this, (i) three amplitude amplification-inspired QAOA variants are introduced and implemented, (ii) the variants are experimentally compared with a standard QAOA implementation, and (iii) the impact on the success probability and ansatz complexity is analyzed. The experiment results show that an improvement in the success probability can be achieved with only a moderate increase in circuit complexity.

Distributed quantum computing leverages multiple quantum devices collectively to perform computations exceeding each device's capabilities. A currently studied technique to enable this distributed approach is wire cutting, which decomposes a quantum circuit into smaller subcircuits by cutting connecting wires. These subcircuits can be executed on distributed devices, and their results are then classically combined to reconstruct the original computation's result. However, wire cutting requires additional circuit executions to preserve result accuracy, with their number growing exponentially with each cut. Thus, minimizing this sampling overhead is crucial for reducing execution time. Employing shared non‐maximally entangled (NME) states between distributed devices reduces this overhead for single wire cuts, approaching ideal teleportation with maximally entangled states. Extending this approach to jointly cutting multiple wires using NME states remained unexplored. This study addresses this gap by investigating the use of NME states for joint wire cuts, aiming to reduce the sampling overhead further. The three main contributions include (i) determining the minimal sampling overhead for this scenario, (ii) analyzing the overhead when using composite NME states constructed from smaller NME states, and (iii) introducing a wire cutting technique that achieves the optimal sampling overhead with pure NME states, advancing toward wire cutting with arbitrary NME states.