This paper presents a novel approach to quantum architecture search by integrating the techniques of ZX-calculus with Genetic Programming (GP) to optimize the structure of parameterized quantum circuits employed in quantum machine learning (QML). Recognizing the challenges in designing efficient quantum circuits for QML, we propose a GP framework that utilizes mutations defined via ZX-calculus, a graphical language that can simplify visualizing and working with quantum circuits. Our methodology focuses on evolving quantum circuits with the aim of enhancing their capability to approximate functions relevant in various machine learning tasks. We introduce several mutation operators inspired by the transformation rules of ZX-calculus and investigate their impact on the learning efficiency and accuracy of quantum circuits. The empirical analysis involves a comparative study where these mutations are applied to a diverse set of quantum regression problems, measuring performance metrics such as the percentage of valid circuits after the mutation, improvement of the objective, and circuit depth and width. Our results indicate that certain ZX-calculus-based mutations perform significantly better than others for quantum architecture search (QAS) in all metrics considered. They suggest that ZX-diagram-based QAS results in shallower circuits and more uniformly allocated gates than crude genetic optimization based on the circuit model. The code used for the numerical experiments is open source and can be found at TODO https://gitlab.cc-asp.fraunhofer.de/itwm-fm-qc-public/cvqa.

Classical Monte Carlo algorithms can theoretically be sped up on a quantum computer by employing amplitude estimation (AE). To realize this, an efficient implementation of state-dependent functions is crucial. We develop a straightforward approach based on pretraining parameterized quantum circuits, and show how they can be transformed into their conditional variant, making them usable as a subroutine in an AE algorithm. To identify a suitable circuit, we propose a genetic optimization approach that combines variable ansatzes and data encoding. We apply our algorithm to the problem of pricing financial derivatives. At the expense of a costly pretraining process, this results in a quantum circuit implementing the derivatives' payoff function more efficiently than previously existing quantum algorithms. In particular, we compare the performance for European vanilla and basket options.

Modeling nonlinear activation functions on quantum computers is vital for quantum neurons employed in fully quantum neural networks, however, remains a challenging task. We introduce an amplitude-based implementation for approximating nonlinearity in the form of the unit step function on a quantum computer. Our approach expands upon repeat-until-success protocols, suggesting a modification that requires a single measurement only. We describe two distinct circuit types which receive their input either directly from a classical computer or as a quantum state when embedded in a more advanced quantum algorithm. All quantum circuits are theoretically evaluated using numerical simulation and executed on Noisy Intermediate-Scale Quantum hardware. We demonstrate that reliable data with high precision can be obtained from our quantum circuits involving up to eight qubits and up to 25 CX-gate applications, enabled by state-of-the-art hardware-optimization techniques and measurement error mitigation.

We develop a novel quantum algorithm for approximating the price of a discrete floating-strike Asian option based on an underlying valuation tree. The paths of the tree are encoded in bit-representation into a qubit register, where quantum state preparation is used to load the corresponding distribution onto the states. We implement the expectation value of the option pricing formula as a composition of the price probabilities, the payout and an indicator function, mapping their respective values to amplitudes of additional qubits. Thus, the underlying no longer has to be discretized into the same bit values for different times, resulting in smaller quantum circuits. The algorithm may be used with quantum amplitude estimation, enabling a quadratic speed-up over classical Monte Carlo methods.

We introduce $${{\texttt {openIRM}}}$$ , the Internal Risk Model of an artificial life insurer, designed to allow an easy benchmarking of nested simulation techniques for Solvency Capital Requirement ( $${{\textrm{SCR}}}$$ ) estimation under Solvency II and other actuarial methods. $${{\texttt {openIRM}}}$$ integrates an economic scenario generator and a cash flow projection model, enabling the computation of the available capital (basic own funds) through both the direct and indirect method. Leveraging a two-factor Gaussian model for stochastic short rates and a generalized Black-Scholes model for stock dynamics, the framework supports policyholder investments via guaranteed minimum-income benefit contracts. We extend the asset-liability management model by Diehl et al. (EAJ 13(1), 2022), and prove the theoretical convergence of the direct and indirect method under appropriate assumptions. Calibrated using interest rate caps from 2016 to the end of 2023, $${{\texttt {openIRM}}}$$ allows estimation of available capital distributions and $${{\,\textrm{SCR}\,}}$$ dynamics for each trading day in that range. The source code of $${{\texttt {openIRM}}}$$ written in is publicly available on at https://zenodo.org/records/23035168 . We also provide standalone executables that, after installation, can be accessed via the command line interface or with the provided wrappers in , and .

Classical Monte Carlo algorithms can theoretically be sped up on a quantum computer by employing amplitude estimation (AE). To realize this, an efficient implementation of state-dependent functions is crucial. We develop a straightforward approach based on pretraining parameterized quantum circuits, and show how they can be transformed into their conditional variant, making them usable as a subroutine in an AE algorithm. To identify a suitable circuit, we propose a genetic optimization approach that combines variable ansatzes and data encoding. We apply our algorithm to the problem of pricing financial derivatives. At the expense of a costly pretraining process, this results in a quantum circuit implementing the derivatives' payoff function more efficiently than previously existing quantum algorithms. In particular, we compare the performance for European vanilla and basket options.