Matti Silveri

Quantum computers are expected to offer significant advantages in solving complex optimization problems that are challenging for classical computers. Quadratic Unconstrained Binary Optimization (QUBO) problems represent an important class of problems with relevance in finance and logistics. The Quantum Approximate Optimization Algorithm (QAOA) is a prominent candidate for solving QUBO problems on near-term quantum devices. In this paper, we investigate the performance of both the standard QAOA and the adaptive derivative assembled problem tailored QAOA (ADAPT-QAOA) to solve QUBO problems of varying sizes and hardnesses with a focus on its practical applications in financial feature selection problems. Our main observation is that ADAPT-QAOA significantly outperforms QAOA with hard problems (trade-off parameter α = 0.6) when comparing approximation ratio and time-to-solution. However, the standard QAOA remains efficient for simpler problems. Additionally, we investigate the practical feasibility and limitations of QAOA by scaling analysis based on the real-device calibration data for various hardware platforms. Our estimates indicate that standard QAOA implemented on superconducting quantum computers provides a shorter time-to-solution compared to trapped-ion devices. However, trapped-ion devices are expected to yield more favorable error rates. Our findings provide a comprehensive overview of the challenges, trade-offs, and strategies for deploying QAOA-based methods on near-term quantum hardware.

The confluence of unitary dynamics and non-unitary measurements gives rise to intriguing and relevant phenomena, generally referred to as measurement-induced phase transitions. These transitions have been observed in quantum systems composed of trapped ions and superconducting quantum devices. However, their experimental realization demands substantial resources, primarily owing to the classical tracking of measurement outcomes, known as post-selection of trajectories. In this work, we first describe the statistical properties of an interacting transmon array which is repeatedly measured, and predict the behavior of relevant quantities in the area-law phase using a combination of the replica method and non-Hermitian perturbation theory. We show numerically that a transmon array, modeled by an attractive Bose-Hubbard model, in which local measurements of the number of bosons are probabilistically interleaved, exhibits a phase transition in the entanglement entropy properties of the ensemble of trajectories in the steady state. Furthermore, by using deterministic feedback operations after the local number measurements, the distribution of the number of bosons measured at a single site carries information on the phase in the entanglement of individual trajectories. Interestingly, we can extract information about the phase and the phase transition from simple observables without considering an absorbing state in the feedback pattern. This implies that the feedback measurement approach might be a viable experimental option to use simple observables to study some aspects of the entanglement phase transition in individual trajectories.