Experimental differentiation and extremization with analog quantum circuits

Solving and optimizing differential equations (DEs) is ubiquitous in both engineering and fundamental science. The promise of quantum architectures to accelerate scientific computing thus naturally involved interest towards how efficiently quantum algorithms can solve DEs. Differentiable quantum circuits (DQC) offer a viable route to compute DE solutions using a variational approach amenable to existing quantum computers, by producing a machine-learnable surrogate of the solution. Quantum extremal learning (QEL) complements such approach by finding extreme points in the output of learnable models of unknown (implicit) functions, offering a powerful tool to bypass a full DE solution, in cases where the crux consists in retrieving solution extrema. In this work, we provide the results from the first experimental demonstration of both DQC and QEL, displaying their performance on a synthetic usecase. Whilst both DQC and QEL are expected to require digital quantum hardware, we successfully challenge this assumption by running a closed-loop instance on a commercial analog quantum computer, based upon neutral atom technology.

Qadence: a differentiable interface for digital-analog programs

Digital-analog quantum computing (DAQC) is an alternative paradigm for universal quantum computation combining digital single-qubit gates with global analog operations acting on a register of interacting qubits. Currently, no available open-source software is tailored to express, differentiate, and execute programs within the DAQC paradigm. In this work, we address this shortfall by presenting Qadence, a high-level programming interface for building complex digital-analog quantum programs developed at Pasqal. Thanks to its flexible interface, native differentiability, and focus on real-device execution, Qadence aims at advancing research on variational quantum algorithms built for native DAQC platforms such as Rydberg atom arrays.

Harmonic (Quantum) Neural Networks

Harmonic functions are abundant in nature, appearing in limiting cases of Maxwell's, Navier-Stokes equations, the heat and the wave equation. Consequently, there are many applications of harmonic functions, spanning applications from industrial process optimisation to robotic path planning and the calculation of first exit times of random walks. Despite their ubiquity and relevance, there have been few attempts to develop effective means of representing harmonic functions in the context of machine learning architectures, either in machine learning on classical computers, or in the nascent field of quantum machine learning. Architectures which impose or encourage an inductive bias towards harmonic functions would facilitate data-driven modelling and the solution of inverse problems in a range of applications. For classical neural networks, it has already been established how leveraging inductive biases can in general lead to improved performance of learning algorithms. The introduction of such inductive biases within a quantum machine learning setting is instead still in its nascent stages. In this work, we derive exactly-harmonic (conventional- and quantum-) neural networks in two dimensions for simply-connected domains by leveraging the characteristics of holomorphic complex functions. We then demonstrate how these can be approximately extended to multiply-connected two-dimensional domains using techniques inspired by domain decomposition in physics-informed neural networks. We further provide architectures and training protocols to effectively impose approximately harmonic constraints in three dimensions and higher, and as a corollary we report divergence-free network architectures in arbitrary dimensions. Our approaches are demonstrated with applications to heat transfer, electrostatics and robot navigation, with comparisons to physics-informed neural networks included.