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Variational quantum algorithms have emerged as a powerful tool for harnessing the potential of near-term quantum devices to address complex challenges across quantum science and technology. Yet, the robust and scalable quantification of…
We study the foundations of variational inference, which frames posterior inference as an optimisation problem, for probabilistic programming. The dominant approach for optimisation in practice is stochastic gradient descent. In particular,…
Variational quantum algorithms (VQAs) are hybrid quantum-classical approaches used for tackling a wide range of problems on noisy intermediate-scale quantum (NISQ) devices. Testing these algorithms on relevant hardware is crucial to…
We consider the problem of minimizing the sum of two convex functions: one is the average of a large number of smooth component functions, and the other is a general convex function that admits a simple proximal mapping. We assume the whole…
The prevalence of variational methods in near-term quantum computing makes optimizer choice critical, yet selection is frequently intuition-based. We therefore present a systematic benchmark of eight classical optimization algorithms for…
Recent developments of experimental techniques in the field of ultra-cold gases open a path to study the crossover from 'few' to 'many' on the quantum level. In this case, accurate description of inter-particle correlations is very…
Many optimization methods for training variational quantum algorithms are based on estimating gradients of the cost function. Due to the statistical nature of quantum measurements, this estimation requires many circuit evaluations, which is…
It is virtually impossible to directly solve the Schr\"odinger equation for a many-electron wave function due to the exponential growth in degrees of freedom with increasing particle number. The two-body reduced density matrix (2-RDM)…
Quantum heuristics have shown promise in solving various optimization problems, including lattice protein folding. Equally relevant is the inverse problem, protein design, where one seeks sequences that fold to a given target structure. The…
This paper considers stochastic optimization problems for a large class of objective functions, including convex and continuous submodular. Stochastic proximal gradient methods have been widely used to solve such problems; however, their…
Quantum many-body control is among most challenging problems in quantum science, due to computational complexity of related underlying problems. We propose an efficient approach for solving a class of control problems for many-body quantum…
An algorithm for generating optimal nonuniform grids for solving the two-body Schr\"odinger equation is developed and implemented. The shape of the grid is optimized to accurately reproduce the low-energy part of the spectrum of the…
In quantum embedding theories, a quantum many-body system is divided into localized clusters of sites which are treated with an accurate `high-level' theory and glued together self-consistently by a less accurate `low-level' theory at the…
The statistical physics approach to the number partioning problem, a classical NP-hard problem, is both simple and rewarding. Very basic notions and methods from statistical mechanics are enough to obtain analytical results for the phase…
In a recent study[Phys. Rev. B 92 (2015) 125427], a hyperspherical approach has been developed to study of few-body fractional quantum Hall states. This method has been successfully applied to the exploration of few boson and fermion…
Estimation of the energy of quantum many-body systems is a paradigmatic task in various research fields. In particular, efficient energy estimation may be crucial in achieving a quantum advantage for a practically relevant problem. For…
The optimal runtime of a quantum computer searching a database is typically cited as the square root of the number of items in the database, which is famously achieved by Grover's algorithm. With parallel oracles, however, it is possible to…
The quantum many-body problem lies at the center of the most important open challenges in condensed matter, quantum chemistry, atomic, nuclear, and high-energy physics. While quantum Monte Carlo, when applicable, remains the most powerful…
Under mild assumptions stochastic gradient methods asymptotically achieve an optimal rate of convergence if the arithmetic mean of all iterates is returned as an approximate optimal solution. However, in the absence of stochastic noise, the…
Stochastic Variational Method (SVM) is the generalization of the variation method to the case with stochastic variables. In the series of papers, we investigate the applicability of SVM as an alternative field quantization scheme. Here, we…