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Machine learning surrogate models of Kohn-Sham Density Functional Theory Hamiltonians provide a powerful tool for accelerating the prediction of electronic properties of materials, such as electronic band structures and density of states.…
In this paper, we design a new iterative algorithm for solving pseudomonotone equilibrium problems in real Hilbert spaces. The advantage of our algorithm is that it requires only one strongly convex programming problem at each iteration.…
In this report, we summarize the set partition enumeration problems and thoroughly explain the algorithms used to solve them. These algorithms iterate through the partitions in lexicographic order and are easy to understand and implement in…
A stochastic optimization algorithm for analyzing planar central and balanced configurations in the $n$-body problem is presented. We find a comprehensive list of equal mass central configurations satisfying the Morse equality up to $n=12$.…
Hypervolume (HV)-based Bayesian optimization (BO) is one of the standard approaches for multi-objective decision-making. However, the computational cost of optimizing the acquisition function remains a significant bottleneck, primarily due…
We propose HAMSI (Hessian Approximated Multiple Subsets Iteration), which is a provably convergent, second order incremental algorithm for solving large-scale partially separable optimization problems. The algorithm is based on a local…
We implement an algorithm which is aimed to reduce the number of basis states spanning the Hilbert space of quantum many-body systems. We test the efficiency of the procedure by working out and analyzing the spectral properties of strongly…
We consider the design of efficient algorithms for a multicore computing environment with a global shared memory and p cores, each having a cache of size M, and with data organized in blocks of size B. We characterize the class of…
An attractive approach for fast search in image databases is binary hashing, where each high-dimensional, real-valued image is mapped onto a low-dimensional, binary vector and the search is done in this binary space. Finding the optimal…
The quantum many-body bound-state problem in its computationally successful coupled cluster method (CCM) representation is reconsidered. In conventional practice one factorizes the ground-state wave functions $|\Psi\rangle= e^S…
The hidden subgroup problem~(HSP) is one of the most important problems in quantum computation. Many problems for which quantum algorithm achieves exponential speedup over its classical counterparts can be reduced to the Abelian HSP.…
Matrix representations are a powerful tool for designing efficient algorithms for combinatorial optimization problems such as matching, and linear matroid intersection and parity. In this paper, we initiate the study of matrix…
Binary classification is one of the most common problem in machine learning. It consists in predicting whether a given element belongs to a particular class. In this paper, a new algorithm for binary classification is proposed using a…
A randomized algorithm for computing a compressed representation of a given rank-structured matrix $A \in \mathbb{R}^{N\times N}$ is presented. The algorithm interacts with $A$ only through its action on vectors. Specifically, it draws two…
In this paper, we propose a quantum algorithm that supports a real-valued higher-order unconstrained binary optimization (HUBO) problem. This algorithm is based on the Grover adaptive search that originally supported HUBO with integer…
We develop a workflow to use current quantum computing hardware for solving quantum many-body problems, using the example of the fermionic Hubbard model. Concretely, we study a four-site Hubbard ring that exhibits a transition from a…
We present a quantum algorithm for simulating the dynamics of Hamiltonians that are not necessarily sparse. Our algorithm is based on the input model where the entries of the Hamiltonian are stored in a data structure in a quantum random…
Quantum computing and modern tensor-based computing have a strong connection, which is especially demonstrated by simulating quantum computations with tensor networks. The other direction is less studied: quantum computing is not often…
Embedding representation learning via neural networks is at the core foundation of modern similarity based search. While much effort has been put in developing algorithms for learning binary hamming code representations for search…
Quantum many-body systems are typically endowed with a tensor product structure. This structure is inherited from probability theory, where the probability of two independent events is the product of the probabilities. The tensor product…