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Coulomb collisions in particle simulations for weakly coupled plasmas are modeled by the Landau-Fokker-Planck equation, which is typically solved by Monte-Carlo (MC) methods. One of the main disadvantages of MC is the timestep accuracy…
Recently, an efficient quantum algorithm for linear systems of equations introduced by Harrow, Hassidim, and Lloyd, has received great concern from the academic community. However, the error and complexity analysis for this algorithm seems…
This paper proposes a frequent itemset mining algorithm based on the Boolean matrix method, aiming to solve the storage and computational bottlenecks of traditional frequent pattern mining algorithms in high-dimensional and large-scale…
We propose a hybrid quantum-classical algorithm to compute approximate solutions of binary combinatorial problems. We employ a shallow-depth quantum circuit to implement a unitary and Hermitian operator that block-encodes the weighted…
Efficiently solving large-scale sparse linear systems poses a significant challenge in computational science, especially in fields such as physics, engineering, machine learning, and finance. Traditional classical algorithms face…
Markov chain Monte Carlo (MCMC) sampling of densities restricted to linearly constrained domains is an important task arising in Bayesian treatment of inverse problems in the natural sciences. While efficient algorithms for uniform polytope…
Finding a maximum or minimum is a fundamental building block in many mathematical models. Compared with classical algorithms, Durr, Hoyer's quantum algorithm (DHA) achieves quadratic speed. However, its key step, the quantum exponential…
Holographic algorithms introduced by Valiant are composed of two ingredients: matchgates, which are gadgets realizing local constraint functions by weighted planar perfect matchings, and holographic reductions, which show equivalences among…
Quantum computers hold promise for solving problems intractable for classical computers, especially those with high time or space complexity. Practical quantum advantage can be said to exist for such problems when the end-to-end time for…
In this work we investigate methods to improve the efficiency and scalability of quantum algorithms for quantum chemistry applications. We propose a transformation of the electronic structure Hamiltonian in the second quantization framework…
After learning basic quantum computing concepts, it is desirable to reinforce the learning using an important and relatively complex algorithm through which the students can observe and appreciate how the qubits evolve and interact with…
The quantum query complexity of Boolean matrix multiplication is typically studied as a function of the matrix dimension, n, as well as the number of 1s in the output, \ell. We prove an upper bound of O (n\sqrt{\ell}) for all values of…
We apply the framework of block-encodings, introduced by Low and Chuang (under the name standard-form), to the study of quantum machine learning algorithms and derive general results that are applicable to a variety of input models,…
We study the Bipartite Boolean Quadratic Programming Problem (BBQP) which is an extension of the well known Boolean Quadratic Programming Problem (BQP). Applications of the BBQP include mining discrete patterns from binary data,…
Solving linear systems is of great importance in numerous fields. Proposed quantum algorithms for preparing solutions for linear systems include the HHL algorithm with subsequent refinements and variational methods. Circulant linear systems…
Previously proposed quantum algorithms for solving linear systems of equations cannot be implemented in the near term due to the required circuit depth. Here, we propose a hybrid quantum-classical algorithm, called Variational Quantum…
A binary constant weight code is a type of error-correcting code with a wide range of applications. The problem of finding a binary constant weight code has long been studied as a combinatorial optimization problem in coding theory. In this…
Efficient characteristic set methods for computing solutions of polynomial equation systems in a finite field are proposed. The concept of proper triangular sets is introduced and an explicit formula for the number of solutions of a proper…
Two contrasting algorithmic paradigms for constraint satisfaction problems are successive local explorations of neighboring configurations versus producing new configurations using global information about the problem (e.g. approximating…
The Goldreich-Levin algorithm was originally proposed for a cryptographic purpose and then applied to learning. The algorithm is to find some larger Walsh coefficients of an $n$ variable Boolean function. Roughly speaking, it takes a…