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We discuss quantum algorithms that calculate numerical integrals and descriptive statistics of stochastic processes. With either of two distinct approaches, one obtains an exponential speed increase in comparison to the fastest known…
In recent years dynamical modelling has been provided with a range of breakthrough methods to perform exact Bayesian inference. However it is often computationally unfeasible to apply exact statistical methodologies in the context of large…
We present a fast algorithm to calculate Coulomb/exchange integrals of prolate spheroidal electronic orbitals, which are the exact solutions of the single-electron, two-center Schr\"odinger equation for diatomic molecules. Our approach…
Evaluating multi-center molecular integrals with Cartesian Gaussian-type basis sets has been a long-standing bottleneck in electronic structure theory calculation for solids and molecules. We have developed a vector-coupling and…
In quantum chemistry, the price paid by all known efficient model chemistries is either the truncation of the Hilbert space or uncontrolled approximations. Theoretical computer science suggests that these restrictions are not mere…
While most work on the quantum simulation of chemistry has focused on computing energy surfaces, a similarly important application requiring subtly different algorithms is the computation of energy derivatives. Almost all molecular…
We extend correlated sampling from classical auxiliary-field quantum Monte Carlo to the quantum-classical (QC-AFQMC) framework, enabling accurate nuclear force computations crucial for geometry optimization and reaction dynamics. Stochastic…
A unitary coupled-cluster (UCC) form for the wavefunction in the variational quantum eigensolver has been suggested as a systematic way to go beyond the mean-field approximation and include electron correlation in solving quantum chemistry…
At large scales, quantum systems may become advantageous over their classical counterparts at performing certain tasks. Developing tools to analyse these systems at the relevant scales, in a manner consistent with quantum mechanics, is…
Quantum computers are emerging as a viable alternative to tackle certain computational problems that are challenging for classical computers. With the rapid development of quantum hardware such as those based on trapped ions, there is…
Quantum computer provides new opportunities for quantum chemistry. In this article, we present a versatile, extensible, and efficient software package, named Q$^2$Chemistry, for developing quantum algorithms and quantum inspired classical…
The development of accurate and fast numerical schemes for the five fold Boltzmann collision integral represents a challenging problem in scientific computing. For a particular class of interactions, including the so-called hard spheres…
Accurate and scalable methods for computational quantum chemistry can accelerate research and development in many fields, ranging from drug discovery to advanced material design. Solving the electronic Schrodinger equation is the core…
In classical computation, a problem can be solved in multiple steps where calculated results of each step can be copied and used repeatedly. While in quantum computation, it is difficult to realize a similar multi-step computation process…
Quantum computing offers the promise of revolutionizing quantum chemistry by enabling the solution of chemical problems for substantially less computational cost. While most demonstrations of quantum computation to date have focused on…
Current and imminent quantum hardware lacks reliability and applicability due to noise and limited qubit counts. Quantum circuit cutting -- a technique dividing large quantum circuits into smaller subcircuits with sizes appropriate for the…
We introduce two efficient algorithms for computing the partial Fourier transforms in one and two dimensions. Our study is motivated by the wave extrapolation procedure in reflection seismology. In both algorithms, the main idea is to…
Based on the Beylkin-Cramer summation rule, we introduce a new fast algorithm that enable us to explore the high order statistics efficiently in large data sets. Central to this technique is to make decomposition both of fields and…
We introduce a theoretical approach to study the quantum-dissipative dynamics of electronic excitations in macromolecules, which enables to perform calculations in large systems and cover long time intervals. All the parameters of the…
This paper proposes an explicit computational method for solving a three-dimensional system of nonlinear elastodynamic sine-Gordon equations subject to appropriate initial and boundary conditions. The time derivative is approximated by…