Related papers: Solving Fractional Differential Equations on a Qua…
A fractional Hamiltonian formalism is introduced for the recent combined fractional calculus of variations. The Hamilton-Jacobi partial differential equation is generalized to be applicable for systems containing combined Caputo fractional…
There are several approaches to the fractional differential operator. Generalized q-fractional difference operator was defined in the aid of q-iterated Cauchy integral and q-calculus techniques. We introduce Caputo type derivative related…
This work proposes a conformable fractional predictor-corrector algorithm for solving conformable fractional differential equations. Fractional calculus is finding applications in various scientific fields, but existing numerical methods…
We introduce a variational hybrid classical-quantum algorithm to simulate the Lindblad master equation and its adjoint for time-evolving Markovian open quantum systems and quantum observables. Our method is based on a direct representation…
This study reexamines diffusive representations for fractional integrals with the goal of pioneering new variants of such representations. These variants aim to offer highly efficient numerical algorithms for the approximate computation of…
The present paper deals with the numerical solution of time-fractional advection-diffusion equations involving the Caputo derivative with source term by means of an unconditionally stable implicit finite difference method on quasi-uniform…
Constraints in power consumption and computational power limit the skill of operational numerical weather prediction by classical computing methods. Quantum computing could potentially address both of these challenges. Herein, we present…
Quantum computers must meet extremely stringent qualitative and quantitative requirements on their qubits in order to solve real-life problems. Quantum circuit fragmentation techniques divide a large quantum circuit into a number of…
Recent studies have shown that fractional calculus is an effective alternative mathematical tool in various scientific fields. However, some investigations indicate that results established in differential and integral calculus do not…
Combinatorial optimization is a promising application for near-term quantum computers, however, identifying performant algorithms suited to noisy quantum hardware remains as an important goal to potentially realizing quantum computational…
Quantum computing holds significant promise for scientific computing due to its potential for polynomial to even exponential speedups over classical methods, which are often hindered by the curse of dimensionality. While neural networks…
This paper develops a high-accuracy algorithm for time fractional wave problems, which employs a spectral method in the temporal discretization and a finite element method in the spatial discretization. Moreover, stability and convergence…
We develop circuit implementations for digital-level quantum Hamiltonian dynamics simulation algorithms suitable for implementation on a reconfigurable quantum computer, such as trapped ions. Our focus is on the co-design of a problem, its…
Based on the continuous time random walk, we derive the Fokker-Planck equations with Caputo-Fabrizio fractional derivative, which can effectively model a variety of physical phenomena, especially, the material heterogeneities and structures…
Imaginary time evolution is a powerful tool for studying quantum systems. While it is possible to simulate with a classical computer, the time and memory requirements generally scale exponentially with the system size. Conversely, quantum…
Quantum computers are known to provide an exponential advantage over classical computers for the solution of linear differential equations in high-dimensional spaces. Here, we present a quantum algorithm for the solution of nonlinear…
This paper provides a probabilistic approach to solve linear equations involving Caputo and Riemann-Liouville type derivatives. Using the probabilistic interpretation of these operators as the generators of interrupted Feller processes, we…
We present a hybrid classical/quantum algorithm for efficiently solving the eigenvalue problem of many-particle Hamiltonians on quantum computers with limited resources by splitting the workload between classical and quantum processors.…
Variational hybrid quantum-classical algorithms are promising candidates for near-term implementation on quantum computers. In these algorithms, a quantum computer evaluates the cost of a gate sequence (with speedup over classical cost…
A new method that enables easy and convenient discretization of partial differential equations with derivatives of arbitrary real order (so-called fractional derivatives) and delays is presented and illustrated on numerical solution of…