Related papers: Variational Quantum Simulation of Partial Differen…
In the context of quantum information, highly nonlinear regimes, such as those supporting solitons, are marginally investigated. We miss general methods for quantum solitons, although they can act as entanglement generators or as…
In this paper we study quantum simulation algorithms on the elastic wave equations using the Schr\"odingerisation method. The Schr\"odingerisation method transforms any linear PDEs into a system of Schr\"odinger-type PDEs -with unitary…
We present a quantum algorithm for systems of (possibly inhomogeneous) linear ordinary differential equations with constant coefficients. The algorithm produces a quantum state that is proportional to the solution at a desired final time.…
Open quantum systems host a wide range of intriguing phenomena, yet their simulation on well-controlled quantum devices is challenging, owing to the exponential growth of the Hilbert space and the inherently non-unitary nature of the…
Computing the ground-state properties of quantum many-body systems is a promising application of near-term quantum hardware with a potential impact in many fields. The conventional algorithm quantum phase estimation uses deep circuits and…
Advances in quantum algorithms suggest a tentative scaling advantage on certain combinatorial optimization problems. Recent work, however, has also reinforced the idea that barren plateaus render variational algorithms ineffective on large…
We explore the possibility of adding complex absorbing potential at the boundaries when solving the one-dimensional real-time Schr\"odinger evolution on a grid using a quantum computer with a fully quantum algorithm described on a $n$ qubit…
Quantum computers are known for their potential to achieve up-to-exponential speedup compared to classical computers for certain problems. To exploit the advantages of quantum computers, we propose quantum algorithms for linear stochastic…
The current generation of noisy intermediate scale quantum computers introduces new opportunities to study quantum many-body systems. In this paper, we show that quantum circuits can provide a dramatically more efficient representation than…
Quantum computing may speed up numerical problems involving large matrices that are demanding for classical computers, and active research on this possibility is ongoing. In this work, we propose quantum algorithms for the exact simulation…
Electromagnetic transient (EMT) simulation is a crucial tool for power system dynamic analysis because of its detailed component modeling and high simulation accuracy. However, it suffers from computational burdens for large power grids…
This paper investigates quantum simulation algorithms for the Liouville equation in geometrical optics with partial transmission and reflection at sharp interfaces, based on the Schr\"odingerization method. By means of a warped phase…
The quantum imaginary time evolution (QITE) methodology was developed to overcome a critical issue as regards non-unitarity in the implementation of imaginary time evolution on a quantum computer. QITE has since been used to approximate…
Quantum algorithms for Hamiltonian simulation and linear differential equations more generally have provided promising exponential speed-ups over classical computers on a set of problems with high real-world interest. However, extending…
The Van der Waals equation (VdW-EoS) is a prototype equation of state for realistic systems, because it contains the excluded volume and the particle interactions. Additionally, the simulated annealing (and the similar simulated…
For electromagnetic transient (EMT) simulation of a power system, a state-space-based approach needs to solve state-space EMT equations by using numerical integration methods, e.g., the Euler method, Runge-Kutta methods, and…
We present a novel approach to solve the advection-diffusion equation under arbitrary transporting fields using a quantum-inspired 'Schrodingerisation' technique for Hamiltonian simulation. Although numerous methods exist for solving…
We present a fault-tolerant quantum algorithm for implementing the Discrete Variable Representation (DVR) transformation, a technique widely used in simulations of quantum-mechanical Hamiltonians. DVR provides a diagonal representation of…
We develop a quantum algorithm for solving high-dimensional time-fractional heat equations. By applying the dimension extension technique from [FKW23], the $d+1$-dimensional time-fractional equation is reformulated as a local partial…
The advection-diffusion equation is simulated on a superconducting quantum computer via several quantum algorithms. Three formulations are considered: (1) Trotterization, (2) variational quantum time evolution (VarQTE), and (3) adaptive…