Related papers: Quantum Algorithm for Simulating the Wave Equation
We present a quantum algorithmic framework for simulating linear, anti-Hermitian (lossless) wave equations in heterogeneous, anisotropic, and time-independent media. This framework encompasses a broad class of wave equations, including the…
Solving partial differential equations for extremely large-scale systems within a feasible computation time serves in accelerating engineering developments. Quantum computing algorithms, particularly the Hamiltonian simulations, present a…
Quantum simulation uses a well-known quantum system to predict the behavior of another quantum system. Certain limitations in this technique arise, however, when applied to specific problems, as we demonstrate with a theoretical and…
We develop a Monte Carlo wave function algorithm for the quantum linear Boltzmann equation, a Markovian master equation describing the quantum motion of a test particle interacting with the particles of an environmental background gas. The…
We propose a quantum algorithm for simulating dissipative waves in inhomogeneous linear media as a boundary-value problem. Using the so-called quantum singular value transformation (QSVT), we construct a quantum circuit that models the…
We describe a quantum algorithm for preparing states that encode solutions of non-homogeneous linear partial differential equations. The algorithm is a continuous-variable version of matrix inversion: it efficiently inverts differential…
We propose an explicit algorithm based on the Linear Combination of Hamiltonian Simulations technique to simulate both the advection-diffusion equation and a nonunitary discretized version of the Koopman-von Neumann formulation of nonlinear…
Simulation of realistic classical mechanical systems is of great importance to many areas of engineering such as robotics, dynamics of rotating machinery and control theory. In this work, we develop quantum algorithms to estimate quantities…
We present a new recipe for relativistic quantum simulation using the first quantisation approach, under periodic (PBC) and Dirichlet (DBC) boundary conditions. The wavefunction is discretised across a finite grid represented by system…
We present a quantum algorithm to obtain the response of the atomic nucleus to a small external electromagnetic perturbation. The Hamiltonian of the system is presented by a harmonic oscillator, and the linear combination of unitaries (LCU)…
A Hamiltonian model for the propagation of internal water waves interacting with surface waves, a current and an uneven bottom is examined. Using the so-called Dirichlet-Neumann operators, the water wave system is expressed in the…
Numerical modeling of radio-frequency waves in plasma with sufficiently high spatial and temporal resolution remains challenging even with modern computers. However, such simulations can be sped up using quantum computers in the future.…
To simulate plasma phenomena, large-scale computational resources have been employed in developing high-precision and high-resolution plasma simulations. One of the main obstacles in plasma simulations is the requirement of computational…
Quantum simulation algorithms often require numerous ancilla qubits and deep circuits, prohibitive for near-term hardware. We introduce a framework for simulating quantum channels using ensembles of low-depth circuits in place of many-qubit…
We propose an efficient quantum algorithm for simulating the dynamics of general Hamiltonian systems. Our technique is based on a power series expansion of the time-evolution operator in its off-diagonal terms. The expansion decouples the…
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…
We present a quantum algorithm based on repeated measurement to solve initial-value problems for nonlinear ordinary differential equations (ODEs), which may be generated from partial differential equations in plasma physics. We map a…
Variational quantum algorithms are one of the most promising methods that can be implemented on noisy intermediate-scale quantum (NISQ) machines to achieve a quantum advantage over classical computers. This article describes the use of a…
Quantum simulation can help us study poorly understood topics such as high-temperature superconductivity and drug design. However, existing quantum simulation algorithms for current quantum computers often have drawbacks that impede their…
We present a quantum algorithm for simulating complex many-body systems and finding their ground states, combining the use of tensor networks and density matrix renormalization group (DMRG) techniques. The algorithm is based on von…