Related papers: Quantum Algorithm for the Vlasov Equation
In computer simulations, quantum delocalization of atomic nuclei can be modeled making use of the Path Integral (PI) formulation of quantum statistical mechanics. This approach, however, comes with a large computational cost. By restricting…
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…
We address the question of how a quantum computer can be used to simulate experiments on quantum systems in thermal equilibrium. We present two approaches for the preparation of the equilibrium state on a quantum computer. For both…
The ZX-calculus is an algebraic formalism that allows quantum computations to be simplified via a small number of simple graphical rewrite rules. Recently, it was shown that, when combined with a family of "sum-over-Cliffords" techniques,…
Digital quantum simulation uses the capabilities of quantum computers to determine the dynamics of quantum systems, which are beyond the computability of modern classical computers. A notoriously challenging task in this field is the…
Although a universal quantum computer is still far from reach, the tremendous advances in controllable quantum devices, in particular with solid-state systems, make it possible to physically implement "quantum simulators". Quantum…
Quantum computers promise to efficiently solve important problems classical computers never will. However, in order to capitalize on these prospects, a fully automated quantum software stack needs to be developed. This involves a multitude…
We propose a quantum algorithm to solve systems of nonlinear algebraic equations. In the ideal case the complexity of the algorithm is linear in the number of variables $n$, which means our algorithm's complexity is less than $O(n^{3})$ of…
The Quantum approximate optimization algorithm (QAOA) is a leading hybrid classical-quantum algorithm for solving complex combinatorial optimization problems. QAOA-in-QAOA (QAOA^2) uses a divide-and-conquer heuristic to solve large-scale…
The dynamics of plasmas are governed by a set of non-linear differential equations which remain challenging to solve directly for large 2D and 3D problems. Here we investigate how tensor networks could be applied to plasmas described by the…
Gaussian processes are widely known for their ability to provide probabilistic predictions in supervised machine learning models. Their non-parametric nature and flexibility make them particularly effective for regression tasks. However,…
Quantum computers may one day enable the efficient simulation of strongly coupled plasmas that lie beyond the reach of classical computation in regimes where quantum effects are important and the scale separation is large. In this article,…
We consider the relativistic Vlasov--Maxwell (RVM) equations in the limit when the light velocity $c$ goes to infinity. In this regime, the RVM system converges towards the Vlasov--Poisson system and the aim of this paper is to construct…
We report the quantum computing of reacting flows by simulating the Hamiltonian dynamics. The scalar transport equation for reacting flows is transformed into a Hamiltonian system, mapping the dissipative and non-Hermitian problem in…
State-of-the-art noisy intermediate-scale quantum devices (NISQ), although imperfect, enable computational tasks that are manifestly beyond the capabilities of modern classical supercomputers. However, present quantum computations are…
Quantum computing promises to solve difficult optimization problems in chemistry, physics and mathematics more efficiently than classical computers, but requires fault-tolerant quantum computers with millions of qubits. To overcome errors…
Near term quantum computers with a high quantity (around 50) and quality (around 0.995 fidelity for two-qubit gates) of qubits will approximately sample from certain probability distributions beyond the capabilities of known classical…
Quantum algorithms for simulating electronic ground states are slower than popular classical mean-field algorithms such as Hartree-Fock and density functional theory, but offer higher accuracy. Accordingly, quantum computers have been…
Landau damping is one of the cornerstones of plasma physics. In the context of the mathematical framework developed by Landau in his original derivation of Landau damping, we examine the solutions of the linear Vlasov-Poisson system for…
The development of quantum computing hardware is facing the challenge that current-day quantum processors, comprising 50-100 qubits, already operate outside the range of quantum simulation on classical computers. In this paper we…