Related papers: H-DES: a Quantum-Classical Hybrid Differential Equ…
Hybrid quantum-classical algorithms hold great promise for solving quantum control problems on near-term quantum computers. In this work, we employ the hybrid framework that integrates digital quantum simulation with classical optimization…
Hybrid classical-quantum algorithms aim at variationally solving optimisation problems, using a feedback loop between a classical computer and a quantum co-processor, while benefitting from quantum resources. Here we present experiments…
Solving and optimizing differential equations (DEs) is ubiquitous in both engineering and fundamental science. The promise of quantum architectures to accelerate scientific computing thus naturally involved interest towards how efficiently…
We address the problem of solving a system of linear equations via the Quantum Singular Value Transformation (QSVT). One drawback of the QSVT algorithm is that it requires huge quantum resources if we want to achieve an acceptable accuracy.…
Quantum chemistry applications on quantum computers currently rely heavily on the variational quantum eigensolver (VQE) algorithm. This hybrid quantum-classical algorithm aims at finding ground state solutions of molecular systems based on…
In this work we demonstrate a practical prospect of using quantum annealers for simulation of molecular dynamics. A methodology developed for this goal, dubbed Quantum Differential Equations (QDE), is applied to propagate classical…
Quantum computing exhibits the unique capability to natively and efficiently encode various natural phenomena, promising theoretical speedups of several orders of magnitude. However, not all computational tasks can be efficiently executed…
In contexts where relevant problems can easily attain configuration spaces of enormous sizes, solving Linear Differential Equations (LDEs) can become a hard achievement for classical computers; on the other hand, the rise of quantum…
To approximate solutions of complex nonlinear partial differential equations remains a computational challenge, especially for sets of equations relevant in industry, such as Euler or Navier-Stokes equations. Even the most sophisticated…
This paper presents a system for solving binary-valued linear equations using quantum computers. The system is called Mod2VQLS, which stands for Modulo2 Variational Quantum Linear Solver. As far as we know, this is the first such proposal.…
The accurate computation of ground and excited states of many-fermion quantum systems is one of the most consequential, contemporary challenges in the physical and computational sciences whose solution stands to benefit significantly from…
We introduce an efficient variational hybrid quantum-classical algorithm designed for solving Caputo time-fractional partial differential equations. Our method employs an iterable cost function incorporating a linear combination of overlap…
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,…
We propose a quantum-classical hybrid algorithm to simulate the non-equilibrium steady state of an open quantum many-body system, named the dissipative-system Variational Quantum Eigensolver (dVQE). To employ the variational optimization…
Partial differential equation (PDE)-constrained optimization, where an optimization problem is subject to PDE constraints, arises in various applications such as design, control, and inference. Solving such problems is computationally…
We describe an algorithm for the numerical solution of second order linear differential equations in the highly-oscillatory regime. It is founded on the recent observation that the solutions of equations of this type can be accurately…
Quantum metrology plays a fundamental role in many scientific areas. However, the complexity of engineering entangled probes and the external noise raise technological barriers for realizing the expected precision of the to-be-estimated…
Quantum algorithms for both differential equation solving and for machine learning potentially offer an exponential speedup over all known classical algorithms. However, there also exist obstacles to obtaining this potential speedup in…
While it seems possible that quantum computers may allow for algorithms offering a computational speed-up over classical algorithms for some problems, the issue is poorly understood. We explore this computational speed-up by investigating…
Differential equations are ubiquitous in models of physical phenomena. Applications like steady-state analysis of heat flow and deflection in elastic bars often admit to a second order differential equation. In this paper, we discuss the…