Related papers: A hybrid quantum-classical algorithm for multichan…
For noisy intermediate-scale quantum (NISQ) devices only a moderate number of qubits with a limited coherence is available thus enabling only shallow circuits and a few time evolution steps in the currently performed quantum computations.…
The transport of charged particles or photons in a scattering medium can be modelled with a Boltzmann equation. The mathematical treatment for scattering in such scenarios is often simplified if evaluated in a frame where the scattering…
We propose a hybrid quantum-classical algorithm, originated from quantum chemistry, to price European and Asian options in the Black-Scholes model. Our approach is based on the equivalence between the pricing partial differential equation…
Quantum computers promise to revolutionize our ability to simulate molecules, and cloud-based hardware is becoming increasingly accessible to a wide body of researchers. Algorithms such as Quantum Phase Estimation and the Variational…
Quantum computing holds promise across various fields, particularly with the advent of Noisy Intermediate-Scale Quantum (NISQ) devices, which can outperform classical supercomputers in specific tasks. However, challenges such as noise and…
We show that nonlinear problems including nonlinear partial differential equations can be efficiently solved by variational quantum computing. We achieve this by utilizing multiple copies of variational quantum states to treat…
Finding the solution to linear systems is at the heart of many applications in science and technology. Over the years a number of algorithms have been proposed to solve this problem on a digital quantum device, yet most of these are too…
Stochastic differential equations (SDEs), which models uncertain phenomena as the time evolution of random variables, are exploited in various fields of natural and social sciences such as finance. Since SDEs rarely admit analytical…
Solving problems related to planning and operations of large-scale power systems is challenging on classical computers due to their inherent nature as mixed-integer and nonlinear problems. Quantum computing provides new avenues to approach…
A hybrid classical-quantum approach for the solution of nonlinear ordinary differential equations using Walsh-Hadamard basis functions is proposed. Central to this hybrid approach is the computation of the Walsh-Hadamard transform of…
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…
The Schr\"odinger equation defines the dynamics of quantum particles which has been an area of unabated interest in physics. We demonstrate how simple transformations of the Schr\"odinger equation leads to a coupled linear system, whereby…
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…
We investigate the electronic structure of methanimine (CH2NH) and water (H2O) molecules in an effort to locate conical intersections (CIs) using variational quantum algorithms. Our approach implements and compares a range of hybrid…
Current noisy intermediate-scale quantum (NISQ) devices remain limited in their ability to perform accurate quantum chemistry simulations due to restricted numbers of high-fidelity qubits and short coherence times. To overcome these…
Quantum query complexity plays an important role in studying quantum algorithms, which captures the most known quantum algorithms, such as search and period finding. A query algorithm applies $U_tO_x\cdots U_1O_xU_0$ to some input state,…
Quantum computing is emerging as a new computing resource that could be superior to conventional computing for certain classes of optimization problems. However, in principle, most existing approaches to quantum optimization are intended to…
We study the non-equilibrium dynamics obtained by an abrupt change (a {\em quench}) in the parameters of an integrable classical field theory, the nonlinear Schr\"odinger equation. We first consider explicit one-soliton examples, which we…
A recently formulated version of the eigenchannel method [R. Szmytkowski, Ann. Phys. (N.Y.) {\bf 311}, 503 (2004)] is applied to quantum scattering of Schr\"odinger particles from non-local separable potentials. Eigenchannel vectors and…
We propose a simple quantum algorithm for simulating highly oscillatory quantum dynamics, which does not require complicated quantum control logic for handling time-ordering operators. To our knowledge, this is the first quantum algorithm…