scholarly journals Numerical hardware-efficient variational quantum simulation of a soliton solution

2021 ◽  
Vol 104 (2) ◽  
Author(s):  
Andrey Kardashin ◽  
Anastasiia Pervishko ◽  
Jacob Biamonte ◽  
Dmitry Yudin
1996 ◽  
Vol 88 (1) ◽  
pp. 33-52 ◽  
Author(s):  
JONATHON GREGORY ◽  
DAVID CLARY

Author(s):  
S. G. Rajeev

Some exceptional situations in fluid mechanics can be modeled by equations that are analytically solvable. The most famous example is the Korteweg–de Vries (KdV) equation for shallow water waves in a channel. The exact soliton solution of this equation is derived. The Lax pair formalism for solving the general initial value problem is outlined. Two hamiltonian formalisms for the KdV equation (Fadeev–Zakharov and Magri) are explained. Then a short review of the geometry of curves (Frenet–Serret equations) is given. They are used to derive a remarkably simple equation for the propagation of a kink along a vortex filament. This equation of Hasimoto has surprising connections to the nonlinear Schrödinger equation and to the Heisenberg model of ferromagnetism. An exact soliton solution is found.


2020 ◽  
Vol 116 (23) ◽  
pp. 230501
Author(s):  
Samuel A. Wilkinson ◽  
Michael J. Hartmann
Keyword(s):  

2010 ◽  
Author(s):  
Y. Ohta ◽  
Wen Xiu Ma ◽  
Xing-biao Hu ◽  
Qingping Liu

2021 ◽  
Author(s):  
Christian Kokail ◽  
Rick van Bijnen ◽  
Andreas Elben ◽  
Benoît Vermersch ◽  
Peter Zoller
Keyword(s):  

2021 ◽  
Vol 4 (1) ◽  
Author(s):  
S. Leontica ◽  
F. Tennie ◽  
T. Farrow

AbstractSimulating the behaviour of complex quantum systems is impossible on classical supercomputers due to the exponential scaling of the number of quantum states with the number of particles in the simulated system. Quantum computers aim to break through this limit by using one quantum system to simulate another quantum system. Although in their infancy, they are a promising tool for applied fields seeking to simulate quantum interactions in complex atomic and molecular structures. Here, we show an efficient technique for transpiling the unitary evolution of quantum systems into the language of universal quantum computation using the IBM quantum computer and show that it is a viable tool for compiling near-term quantum simulation algorithms. We develop code that decomposes arbitrary 3-qubit gates and implement it in a quantum simulation first for a linear ordered chain to highlight the generality of the approach, and second, for a complex molecule. We choose the Fenna-Matthews-Olsen (FMO) photosynthetic protein because it has a well characterised Hamiltonian and presents a complex dissipative system coupled to a noisy environment that helps to improve the efficiency of energy transport. The method can be implemented in a broad range of molecular and other simulation settings.


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