#### Student Status

Undergraduate

#### Abstract

Quantum computing is one of the promising active areas in physics research. This is because of the potential of quantum algorithms to outperform their classical counterparts. Grover’s search algorithm has a quadratic speed-up compared to the classical linear search. The quantum simulation of Schrödinger’s equation has an exponential memory save-up compared to the classical simulation. In this thesis, the ideas and tools of quantum computing are reviewed. Grover’s algorithm is studied and simulated as an example. Using the Qiskit quantum computing library, a code to simulate Schrödinger’s equation for a particle in one dimension is developed, simulated locally, and run on an actual IBM quantum computer. Several initial states are evolved in zero, harmonic, and linear potential fields. The results obtained are compared with similar results found in the literature

#### Department

Physics Department

#### First Advisor

Tarek Elsayed

#### Extent

49 p.

#### Institutional Review Board (IRB) Approval

Not necessary for this item

#### Recommended Citation

Eltohfa, Mohamed, "Quantum Simulation of Schrödinger's Equation" (2021). *Capstone and Graduation Projects*. 23.

https://fount.aucegypt.edu/capstone/23

#### Publication Date

3-11-2021

*python code of the simulation of the simple harmonics oscillator*

AUC_endorsement-Tohfa.pdf (529 kB)

*endorsement_Mohamed_Eltohfa*

Coherent_State_harmonic_potential.mp4 (17 kB)

*Coherent state animation*

Linear_Potential.mp4 (18 kB)

*Linear potential animation*

n=7_k=0_Phi=1pi_stepnum=100_int=100_FreeDissipating.mp4 (19 kB)

*Dispersing Gaussian animation*

n=7_k=0_Phi=1pi_stepnum=100_int=100_q_Freeeigen.mp4 (15 kB)

*Sinusoidal eigenstate animation*

n=7_k=2_Phi=1pi_Freemoving.mp4 (71 kB)

*Moving Gaussian animation*

#### Included in

Numerical Analysis and Scientific Computing Commons, Quantum Physics Commons, Theory and Algorithms Commons