A conceptual introduction to Quantum Mechanical Systems, their properties and qubits. Research focused on Chapters of * Quantum Computing for Everyone by Chris Bernhardt* and Section II & IV of Quantum Sensing by C.L. Degen, F. Reinhard and P. Cappellaro.. The weekly content here is representative of assignments and exercises related to my coursework for ECE 802 – 730 | Quantum Sensor and System Engineering at Michigan State University.

#### Application of Shor’s Algorithm

Shor’s algorithm is applied in the area of cryptographic communications. Circuits have yet to be

developed that fully realize the potential of Shor’s algorithm, but it’s clear that it is only a matter of

time before technology unlocks the potential of Shor’s algorithm to break classical encryption

methods. While troubling, this revelation has led to a focus on post-quantum cryptography and

quantum key distribution (QKD) schemas such as BB84 and Ekert’s protocols.

#### Application of Grover’s Algorithm

Grover’s algorithm addresses computing answers to questions that involve large unstructured

datasets. Leveraging quadratic speedup (vs exponential speedup of classical computing algorithms), Grover’s algorithm can maximize the time spent on unstructured searches within massive sets of

data.

#### Exercise 1

Solve the time independent Schrodinger Equation for a particle of the mass and the infinite potential well of width . Refer to Particle in a Box Model; “*a particle in a 1-dimensional box is a fundamental quantum mechanical approximation describing the translational motion of a single particle confined inside an infinitely deep well from which it cannot escape*“. Show the first two energy levels and the first two wave functions. Calculate values of the first two energy levels for an electron in a box of size, .

If then,

**∴** the solution for the time independent Schrodinger Equation is:

If , then and

**∴**

From earlier,

If