The following represents key elements of **Quantum computing** which needs to be emphasized during **learning** stages:

- Understanding of Bits and Qubits
- Fundamentals of Linear Algebra
- Quantum mechanics principles
- Quantum computation models
- Quantum Factoring
- Complexity theory
- Search algorithms
- Quantum computing applications

These topics can form part of **syllabus** if you are planning to **design a course on Quantum computing**.

### Understanding Qubits vs Bits

Coming from a traditional classical computing background, it would be important to understand some of the following:

- What are Qubits?
- How does Qubit relates to Bits?
- Introduction to Superposition and Entanglement concepts
- Qubits examples

### Linear Algebra Fundamentals

Given the state space of a quantum system is described in terms of a vector space, It is important to understand linear algebra concepts of some of the following in relation to vectors:

- Vector spaces
- Basis of vector space
- Inner, outer and tensor products
- Linear, Unitary, Normal and Hermition operators
- Matrices
- Norms
- Eigenvalues
- Adjoints

### Quantum Mechanics Principles

The following are some of key quantum mechanics principles which can be used for describing the behavior of a physical system.

**Quantum state can be defined using a state space**: Any physical system can be associated with a state space. The system is completely described at any given point in time by its state vector. A closed system is described by a unit vector in a complex inner product space.**Quantum state evolves with time**: The state of a closed quantum system at time t1 is related to the another state at time t2 by a unitary operator which depends only on t1 and t2. The evolution of a closed system in a fixed time interval is described by a unitary transform.**Quantum state can be measured**: A measurement on a quantum system has some set M of outcomes. Quantum measurements are described by a collection {Pm : m ∈ M} of measurement operators.**State space of composite physical system can be measured**: The state space of a composite physical system is the tensor product of the state spaces of the individual component physical systems.

### Quantum Computation Models

The following concepts need to be understood in relation with models for quantum computing:

**Quantum Circuits**: In quantum information theory, a quantum circuit is a model for quantum computation in which a computation is a sequence of quantum gates, which are reversible transformations on a quantum mechanical analog of an n-bit register. Read further details on Wikipedia page for quantum circuits**Quantum Algorithms**: In quantum computing, a quantum algorithm is an algorithm which runs on a realistic model of quantum computation. Read further details on Wikipedia page on Quantum Algorithms**N-Gates**: Different types of Gate and related operations- One qubit gate (Pauli gate, Hadamard gate)
- 2-qubit gate (Controlled Not)
- 3-qubit gate (Toffoli gate)

### Quantum Computing Applications

There should be emphasis on explaining quantum computing using some of the example applications. One could choose some of the following examples:

- Quantum cryptography
- Quantum teleportation
- Superdense coding

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