# Quantum Computing and Syllabus Topics for Learning 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

### 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 • 