PHY 3570 - Introduction to Quantum Computing

• Explain and describe key properties of physical quantum states
• Describe a qubit and contrast it with a classical bit
• Explain superposition qualitatively and mathematically
• Be able to graphically represent and manipulate qubits: i.e. make use of the Bloch sphere
• Explain and perform calculations for single qubit gate operations
• Explain and perform calculations involving quantum phase and measurement
• Explain entanglement qualitatively and mathematically
• Explain and perform calculations for multi-qubit gate operations
• Utilize linear algebra to represent qubits and gate operations
• Be able to interpret quantum computing circuit diagrams
• Be able to implement simple quantum circuits using a programming environment such as Qiskit
• Describe fundamental features of implementing quantum gates and algorithms
• Explain the role and importance of phase kick-back and quantum interference to the functioning of quantum algorithms
• Explain how decoherence and the challenge of executing high-fidelity gate operations necessitates error correction in quantum computing
• Explain error correction techniques in quantum computing and the distinction between physical and logical qubits
• Describe computation problems where a quantum speedup could be exploited
• Explain important algorithms such as Grover’s search or Shor’s factoring algorithm

• Energy and energy conservation
• Basic atomic structure
• Electric force, magnetic force
• Wave nature vs photon picture for light
• Basic linear algebra such as matrix multiplication and multiplying vectors and matrices

• Algorithmic complexity
• Motivations for quantum computing
• Quantum superposition
• Quantum measurement
• Qubits and different qubit representations
• Quantum entanglement
• Single qubit gates
• Multi-qubit gates
• Linear algebra implementations of qubits, multiple qubits and gates
• Quantum algorithms including: Deutch-Jozsa, Bernstein-Vazirani, Grover’s search and Shor’s factoring algorithm
• The need for error correction and the difference between physical and logical qubits
• Quantum networking and post-quantum encryption, e.g. BB84
• Physical implementations of quantum computers
• Engineering technologies relevant to working in quantum computing
• Programming environments available for quantum computing, e.g. Qiskit
• Running quantum algorithms on commercially available quantum computers