learning-objectives.md

Course learning objectives

Module 1: the basics (states, gates, measurements, and circuits)

• perform quantum computations using Dirac notation and matrix algebra
• express quantum computations using quantum circuits
• program quantum circuits in PennyLane
• use the Bloch sphere to represent states and the action of quantum operations
• list and define the core set of elementary quantum operations
• define and give examples of entangled states
• compute the result of measurements on one or more qubits in multiple bases
• use Bell basis measurements to implement superdense coding and teleportation
• describe the structure of variational quantum algorithms

Module 2: oracle-based algorithms, complexity, and quantum resources

• explain what it means for an algorithm to have a quantum speedup
• define quantum oracles and query complexity
• implement oracles and Grover's algorithm in PennyLane
• identify the different components of the quantum compilation stack
• define and list common universal gate sets
• estimate the resources required to run a quantum algorithm
• implement quantum transforms to perform simple circuit optimization in PennyLane

Module 3: QFT-based algorithms

• define and state the scaling of the quantum Fourier transform
• implement the quantum Fourier transform in PennyLane
• use quantum phase estimation (QPE) to estimate the eigenvalues of a unitary matrix
• use QPE to implement order finding, and simulate Shor's factoring algorithm
• identify cryptographic schemes that are susceptible to quantum attack
• implement an alternative key distribution protocol based on quantum mechanics, and describe conditions under which it is robust to quantum attack

Module 4: simulating physical systems

• describe physical systems using Hamiltonians
• Trotterize a Hamiltonian and state key bounds on the approximation accuracy of the simulations
• construct quantum circuits to simulate time evolution of quantum systems
• use QPE to determine the ground state energy of a quantum system
• implement a variational quantum eigensolver to determine the ground state energy of a quantum system, and discuss its limitations

Module 5: characterizing noise in quantum systems

• represent quantum states and measurements in the density matrix formalism
• express quantum operations as quantum channels, and state their key mathematical properties
• discuss the strengths and limitations of key metrics used to quantify the performance of today's quantum computers
• perform quantum state tomography using PennyLane
• describe the randomized benchmarking protocol, and apply it to estimate the average gate fidelity for a simulated noisy system