Quantum Mechanics Flashcards
What are the five features of quantum computing (compared to stocastic)?
- Exponential Stochasticity
- Superpositions
- (Destructive) Interference
- Measurement
- Entanglement
How do the sum of probabilities in quantum computing compare to stocastic?
How do you derive the Bloch sphere for non-relativistic electron.
What is the matrix form of this operator, and what can it be used for?
It is both Hermitian and Unitary, so it can both evolve and collapse the state.
What is the expectation value of this operator?
Hint: prove using the Bloch sphere electron representation.
How does this tensor product of operators act on this singlet state?
How do you prove the no-cloning theorem?
What is quantum copying?
We copy the basis vectors. Not quite “cloning”
- What is the definition of an entangled state?
- How do you rigoursly prove it?
- A state that can’t be decomposed into tensor products.
- You show that it violates Bell’s inequalities.
What is Bell’s / CHSH Inequalities argument?
Via the Clauser-Horne-Shimony inequality
What is the GHZ argument?
Local reality implies contradiction.
This is stronger than Bell/CHSH, as it isn’t statistical.
What are the two types of evolution of quantum states?
- Continuous : Unitary evolution of a quantum state.
- Discontinuous : The non-unitary irreversible jump when a measurement is made.
Why do many quantum algorithms begin with a Hadamard operation?
Because this creates a superposition of states, which enables us to exploit quantum effects such as interference & entanglement. Many algorithms (Grover’s, Shor’s, Fourier’s) rely on these effects, so we must move into the Hadamard basis first.
What is the difference between measurement & observation?
- Measurement Determines the physical properties of the system.
- Observation Looks at the different possible states of the system.
