Quantum Computing Lecture Notes

Classical vs Quantum Bits

Classical Bits: Classical computers use classical bits, which can be either 0 or 1.
Quantum Bits (Qubits): Quantum computers use qubits, which can exist in both 0 and 1 states simultaneously, giving quantum computers superior computing power.

Qubits can be represented by physical objects such as:
- Single photon
- Nucleus
- Electron
Example: Researchers use the outermost electron in phosphorous as a qubit.

Spin: Electrons have magnetic fields and behave like tiny bar magnets.
- Align with magnetic fields in the lowest energy state (spin down or 0 state).
- Can be flipped to the highest energy state (spin up or 1 state) by applying energy.
Superposition: Electrons in quantum superposition can exist in both spin states simultaneously until measured.

Two qubits can form four possible states: 00, 01, 10, 11.
Quantum mechanics allows superposition of these states, requiring four coefficients to describe their state, compared to two bits in classical systems.

For N qubits, the equivalent classical information is 2^N classical bits.
Example: 300 qubits can represent 2^300 classical bits, comparable to the number of particles in the universe.

Upon measurement, qubits collapse into one of the basis states, losing any superposition information.
Goal: Design quantum operations so the final result is a measurable basis state.

Not a Replacement: Quantum computers are not universally faster than classical computers.
- Only faster for specific calculations leveraging quantum superposition for computational parallelism.
- Not beneficial for tasks like video watching or document creation using classical algorithms.
Performance: Individual operations in quantum computers may be slower, but the number of operations to reach a result can be exponentially reduced in certain algorithms.
Conclusion: Quantum computers excel in particular algorithms but are not a general replacement for classical computers.