Lecture on Quantum Computing vs. Classical Computing

Classical Computing

• Uses classical bits: 0 or 1
• Classical operations based on these bits

Quantum Computing

• Uses quantum bits (qubits)
• Qubits can be both 0 and 1 simultaneously (quantum superposition)
• Superior computing power to classical computers

Types of Qubits

• Single photon
• Nucleus
• Electron (outermost electron in phosphorous used by researchers)

How Qubits Work

• Electrons have magnetic fields (tiny bar magnets)
• Spin: Property of electrons, similar to compass needle aligning with Earth's magnetic field
  • Zero state (spin down): Aligns with magnetic field
  • One state (spin up): Requires energy to flip

Quantum Superposition

• Electrons can be in both spin up and spin down states simultaneously
• Measurement forces electron into one state
• Coefficients indicate probability of states

Two Qubits Interaction

• Four possible states: 00, 01, 10, 11
• Quantum mechanics allows superpositions of these states
• Information Content:
  • Two classical bits: 2 pieces of information
  • Two qubits: Requires 4 coefficients (4 pieces of information)
• For N qubits: Contains 2^N classical bits

Example

• 300 qubits: 2^300 classical bits
• Equivalent to number of particles in the universe

Measurement and Information Loss

• Measurement collapses qubit into one of the basis states
• Information about pre-measurement state is lost
• Final computational result must be a unique state (not a superposition)

Limitations of Quantum Computers

• Not a replacement for classical computers
• Faster only for specific types of calculations and algorithms
• Quantum operations may be slower than classical
• Efficient in reducing total number of operations needed for special calculations

Key Takeaways

• Quantum computers are powerful for specific tasks using quantum superposition and parallelism
• Not universally faster; classical algorithms and general tasks remain better suited for classical computers.