1. History, Theory, and Basics

1.1 History

Transistor Invention (1947): John Bardeen, William Shockley, and Walter Brattain invented the transistor, which paved the way for technological advancements.
Quantum Mechanics Foundations:
- Ernest Rutherford (1909): Introduced the atomic model with a dense nucleus.
- Niels Bohr (1913): Proposed a quantum model of the atom with quantized energy levels.
- Max Planck (1900): Introduced the concept of energy being emitted in discrete units (quanta).
- Albert Einstein (1905): Developed the photoelectric effect theory, linking light to quantized energy.
Advancements in Quantum Theory:
- Heisenberg (1925): Formulated matrix mechanics and the uncertainty principle.
- Erwin Schrödinger: Developed wave mechanics, describing particles as wave-like entities.
Richard Feynman’s Contribution (1981): Proposed the idea of quantum computers to efficiently simulate quantum phenomena, highlighting the limitations of classical computers.
Theoretical Advances (1980s-1990s): Researchers like David Deutsch and Peter Shor laid the groundwork for quantum algorithms and cryptography.

Qubits: The Building Blocks.
Quantum Gates and Circuits, fundamental operations that manipulate qubits.
Quantum Algorithms. e.g. Shor’s Algorithm, Grover’s Algorithm.
Technical Challenges:
- Qubit Stability
- Quantum Error Correction
- Scalability

𐙚‧₊˚📜✩ ₊˚⊹♡ Readings:

Superposition; Quantum Interference; Entanglement.

classic gates : AND, OR, XOR (irreversible), form a universal set.
- XOR ($\oplus$) is equivalent to x+y(mod2) operation.
- unitary operator : quantum gates must be reversible (no information is lost).
- CNOT (controlled-NOT) gate (reversible). $\begin{pmatrix} x \\ y \end{pmatrix} \to \begin{pmatrix} x \\ x \oplus y \end{pmatrix}$
Quantum Circuit : Each qubit is represented by a line in the circuit diagram and time runs from left to right.
- Gates and circuits are linear.
- No loop, cannot splay out, cannot merge.

1. Classical vs. Quantum Logic

Feature	Classical Logic	Quantum Logic
Basic Concept	Based on binary values (true/false) and definite states	Based on probability distributions and quantum states
Principle	Law of the excluded middle (a statement is either true or false)	Superposition (a state can be both true and false simultaneously)
Handling Uncertainty	Limited; cannot handle uncertainty or vagueness well	Handles uncertainty and probability inherently
Formal Systems	Propositional logic, predicate logic	Quantum mechanics framework
Applications	Philosophy, mathematics, computer science	Quantum computing, quantum information theory

2. Classical vs. Quantum Gates

Feature	Classical Gates	Quantum Gates
Basic Concept	Process binary inputs (0 or 1) to produce binary outputs	Operate on qubits (quantum bits) and enable superposition and entanglement
Common Types	AND, OR, NOT, NAND, NOR, XOR, XNOR	Single-qubit gates (e.g., NOT, Hadamard), multi-qubit gates (e.g., CNOT, SWAP)
Output Determinism	Deterministic; output is fixed for given inputs	Probabilistic; output depends on quantum state and measurement
Reversibility	Most classical gates are irreversible (e.g., AND, OR)	Quantum gates are reversible (unitary operations)
Applications	Digital circuits, memory circuits, arithmetic circuits	Quantum circuits, quantum algorithms, quantum error correction

3. Classical vs. Quantum Transistors

Feature	Classical Transistors	Quantum Transistors
Basic Concept	Three-terminal device (source, drain, gate) controlling current flow	Manipulate quantum states of electrons to control current flow
Operation	Use electric field to control current between source and drain	Use quantum mechanics principles to enable superposition and entanglement
Information Unit	Binary digits (bits)	Quantum bits (qubits)
Performance	Suitable for classical computing; limited by binary nature	Potentially faster due to parallel processing; suitable for quantum computing
Challenges	Scalability limited by physical size; heat dissipation	Fragility of quantum states; error susceptibility; requires advanced technologies
Applications	Classical computers, digital devices	Quantum computers, quantum communication systems

4. Classical vs. Quantum Computing

Feature	Classical Computing	Quantum Computing
Basic Concept	Based on classical logic and binary arithmetic	Based on quantum mechanics and qubits
Information Unit	Binary digits (bits)	Quantum bits (qubits)
Computation Model	Sequential processing; limited by binary nature	Parallel processing; exponential growth in computational power
Handling Uncertainty	Limited; not suitable for probabilistic tasks	Handles uncertainty and probability inherently
Applications	General-purpose computing, office applications, complex simulations	Cryptography, drug discovery, optimization, artificial intelligence, quantum simulations
Current State	Well-established; widely used in daily life	Emerging technology; still in development stage
Future Potential	Limited by physical constraints	High potential for revolutionizing various fields; still facing technical challenges

Superconducting Qubits: Widely used, relying on superconducting circuits at low temperatures, allowing for easy fabrication and scalability. Companies like IBM and Google are leading in this area.
Trapped Ions: Utilize individual ions manipulated by lasers for high fidelity operations and longer coherence times, with companies like IONQ making significant progress.
Photonic Quantum Computing: Uses photons for encoding and processing information, ideal for communication applications. Companies like Xanadu are exploring this technology.
Topological Quantum Computing: Based on exotic particles called anions, which are resistant to errors. Microsoft is a key player in this field.
Analog Quantum Computing: Focuses on evolving quantum systems over time to find optimal solutions, with D-Wave systems pioneering this approach.
Quantum Computer Components: Discusses the quantum data plane, control processor plane, and host processor, which are essential for managing qubit states and processing information.