I. Fundamental Physics & Concepts
Qubit (Quantum Bit): The fundamental unit of quantum information, analogous to a classical bit. Unlike a classical bit (0 or 1), a qubit can be in a superposition of both 0 and 1.
Bit: Classical unit of information (0 or 1).
Superposition: The ability of a quantum system to be in multiple states at the same time. A qubit is in a superposition of |0⟩ and |1⟩ until it is measured.
Entanglement: A profound quantum connection between two or more qubits where the state of one cannot be described independently of the state of the other(s). Measuring one entangled qubit instantly influences the state of the other, no matter the distance.
Quantum State: The complete description of a quantum system (e.g., a qubit or a set of qubits), represented by a state vector (e.g., |ψ⟩).
Coherence: The property that allows qubits to maintain their quantum state (superposition and entanglement).
Coherence Time: How long a qubit maintains its quantum state before decohering.
Decoherence: The process by which a quantum system loses its quantum properties and becomes classical due to interaction with its external environment.
Measurement: The act of observing a quantum system, which causes its wavefunction to collapse into a single, definite classical state (e.g., either 0 or 1).
Wavefunction Collapse: The phenomenon where a quantum system in superposition randomly settles into one of its possible definite states upon measurement.
Interference: Quantum waves can add constructively (amplify correct answers) or destructively (cancel wrong answers) in algorithms.
No-Cloning Theorem: A fundamental theorem stating that it is impossible to create an identical copy of an arbitrary unknown quantum state.
II. Quantum Hardware & Technologies
Quantum Processing Unit (QPU): The core processor of a quantum computer, which contains the qubits.
Qubit Modalities (Types of Qubits):
Superconducting Qubits: Use superconducting electrical circuits to create artificial atoms.
Trapped Ions: Use individual atoms suspended in a vacuum by electromagnetic fields.
Photonic Qubits: Use particles of light (photons) to represent quantum information.
Semiconductor Spin Qubits: Use the spin of an electron or nucleus in a semiconductor material.
Topological Qubits: A theoretical approach that encodes information in non-local properties that are highly resistant to decoherence.
Cryogenics: The technology required to cool superconducting qubits to temperatures near absolute zero (~10-15 millikelvin).
Dilution Refrigerator: The extremely powerful refrigerator used to achieve cryogenic temperatures.
Fidelity / Gate Fidelity: A measure of the accuracy of a quantum operation. High fidelity means the quantum computer is performing as expected with minimal error.
Quantum Volume (QV): A holistic metric invented by IBM to measure the performance of a quantum computer, considering the number of qubits, connectivity, and error rates.
NISQ (Noisy Intermediate-Scale Quantum): The current era of quantum computing, characterized by processors with 50-1000 qubits that are "noisy" (prone to errors) and not yet fault-tolerant.
T1, T2: Relaxation (T1) and dephasing (T2) times; measures of coherence.
Physical vs. Logical Qubit:
Physical Qubit: The actual hardware qubit (error-prone).
Logical Qubit: A group of many physical qubits working together to act as one error-free, reliable qubit.
III. Quantum Algorithms & Software
Quantum Algorithm: A step-by-step procedure designed to run on a quantum computer to solve a specific problem.
Quantum Circuit: A model for quantum computation where a sequence of quantum gates is applied to a set of qubits.
Quantum Gate (Logic Gate): The basic operation in a quantum circuit that manipulates the state of qubits (e.g., Pauli-X, Hadamard, CNOT).
Universality: Any quantum computation can be built from a small set of universal gates.
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Quantum Supremacy / Quantum Advantage: The milestone where a quantum computer solves a problem that is practically impossible for any classical computer to solve in a reasonable time.
Quantum Error Correction (QEC): Techniques to protect quantum information from errors by using multiple physical qubits to create one stable logical qubit.
Fault-Tolerant Quantum Computing (FTQC): The ultimate goal where QEC is so effective that computations of arbitrary length can be performed reliably.
Quantum Simulation: Using a quantum computer to simulate and understand other quantum systems (e.g., molecules).
Variational Quantum Algorithm (VQA): Hybrid quantum-classical algorithms where a classical computer optimizes parameters for a quantum state.
Quantum Software Development Kit (SDK): Frameworks for developing quantum applications (e.g., Qiskit, Cirq, Braket).
Specific Algorithms:
Deutsch–Jozsa: First quantum algorithm showing exponential speedup for a specific problem.
Shor’s Algorithm: Factors large numbers exponentially faster than classical computers; threatens RSA encryption.
Grover’s Algorithm: Provides quadratic speedup for unstructured search (e.g., finding an item in an unsorted database).
VQE (Variational Quantum Eigensolver): Hybrid algorithm for finding ground states of molecules.
QAOA (Quantum Approximate Optimization Algorithm): For combinatorial optimization problems.
Quantum Fourier Transform (QFT): The quantum analogue of the discrete Fourier transform, a key component of Shor’s algorithm.
IV. Quantum Networking & Communication
Quantum Key Distribution (QKD): A secure communication method using quantum mechanics to generate a shared random secret key.
Quantum Repeater: A device to extend the range of quantum communication by performing entanglement swapping.
Entanglement Swapping: A technique to entangle two quantum particles that have never directly interacted.
Quantum Internet: A theoretical network connecting quantum processors to distribute quantum information over long distances.
Quantum Teleportation: A protocol for transferri
ng an unknown quantum state from one location to another using entangled qubits and classical communication.
V. Advanced Concepts & Paradigms
Bell State: A specific, maximally entangled state of two qubits.
Bloch Sphere: A geometrical representation of the pure state space of a single qubit.
Gate-based (circuit model): The most common model (IBM, Google, Rigetti, IonQ).
Adiabatic Quantum Computing: Slowly evolves a system to minimize energy (D-Wave's approach).
Quantum Annealing: Specialized form of adiabatic computing for optimization.
BPP, BQP: Classical (BPP) and Quantum (BQP) polynomial-time complexity classes.
Quantum Speedup Types: Exponential (Shor), Quadratic (Grover), or Potential/Heuristic.