Qubits are the building blocks of quantum computing, offering a leap beyond classical bits. Unlike their binary counterparts, qubits can exist in multiple states simultaneously, unlocking powerful computational possibilities through superposition and entanglement.

Harnessing qubits' unique properties enables quantum computers to solve complex problems faster than classical machines. From superconducting circuits to trapped ions, various physical systems are being explored to create and manipulate qubits, paving the way for groundbreaking applications.

Quantum Bits (Qubits)

Qubits vs classical bits

• Qubits serve as the fundamental unit of information in quantum computing, analogous to classical bits in classical computing
• Classical bits can only exist in one of two discrete states: 0 or 1
• Qubits can exist in a superposition of states, allowing them to be in a linear combination of |0⟩ and |1⟩ states simultaneously
• The state of a qubit is represented by a linear combination of basis states: $|ψ⟩ = α|0⟩ + β|1⟩$
  • $α$ and $β$ are complex numbers called probability amplitudes
  • The probabilities of measuring the qubit in the respective states are given by $|α|^2$ and $|β|^2$, which must sum to 1 ($|α|^2 + |β|^2 = 1$)

Properties of qubits

• Superposition enables a qubit to exist in multiple states simultaneously, allowing for parallel computation and exponential speedup in certain algorithms (Shor's algorithm, Grover's search)
• Entanglement is a quantum phenomenon where two or more qubits become correlated, such that the state of one qubit cannot be described independently of the others, enabling powerful quantum algorithms (quantum teleportation) and secure communication protocols (quantum key distribution)
• Coherence refers to the ability of a qubit to maintain its quantum state over time, which is essential for performing quantum operations and algorithms
• Measurement of a qubit collapses its superposition into a definite state (0 or 1), with the probability of measuring a particular state depending on the probability amplitudes

Significance in quantum computing

• Qubits provide exponential computational power, as N qubits can represent $2^N$ states simultaneously, enabling the solving of certain problems much faster than classical computers
• Qubits enable the implementation of quantum algorithms that can provide exponential speedup over classical algorithms for specific problems (factoring large numbers, searching unstructured databases)
• Quantum error correction schemes are necessary to maintain the integrity of quantum information, as qubits are prone to errors due to decoherence and noise

Physical systems for qubits

• Superconducting circuits implement qubits using superconducting Josephson junctions (transmon qubits) and are used by companies like IBM, Google, and Rigetti
• Trapped ions implement qubits using the internal states of trapped atomic ions (calcium-40, ytterbium-171) confined using electromagnetic fields
• Photonic systems implement qubits using the polarization (horizontal/vertical, left/right circular) or path (dual-rail encoding) of single photons and are suitable for quantum communication and networking
• Nitrogen-vacancy (NV) centers in diamond implement qubits using the spin states of electrons and nuclei in NV centers and are promising for quantum sensing and nanoscale imaging applications (magnetometry, thermometry)