The Qubit: Physical Foundations
A qubit is any quantum two-level system whose superposition and entanglement encode information a classical bit cannot.
What a qubit is
A classical bit is either 0 or 1. A qubit is a normalized state in a two-dimensional complex vector space: |psi> = a|0> + b|1>, with |a|^2 + |b|^2 = 1. The coefficients a and b are amplitudes, not probabilities; their relative phase is physically real and drives interference.
Any pure single-qubit state maps to a point on the Bloch sphere: |psi> = cos(theta/2)|0> + e^{i*phi} sin(theta/2)|1>. The north and south poles are |0> and |1>; the equator holds equal superpositions differing only in phase. Gates are rotations of this sphere.
Why two levels
Nature offers many two-level systems: electron or nuclear spin up and down, the ground and excited state of an atom, two charge or flux configurations of a superconducting circuit, or the presence of a single photon in one of two paths. A useful qubit needs these levels to be well isolated from all other states so control pulses do not leak population elsewhere.
DiVincenzo criteria
- A scalable system of well-characterized qubits
- The ability to initialize to a known state such as |0>
- Long coherence times relative to gate times
- A universal set of gates
- Qubit-specific measurement (readout)
No physical qubit is a perfect two-level system. Real hardware has extra levels, couples weakly to its environment, and drifts. The engineering of quantum computers is largely the fight to keep these imperfections below the thresholds at which computation and, later, error correction remain possible.
Kronos runs quantum and classical solvers on isotope-platform and plasma-physics problems; understanding the physical qubit clarifies why present machines are error-limited and why results are cross-checked against classical simulation.