# Superconducting Qubits

**Superconducting qubits** are two-level quantum systems built from superconducting circuits—Josephson junctions and capacitors. A Josephson junction is a tunnel junction between two superconductors separated by a thin insulator; it exhibits nonlinear inductance and can act as a nonlinear resonator.

Superconducting qubits are among the most mature quantum computing platforms (IBM, Google, Rigetti, IonQ). They operate at millikelvin temperatures and reach coherence times of microseconds to milliseconds. The nonlinearity enables selective two-level coupling while suppressing higher levels.

## Key Properties

**Frequency**: typically 4–7 GHz (controlled by inductance and capacitance)

**Anharmonicity**: the qubit's energy levels are nonequally spaced (unlike a harmonic oscillator). This nonlinearity is what makes it a qubit: transitions between specific levels can be addressed without affecting others.

**Quality factor**: Q = $\omega_0 / \gamma$ where $\gamma$ is the decay rate. High-Q qubits have long coherence times. State-of-the-art superconducting qubits reach Q ~ 10^4 – 10^5.

## Types of Superconducting Qubits

**Transmon**: charge-insensitive qubit, reduced sensitivity to charge noise, most common

**Fluxonium**: flux-tunable qubit, compact, strong nonlinearity

**Charge qubit**: sensitive to gate voltage, simple design but noisy

**Phase qubit**: biased near the maximum of Josephson potential

scqubits provides models for each type. Choose based on your application: transmons for robust qubits, fluxoniums for strong nonlinearity, etc.