Superconducting Qubits & Josephson Junctions

Superconducting Qubits & Josephson Junctions

Superconducting qubits are the most commercially advanced qubit technology in production today. IBM's Eagle (127 qubits), Osprey (433 qubits), Heron (156 qubits), and Google's Sycamore and Willow processors are all built from superconducting circuits. Understanding how they work reveals the physics that limits today's quantum computers and what improvements are needed.

Superconductivity and the Josephson Effect

At temperatures below ~1 K (often 10-20 mK in practice), certain metals (aluminum, niobium, indium) transition to a superconducting state where electrical resistance drops to exactly zero. More importantly for quantum computing, electrons form Cooper pairs: bound pairs that move through the lattice without scattering.

Cooper pairs are bosons (integer spin) and obey Bose-Einstein statistics. They condense into a macroscopic quantum state described by a single wavefunction with amplitude and phase:

where $n$ is the Cooper pair density and $\varphi$ is the macroscopic quantum phase. This phase is the key quantum variable.

The Josephson Junction

A Josephson junction is a thin insulating barrier (1-2 nm of aluminum oxide) between two superconductors. Quantum mechanics allows Cooper pairs to tunnel through this barrier, even though classically they cannot penetrate an insulator.

The Josephson equations describe the dynamics:

where $\delta$ is the phase difference across the junction and $I_c$ is the critical current. The junction acts as a non-linear inductor with inductance:

This non-linearity is the crucial property: it makes the Josephson junction a quantum oscillator with unequally spaced energy levels.

From LC Oscillator to Qubit

A simple LC circuit (inductor + capacitor) is a quantum harmonic oscillator with equally spaced energy levels at $E_n=\hslash \omega (n+\frac{1}{2})$. This is useless as a qubit because you cannot address the $|0⟩$-$|1⟩$ transition without also driving $|1⟩$-$|2⟩$, $|2⟩$-$|3⟩$, etc.