Flux Qubit

A flux qubit is a type of superconducting qubit that stores quantum information in the direction of persistent current circulating in a superconducting loop containing one or more Josephson junctions. The two qubit states correspond to clockwise and counterclockwise current flow, generating magnetic flux in opposite directions through the loop. Flux qubits are notable for their large anharmonicity and their role in quantum annealing architectures.

How it works

A flux qubit consists of a superconducting loop interrupted by three (or four) Josephson junctions. When an external magnetic flux $\Phi_{\text{ext}}$ close to half a flux quantum $\Phi_0/2$ is threaded through the loop, the potential energy landscape forms a double-well potential. The two wells correspond to persistent currents circulating in opposite directions, carrying currents of order $300$ to $600$ nanoamperes.

The qubit states are:

$|0\rangle \equiv |\circlearrowleft\rangle, \quad |1\rangle \equiv |\circlearrowright\rangle$

At the degeneracy point ($\Phi_{\text{ext}} = \Phi_0/2$), quantum tunneling between the two wells creates an energy splitting. The qubit Hamiltonian near this point is:

$H = -\frac{\epsilon}{2}\sigma_z - \frac{\Delta}{2}\sigma_x$

where $\epsilon \propto (\Phi_{\text{ext}} - \Phi_0/2)$ is the flux detuning (controllable via external flux) and $\Delta$ is the tunnel splitting (set by the junction parameters).

Variants

Three-junction flux qubit: The original design by Mooij et al. (1999). One junction is smaller than the other two by a factor $\alpha \approx 0.8$, creating the asymmetric potential needed for qubit operation.

Capacitively shunted flux qubit (CSFQ): A more modern variant that adds a large shunt capacitor, similar to how the transmon improved the Cooper pair box. This reduces sensitivity to charge noise while maintaining the large anharmonicity of the flux qubit. CSFQs achieve $T_1$ times exceeding 40 microseconds.

Fluxonium: A related design that replaces two of the three junctions with a large inductance (a chain of many Josephson junctions). Fluxonium qubits have demonstrated exceptionally long coherence times ($T_1 > 1$ ms) and are an active area of research at institutions including MIT and Yale.

Role in quantum annealing

D-Wave’s quantum annealers use flux qubits as their fundamental building blocks. In the annealing architecture, flux qubits are initialized in a superposition state, and the system slowly evolves from a simple Hamiltonian (transverse field) to a problem Hamiltonian (encoded in the coupling between flux qubits). The flux qubit’s large energy scale and its natural $\sigma_z$ coupling make it well-suited for this application.

D-Wave’s Advantage system uses over 5,000 flux qubits with a Pegasus connectivity graph.

Comparison with transmon qubits

Property	Flux qubit	Transmon
Anharmonicity	Large (1 to 10 GHz)	Small (200 to 300 MHz)
Charge noise sensitivity	Low (at sweet spot)	Very low
Flux noise sensitivity	Higher	Lower (fixed-frequency)
Typical $T_1$	10 to 100 microseconds	100 to 500 microseconds
Primary use	Annealing, specialized circuits	Gate-based quantum computing

Why it matters for learners

The flux qubit illustrates how different physical encodings of quantum information lead to different computational architectures. While transmon qubits dominate gate-based quantum computing, flux qubits underpin the quantum annealing approach and continue to inspire new designs like fluxonium. Understanding flux qubits also provides insight into how macroscopic quantities (circulating currents of hundreds of nanoamperes) can exhibit quantum behavior.

See also

• Superconducting Qubit
• Josephson Junction
• Transmon Qubit
• Quantum Annealing
• Coherence Time