# Coupling superconducting qubits

These seems to be a lot of confusion about how to make two superconducting qubits talk to each other, so I’m going to explain how one of the couplers we’ve developed works.

First a word about the qubits. This coupler is designed for flux qubits. Flux qubits are loops of metal, interrupted by one or more weak links (called Josephson junctions). The qubits are operated so that the bit state zero (0) corresponds to current circulating clockwise around the loop, and bit state one (1) corresponds to current circulating in the counterclockwise direction. The magnitude of these currents is about one microamp, and they are persistent currents – no dissipation.

The bit states (circulating currents) generate magnetic fields. Another way of thinking about the information that the qubits store is to think bit state zero = magnetic field pointing down through the loop, bit state one = magnetic field pointing up through the loop.

These magnetic fields are very useful “handles” we can use to interact with the qubits.

Here’s how the coupler works: Put two of these qubits down somewhere on the chip. Inductively couple both of these qubits to a third loop of metal (the coupler).

If the coupler has a Josephson junction (a weak link) in its loop, the effect it has on the induced coupling between the two qubits can be tuned from anti-ferromagnetic (qubits prefer to be aligned oppositely) through zero (no coupling) to ferromagnetic (qubits prefer to align in the same bit state).

Here is a schematic of two qubits plus a coupler:

For the experts: This system has the effective Hamiltonian

where we can slowly change the terms (on scales of microseconds) with a high degree of precision on the final target values.

The coupler allows us to tune the J term over some range [-J_max^0..0..+J_max^1].

So how is it able to do this? For a full description you can read this. The short version is that the magnetic susceptibility of the coupler loop as a function of magnetic flux applied through the loop changes sign, and the induced coupling between the qubits is proportional to the magnetic susceptibility of the coupler. Nice.

## 9 thoughts on “Coupling superconducting qubits”

1. Don’t put that Hamiltonian in a linear architectuređź™‚

2. Yeah. Damn exactly solvable one dimensional models.

The actual Hamiltonian of the full circuit is the 2D Ising model in a magnetic field. Tiling the plane with integrated circuit stuff is pretty straightforward. Better fab might allow 3D but I’m not sure it actually buys us much.

3. i love that metal!

4. Hi — what are the numerical values of the achieved parameters
in the hamiltonian?, eg. what is J_max in meV / microeV, etc ?

5. The next to last sentence, the one that starts “The short version…” might be a wonderful explanation for some people, but for me there are too many prepositions and subjunctive clauses (whatever they are) to make any sense of it. Could you please try again?

6. I am trying to sort out this qubit business and this post confuses me. Supposedly qubits can hold more than one state: they can hold two states in superposition. What you are describing here with the current running clockwise or anti-clockwise, sounds like a plain old everyday bit with a value of 0 or 1.

All of which leads to another question: how do you encode two states in a qubit? This computer uses electricity, so you must be sending electrical signals to the qubit, or to something attached to the qubit structure. Or maybe this is a trade secret?