What is happening at Alice & Bob these days? The summer is coming and new fridges have been installed. But it’s not to increase our capacity for nice cold drinks when things get hot. No, we’re going to put our cats in them. But then, maybe you didn’t know, A&B’s cats are really very cool cats.

I am **Paul Magnard**, quantum physicist at Alice & Bob, we are building the first fault-tolerant quantum computer using **cat qubits**, let me explain. We have to go back to **Schrödinger’s cat paradox**. Schrödinger showed that it should be possible for a macroscopic object to be in a superposition of two quantum states corresponding to two very different materializations, the cat being at the same time dead and alive.

So, these states should exist, but we never witness them in real life. Or do we? As a matter of fact, it’s been done in many labs using many different approaches. And we actually **do this on a regular basis at Alice & Bob**.

Naturally, the cats we put in the fridge at A&B are not real ones. They are *coherent states* of light, rather like a classical sinusoidal standing wave, in a superconducting microwave resonator.

Now, to create a dead cat or a living one is rather straightforward, just as with real cats. But how do we create a quantum superposition of these two opposite-phase electromagnetic vibrations? This is where the fridges come in.

## Cryogenics

Our device can only work at **very low temperatures**. In fact, cryogenic temperatures. There are two reasons. First, our chip uses **Josephson junctions** so it needs to be superconducting. This ensures that the resonator supporting our cat is long-lived. The second reason is that our resonator typically resonates at 4 GHz and we need to **avoid the generation of thermal photons** at anything like this frequency. It turns out that there would already be a thermal photon in the resonator if the temperature were even as high as a mere 200 mK, a fraction of one degree above absolute zero! To be quite sure that the quantum properties of our cat do not get spoiled by those warm photons, we need to make things much colder: **around 10 mK**. Not a place to keep summer drinks!

Where would you go if you really wanted to cool down? Finland, maybe? Our lab is equipped with dilution refrigerators from the **Finnish company Bluefors**, based in Helsinki. At the top end of their mission: to enable the quantum technology breakthrough. That’s spot on for Alice & Bob. The Bluefors cryostats installed in our Paris lab provide a 10 mK environment at the push of a button. We place our device below the coldest plate of one of these stunningly beautiful machines, put up the shields, and turn the fridge on. Two days later, our chip is quantum, and we can start making cats.

## The physics behind our cat states

There are many ways to create a **superposed cat quantum state** in the lab. But our approach at Alice & Bob is unique, it relies on **dissipation**. Let’s start with a simple example of how we use dissipation to stabilize a state.

The idea is to both drive and damp our cat resonator at the same time. Then it turns out that it will go into one of the required coherent states when the system eventually reaches a steady state. And this final state is stable: if it is perturbed, the combination of drive and dissipation will return your resonator to that stabilized coherent state.

However, although that’s enough to stabilize a living cat, it won’t stabilize a dead one, because the opposite-phase coherent state is not an equilibrium point.

### Creating the superposition of cat states.

To get a cat qubit, we need to stabilize both cat states at once. And the secret is to implement a *two-photon* dissipation and drive. This allows us to stabilize two opposite-phase oscillations, whose amplitude and phase are also dictated by that of the two-photon drive. But this time there are two-simultaneously stable oscillatory states. So, how do we achieve this?

We have invented a special device called an **asymmetrically threaded SQUID (ATS)**, patented by Alice & Bob, which allows us to generate a special type of interaction between the cat and another resonator we call the buffer.

**Pairs of photons in the cat resonator are transformed into a single photon in the buffer resonator**, and vice versa. However, because the buffer is lossy, each time two photons are transferred to a single photon in the buffer, this photon is dissipated to the environment. Effectively, this dissipates photons from the cat resonator *in pairs*. In addition, driving the buffer drives the resonator with a two-photon drive.

These two ingredients damp the resonator with two stable coherent states of opposite phase: our living and our dead cat. And what’s even more remarkable, it also stabilizes the quantum superposition of these states.

### So, here’s the final recipe:

- Place the chip inside your favourite dilution refrigerator.
- Let the fridge cool down for one or two days.
- Wait an extra 500 µs for your resonator to relax thermally to its vacuum state, i.e., no photons in the resonator
- Then bias the ATS, pump the ATS while driving the buffer, and …

Hey presto! You have just prepared a version of Schrödinger’s superposition state: not a superposition of dead and alive cats, but nevertheless a superposition of two macroscopic quantum states.

## Why cat qubits are great to build fault tolerant quantum computers?

Those who are more familiar with quantum computing may already have got why this matter. Information in quantum computers is stored in qubits. These are little physical systems associated with a physical measurement that can give one of two results – in this case our coherent states, 0 (dead) or 1 (alive).

The problem is that qubits are delicate and tend to flip randomly between 0 and 1, when they do, an error is produced, and the computation has to start over. But a qubit whose 0 and 1 states correspond to our coherent states are extremely robust to such bit-flip errors due to the wide separation of the dead and alive cat states in phase space.

In fact, we have shown that our qubits remain stable for several seconds or more, long enough to use them in quantum algorithms. That’s why at Alice & Bob we are counting on these qubits to build **error-free quantum computers**: one of the two main error channels is heavily suppressed.

These cat qubits will greatly **reduce the effort required to carry out quantum error correction,** saving a huge number of resources and making it much easier to scale up our quantum computers as our Diego Ruiz explains in this blogpost.