Squeezing Cats: Pushing the Frontiers of Error Protection

The quantum error problem

Quantum computing has the potential to solve some of our hardest problems, but a major roadblock stands in the way: errors. Qubits, the basic building blocks of quantum computers, are constantly making errors. They get disturbed by the “noise” of our classical world, which causes them to lose their quantum state and information. The problem is correcting these errors, which involves huge engineering, cost and resource overheads that only grow with scale. But what if we could reduce this monumental hardware challenge by starting with the qubit itself, and “protecting” it from noise from the start?

Error protection by design

Fortunately, this notion of “protected” qubits exist, and candidates are already being developed. Take Microsoft’s Majorana qubits, for example. These are topologically protected qubits that if proven, would resist the two main types of quantum errors: bit-flips and phase-flips. The problem is that these qubits are very hard to make. At Alice & Bob, we’re also working with “protected” qubits in the form of cat qubits that resist bit-flips errors.

*Non-locality in Alice & Bob’s cat qubit compared with Microsoft’s majorana qubit*

To protect against errors, majorana qubits and cat qubits both harness non-locality – the idea that quantum information can be spread across space – but they do it in different ways. Majorana qubits are separated in physical space, while cat qubits in phase space. This distributed nature makes the two approaches more resilient to errors, reducing the hardware overheads for error correction. In the case of our cats, we recently showed that our architecture would require 200x less resources to run Shor’s famous algorithm.

To run Shor’s algorithm, our cat qubits – with the LDPC error correction architecture – would require 100,000 physical qubits, compared with 20 million standard superconducting physical qubits in other state-of-the-art approaches.

Our latest research, “Enhancing dissipative cat qubit protection by squeezing”, takes the design of our qubits even further. By applying a technique called “squeezing,” we have experimentally demonstrated how to drastically enhance our cats’ ability to resist errors, without extra hardware. Before we drive you through our experiment and the thinking behind, let’s refresh ourselves on the workings of our cat qubits.

Our cats have the power of lasers inside of them

One of the earliest and most successful applications of quantum principles is the laser. But what’s the secret behind lasers? They are made up of highly coherent states of light, meaning all photons within the laser share the same frequency and phase. This coherence is key to having a beam of light that is very stable and predictable. The cat qubit follows a similar principle. It’s a quantum superposition of two coherent states, meaning it can be in two distinct states at the same time. The logical 1 is one coherent state and the logical 0 is another, with an opposite phase. This coherence also gives our cat qubits their unique strength – they stay incredibly stable against local disturbances.

So, what’s the link with errors? Just like ramping up the beam intensity in our laser analogy, increasing the number of photons makes it much harder for the environment to change the phases. Increasing the photon count boosts our cat qubits’ stability by increasing the separation between the cat states, making our cats resilient to bit-flips. However, this power comes at a cost…

The trade-off: bit-flip protection vs phase-flip errors

As we increase photons to boost our cat’s bit-flip protection, we increase our other form of error: phase-flips. The higher the average number of photons in our cat, the more these photons “escape”, creating phase-flips. For an exponential increase in bit-flip protection, we get a linear increase in phase-flips. In other words, we have a trade-off working strongly in our favor. Nevertheless, we still need to be able to correct these errors, and we need to do so the whole time we run our algorithm.

We correct phase-flips with a repetition code, which works by encoding one qubit’s information across multiple physical qubits. Adding physical qubits helps us to correct errors, but only to a point. We are constrained by the threshold, meaning the maximum number of errors a quantum system can tolerate before it’s no longer able to correct them. If we kept increasing photons, and therefore creating phase-flips, we would reach a point where our error correction became overwhelmed. The goal for our error correction is therefore to get below threshold, the critical tipping point at which scaling our error correction will lead to fewer errors. Considering this, reducing overall errors is fundamental for realizing practical error correction. And here’s where Squeezing comes in.

How squeezing works: getting more out of our cats

The concept of squeezing isn’t new. Other fields have used squeezed states of light to enhance performance and overcome a specific limitation. A prime example is LIGO, the large interferometer designed to detect gravitational waves by measuring tiny changes in distance.

LIGO wanted to enhance sensitivity and precision, so they reshaped quantum states of light waves to extract more information. Today, thanks to this technique, LIGO has successfully detected gravitational waves. So, how do we apply this principle to cats?

At its core, the principle of Squeezing is pretty simple: by altering the shape of the coherent cat states, we can optimize the error trade-off and reduce the number of errors that arrive in our in our system.

Principle of protection enhancement by squeezing. Wigner functions W (β) of cat states. The first two panels show coherent state-based standard cat states while the third panel illustrates a squeezed moon cat state. Solid black lines delineate the extent of the basis states at W = 0.5/π, and dashed lines indicate the extent of the left panel cat state. Arrows indicate modifications of the basis state. (D) Probability density of the cat basis states (red dashed lines) plotted in logarithmic scale, as a function of R(β). The dashed region highlights the overlap between the two basis states.

Let’s take a look at our cat states’ Wigner function in the image above – a way to visualize the qubit’s quantum state. The unsqueezed cat in the first panel and the squeezed cat in the third panel have the same number of photons – so the same risk of phase-flips – the difference is in the distance between the red “blobs.” The larger the distance between these blobs – as in our squeezed state – the longer the bit-flip lifetime becomes. Since there is no increase in photons, we don’t create any additional phase-flips.

By applying squeezing, we achieved a 160x increase in bit-flip lifetime, while keeping phase-flips constant, as well as a 50% reduction in Z-gate infidelity. Crucially, squeezing drastically enhances the performance of cat qubits without needing major design changes or extra hardware, bringing us a step closer to practical and fault-tolerant quantum computing.

What’s next?

We’ll be working to demonstrate the benefits of Squeezing in a multi-cat qubit architecture. Once we have a few more cats, we’ll get closer to beating the threshold and creating our first logical qubit. Stay tuned!