# Our Technology

# Why building a computer out of quantum systems ?

Contrary to its classical counterpart, a quantum computer uses quantum bits to compute. A quantum bit (qubit) is any physical system that has two distinct states noted and , just as a classical bit, but with the crucial property that these two states can be put into a quantum superposition. In the 80s, physicists started wondering what could be gained with this intriguing feature. They developed the concept of a quantum computer and realized that it could be extremely efficient in solving chemistry problems or certain types of problems such as factoring prime numbers. Forty years later, quantum computers attract more and more attention as we are on the verge of harnessing their exponential computing power.

## What can a quantum computer do for you and your business?

Quantum computers are well suited for a specific set of tasks that are notoriously difficult for classical computers such as very large optimization and linear algebra problems or chemical simulations.

Of course you will never use a quantum computer to do a simple multiplication, it would be like trying to slice butter with a lightsaber : it is not only overkill, it is highly inefficient.

If your business relies on optimization problems, which is the case for almost any business, then using quantum computing may give you an unfair advantage. Whether you are optimizing a financial portfolio or designing a spacecraft, you are facing a problem whose complexity rises very rapidly with the number of variables. Quantum computers may help you tunnel to the optimal solution and crush your competition with uncanny strategies.

If you are fooling around with deep-learning or complex fluidic simulations, you are trying to solve large scale linear algebra problems. Think of how an exponential speedup would change your field of possibilities. The HHL quantum algorithm leverages the power of quantum computers to rethink the way we solve linear algebra. Just like classical computers in the 60s and 70s, quantum computers will drastically enhance the design capabilities of engineers and be at the root of a global engineering revolution. Your competitors will not miss the mark. Get a head start by diving in right now !

To us, the most exciting impact of quantum computers will be for chemical simulations and the unprecedented possibilities it might open. Indeed, even though we know perfectly the rules governing molecules and materials, it is almost always impossible to predict exactly the behaviour of a molecule or a material. This comes from the fact that these latter are ruled by quantum mechanics and it takes a quantum machine to solve it precisely. Now imagine the possibilities opened as soon as material and drug design becomes an engineering problem instead of an empirical science. It may very well be the beginning of a new era for mankind. But for that, we need a very reliable quantum computer.

## Why is it difficult ?

The main challenge in building a quantum computer is that the exotic features of quantum mechanics are extremely sensitive. They vanish in a process known as decoherence due to unwanted interactions with our classical world.

Think of the Schrödinger’s cat thought experiment : a cat is placed in a sealed box and put in a quantum superposition of dead and alive. When the box is opened, the superposed cat collapses randomly into one of the two possible states, either dead or alive. It is the interaction of the cat with our classical world that destroyed the quantumness of the cat.

Building a quantum computer hence means designing an isolated box in which we perform quantum algorithms. But, to be able to run them, the computer must be controllable. Hence the main paradox of this extraordinary quest : isolating part of our universe while controlling it at the same time.

## Our philosophy

Decoherence leads to errors during computation. More precisely, it randomly switches the phase of quantum superpositions inducing errors called phase-flips. Quantum bits also suffer from a “classical” error, the bit-flip that randomly swap 0s and 1s.

Surprisingly, the bit-flip rate in quantum systems is many orders of magnitude higher than in classical ones. There is no fundamental reason for such a discrepancy : the only error intrinsically tied to quantum systems is the phase-flip. We have designed a pioneering quantum bit, the cat qubit, that is presumably as insensitive to bit-flips as a classical bit while remaining both coherent and controllable. This way only phase-flips require to be actively corrected. It drastically simplifies the design of the ideal quantum computer.

Cat qubit are just the tip of the iceberg of a new generation of quantum bits, elegantly designed to be inherently robust to errors and scalable. Even though they might not be the end of the game, cat qubit should already enable the design of quantum computers with error rates so low, that most envisioned applications will be within our reach.

## For experts

We are working with superconducting circuits which is one of the most promising platforms for building a quantum computer. They provide state-of-the-art performances with accurate control and have unique flexibility of design.

Among the superconducting circuits that implement qubits, a particular one, the transmon has drawn most of the attention and has been chosen by many of the current players. Inherently, it has long coherence times and is easy to fabricate and manipulate, which makes it a prime candidate. However, despite continuous progress in the past 10 years, its error rate improvement has slowed down which makes active quantum error correction necessary in order to further progress.

Among the many quantum error correction strategies, the surface code has been the most theoretically studied. However, it remains very challenging to implement due the large number of qubits required. In short, the surface code needs a 2D array of qubits to perform quantum error correction. The two directions are required to correct the two types of error, the bit-flips and the phase-flips. One can already imagine how one could gain using a qubit with a single type of error.

The cat qubit, just like many other bosonic codes (GKP, binomial) reduces the hardware required for error correction by leveraging the large Hilbert space of a harmonic oscillator. With the same amount of physical systems, the bosonic codes are able to delocalise quantum information over more states, achieving the same amount of protection with fewer physical systems, a property known as “hardware efficiency”. However, this infinite dimension space one should be able to stabilize two particular states, in which quantum information is encoded. With cat qubit, it is possible to do so autonomously. More precisely, we have realised a simple dynamics that is able to stabilize two coherent states with amplitude and opposite phase in a harmonic oscillator. Crucially, this stabilisation exponentially reduces the probability of bit flip (going from to ) exponentially in while only increasing linearly the phase flip rate (probability of losing 1 photon). To correct the remaining error a linear repetition code can be used to reach an error rate small enough for most impactful applications (from RSA cracking to denovo drug design).

How is this stabilization done ? Classically, we engineer a non-linear driven system that exhibits sub-harmonic generation. In particular, thanks to period doubling we can generate two steady-states which are stable. Quantum mechanically, we make a microwave resonator exchange photons by pair with its environment. When, driven, this system has two steady-states, the coherent states and which only differ by a phase.

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