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Building an ideal quantum computer

Until now, errors have remained the main obstacle to the creation of efficient quantum computers.

An unique self-correcting superconducting quantum bit technology, the cat qubit, paves the way for universal, error-resistant quantum computing.

A french startup is currently developing the first logical cat qubit. It will then use a modular approach to scale up and solve the toughest problems.

A UNIQUE TECHNOLOGY

An unique approach takes advantage of the autonomous error correction of the superconducting cat qubit.

Why build a computer from quantum systems ?

Unlike its classical counterpart, a quantum computer uses quantum bits to perform its calculations. A quantum bit or qubit is a physical system with two states noted |0> and |1>, just like a classical bit, but with a crucial property : these two states can be placed in a quantum superposition. In the 1980s, physicists wondered what interest this fascinating property could have. They then developed the concept of a quantum computer and realized that it could be extremely effective in solving chemical structures or factoring prime numbers. Forty years later, as we are about to harness their exponential computing power, quantum computers are the center of attention and captivating.

Quantum computers are suitable for solving specific tasks known to be too complex for a classical computer, such as optimization problems or high-dimensional linear algebra.

Of course, you would never use a quantum computer to perform simple multiplication. It would be like trying to cut butter with a lightsaber : not only is it disproportionate, but it’s also very inefficient.

If you are solving optimization problems, which many companies are, then quantum computing can give you a significant competitive advantage. Whether you’re optimizing a financial portfolio or designing a spaceship, you’re faced with a problem that grows in complexity as quickly as the number of variables. A quantum computer can propel you towards the optimal solution and set you apart from your competition in ways never before possible.

Do you do Deep Learning or complex fluid mechanics simulations ? Imagine how exponentially increasing your computing speed could drastically expand your range of possibilities ! The HHL quantum algorithm harnesses the power of quantum computers to rethink the way we solve linear algebra. Much like the classic computers of the 60s and 70s in their day, quantum computers will dramatically improve the design capabilities of engineers and spark a global technological revolution. What if you took a step ahead of your competitors by immersing yourself in it now ?

In our view, the numerical simulation of materials or molecular structure is the most interesting field of application. Quantum computing opens up a world of possibilities with significant impact. Thus, even if we know perfectly the rules that govern molecules and materials, it is almost always impossible to predict their properties exactly. These derive from quantum mechanics and only a quantum computer can reveal them precisely. What do you think the world will look like when the design of materials and drugs becomes an engineering problem and no longer an empirical science ?

Why is it difficult ?

The main challenge in building a quantum computer is the extreme sensitivity to the exotic properties of quantum mechanics. They disappear in a process known as decoherence due to unwanted interactions with our classical world.

Take the example of Schrödinger’s cat thought experiment : a cat is placed in a sealed box in a quantum superposition of the living or dead state. When the box is opened, the superimposed cat randomly collapses into one of two possible states : either dead or alive. It was the cat’s interaction with our classical world that destroyed the quantum aspect of the cat state.

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

The only error inherently related to quantum systems is the “phase-flip” or phase shift

Decoherence leads to errors during the calculation. More specifically, it randomly changes the phase of quantum superpositions inducing errors called phase inversions. Quantum bits also suffer from a classic error, the bit-flip which randomly swaps |0> and |1>.

Surprisingly, the bit flip rate in quantum systems is several orders of magnitude higher than the case of classical systems. There is no fundamental reason for such a discrepancy : the only error intrinsically linked to quantum systems is phase switching. A pioneering quantum bit has been designed, the cat qubit, which is probably as insensitive to bit flips as a classical bit while remaining both coherent and controllable. In this way, only phase inversions need to be actively corrected. This qubit therefore greatly simplifies the design of the ideal quantum computer.

Cat qubits are just the tip of the iceberg of a new generation of quantum bits, elegantly designed to be inherently error-proof and scalable. While it may not be the silver bullet, the cat qubit should already enable the design of quantum computers with such low error rates that most of the applications envisioned will be within the reach.

The scientists work with superconducting circuits which are one of the most promising platforms for building a quantum computer. They deliver cutting-edge performance with precise control and unique design flexibility.

Among the superconducting circuits implementing qubits, one in particular, the transmon, has attracted the most attention and has been chosen by many players. By nature, it has long coherence times and is easy to manufacture and handle, making it a prime candidate. However, despite continued progress over the past 10 years, improvement in its error rate has slowed, making active quantum error correction necessary in order to make further progress.

Among the many quantum error correction strategies, the surface code has been the most studied theoretically. However, it is still very difficult to implement due to the large number of qubits required. In short, the surface code needs a 2D array of qubits to perform quantum error correction. Both dimensions are needed to correct for both types of error : bit flips and phase reversals. We can already imagine how we could win by using a qubit with only one type of error.

The cat qubit, just like many other bosonic codes (GKP, binomial) reduces the hardware required for error correction by exploiting the large Hilbert space of a harmonic oscillator. With the same number of physical systems, bosonic codes are able to delocalize quantum information to more states, achieving the same level of protection with fewer physical systems, a property known as “material efficiency.” This infinite dimensional space should be able to stabilize two particular states, in which quantum information is encoded. With the cat qubit it is possible to do this autonomously. More precisely, a simple dynamics is realized capable of stabilizing two coherent states with amplitude \alpha and opposite phase in a harmonic oscillator. This stabilization reduces the bit flip probability (going from +\alpha to -\alpha) exponentially in \alpha^2 while only linearly increasing the phase flip rate (probability of losing 1 photon). To correct the remaining error, a linear repetition code can be used to achieve an error rate small enough for most impactful applications (from RSA decryption to novo drug design).

How does this stabilization take place ? Classically, a nonlinear driven system is designed that exhibits subharmonic generation. In particular, thanks to the doubling of the period, two stationary states can be generated which are stable. In a quantum way, a microwave resonator exchange photons in pairs with its environment. When driven, this system has two stationary states, the coherent states |\alpha> and |-\alpha> which differ only by one \pi phase.

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