Quantum computing: an unprecedented architecture to eliminate errors

Is the quantum computer to remain an inaccessible dream? Some scientists think so, because to them, it seems impossible to build qubits capable of withstanding the billion operations carried out by such computers. The solution could reside in the correction of errors by exploiting qubit redundancy in error-correcting codes. As it is highly unlikely for a flaw to affect several qubits simultaneously, errors are detected and can be eliminated. “Theoretically, it works”, says Diego Ruiz, a PhD student working with the joint project team, QUANTIC (ENS-PSL, Mines Paris-PSL, CNRS) of the Paris Inria Centre and the Alice & Bob startup. “But in practice, this approach requires a colossal number of qubits, which would result in quantum computers of excessive proportions!”  

Inria researchers, in cooperation with the startup Alice & Bob, have found a more ingenious alternative. A solution that reduces errors but also avoids the need for excessively large quantum computers. The secret? A combination of cat qubits and LDPC codes within an optimised architecture. Terms that require a little explanation...

What is a cat qubit? To explain this properly, let’s go back to basics. The qubit is to quantum computing what the bit is to traditional computing: a unit of information. The difference resides in the fact that qubits can be simultaneously in state 1 and state 0, resulting in a parallelism that can be exploited to carry out certain calculations much faster. 

A popular approach to building qubits is based on superconducting circuits at temperatures close to absolute zero. These are called ‘physical’ qubits. As for ‘logical’ qubits, these are sets of physical qubits grouped together to correct errors through redundancy. Among superconducting physical qubits, ‘transmons’ are the most widespread. “Cat qubits are also superconductors”, explains Diego Ruiz. “They were invented in the 2010s, mainly thanks to the work of Mazyar Mirrahimi, the QUANTIC manager who is co-directing my thesis, and other researchers from Inria and Yale University in the United States. Their name is a reference to the famous Schrödinger experiment, involving a cat that is both alive and dead at the same time.”

Which errors disrupt quantum algorithms requiring billions of operations? “There are two types of error”, explains the PhD student. Firstly, ‘bit flip’ when the qubit switches from state 0 to state 1 and vice-versa. Secondly, ‘phase flip’ when the qubit switches from state 0+1 to state 0-1.” Error correction is further complicated by the need to handle both these types of error. What is the advantage of cat qubits? By their very nature, they eliminate bit flip errors. Therefore, only phase flip errors have to be corrected, which makes things considerably more straightforward.

To eliminate phase flip errors, Mazyar Mirrahimi suggested using LDPC (Low-Density Parity-Check) correcting codes. These codes allow efficient correction with very little redundancy. However, until now they have been difficult to implement, because they require multiple long-distance connections between qubits which, in practice, are very difficult to achieve for superconducting qubits.

The solution? “We worked with Anthony Leverrier, an LDPC code specialist from the COSMIQ project team, and Christophe Vuillot from Inria’s MOCQUA team, a joint initiative with CNRS and the University of Lorraine and in conjunction with the Loria laboratory, to develop efficient LDPC codes that do not require long-distance connections”, Diego Ruiz specifies. The researchers can therefore build cat qubits based on superconducting circuits in which each qubit is connected only to its neighbours, facilitating experimentation on the circuit.

“It is a very economical architecture in terms of qubit volumes”, says Diego Ruiz, enthusiastically. Our first tests show that only four physical qubits would be needed per logical qubit, compared to several hundred with traditional error-correction methods.” 

Result: the team estimate that, by combining cat qubits and LDPC codes, they can perform useful calculations of around 1,500 qubits only.  “This is far from the millions of qubits envisaged initially”, concludes the researcher. In fact, it’s close to today’s largest quantum chips that reach approximately 1,000 qubits.” So, thanks to the collaboration between Inria and Alice & Bob, the quantum computer is becoming a more tangible prospect. When is it likely to materialise? Impossible to predict with any certainty, but one thing’s for sure: quantum computing is on its way to becoming a reality. 

The research described by Diego Ruiz is the outcome of a collaboration between five scientists, himself included. Presentation of these quantum experts.

• Mazyar Mirrahimi leads the QUANTIC joint project team (ENS-PSL, Mines Paris-PSL, CNRS) which brings together physicists and mathematicians from Inria, ENS, Mines Paristech and CNRS. These researchers are working to develop robust quantum information processing methods.
• Anthony Leverrier, a member of the COSMIQ project team from the Inria Centre, Paris, specialises in LDPC codes. He has discovered good correcting codes capable of efficient, real-time error correction. He continues to enhance these correction strategies with the aim of developing fault-tolerant quantum computers.
• Christophe Vuillot, formerly a researcher with Inria’s MOCQUA team set up jointly with CNRS and the University of Lorraine in conjunction with the Loria laboratory, is now on secondment at Alice & Bob. Previously a postdoctoral researcher under the supervision of Anthony Leverrier, he is an expert in quantum error correction and fault-tolerant calculation.
• Jérémie Guillaud joined Alice & Bob as head of the theory team, following his thesis with the QUANTIC team. Now the startup’s Firmware vice-president, he is considered a leading expert in quantum computing. He also works on cat qubits and large-scale fault-tolerant quantum computing.

• Quantum dissipation under control: making cat qubits reliable for a faultless quantum computer, Mines Paris - PSL, 16/4/2025.
• Quantum computing: the Defence Innovation Fund is participating in a 100 million euro fundraising campaign for the development of the company Alice & Bob, Directorate General of Armaments, Ministry for the Armed Forces, 31/1/2025.
• Alice & Bob raises 100 million euros to create an error-free quantum computer, L’Usine Digitale, 28/1/2025.
• Philippe Campagne-Ibarcq: overcoming a major technological barrier in quantum computing, Inria, 22/1/2024.
• Alice & Bob: cat qubits for an error-free quantum computer, Inria, 11/3/2021.

For experts

• LDPC-cat codes for low-overhead quantum computing in 2D, Nature Communications, 26/01/2025.
• Quantum control of a cat qubit with bit-flip times exceeding ten seconds,  Nature, 17/05/2024.
• Two-photo driven Kerr quantum oscillator with multiple spectral degeneracies, Physical Review A, 06/04/2023.