# Alice & Bob go to March Meeting

**Assembling a chain of 3 cat-qubits for phase-flip error detection (Part 1 & 2)**

**Tue. March 7, 12:42 p.m. – 12:54 p.m. & 12:54 p.m. – 1:06 p.m., Room 415**

*J. Stevens, J-L. Ville & Alice&Bob team**

Bosonic codes provide a first level of error protection to limit the hardware overhead required for quantum error correction. However, to reach low enough error rates for practical quantum algorithms, these codes have to be concatenated with a discrete variable quantum error correction code, such as the surface code. Like other bosonic codes, autonomously stabilized cat-qubits have demonstrated this first layer of error correction, suppressing bit-flips exponentially with average photon number at a linear cost in phase-flips. However, the necessary concatenation with a repetition code to correct against phase-flip has yet to be demonstrated.

In this work, we show how to implement a phase-flip error detection scheme with 3 stabilized cat qubits by post-selecting on the negative/trivial error syndromes. This requires accurate error syndrome extraction which relies both on high fidelity CNOT gates and fast parity measurements. Performing error detection is an important milestone towards error correction. Further improving error syndrome extraction will enable full quantum error correction of a small scale repetition code in the near future.

**Towards a bias-preserving CNOT gate between stabilized cat qubits (Part 1 & 2)**

**Tue. March 7, 4:48 p.m. – 5:00 p.m. & 5:00 p.m. – 5:12 p.m., Room 401/402**

*A. Essig, N. Cottet & Alice&Bob team**

Bosonic codes enable hardware-efficient quantum error correction by exploiting the infinite-dimensional Hilbert space of a quantum harmonic oscillator to implement some of the required redundancy for error correction. Autonomously stabilized cat qubits have demonstrated an exponential suppression of bit-flips errors with the average number of photons of the cat states, at the cost of a linear increase of phase-flips. This results in a strong noise-bias that reduces the hardware requirements for further error correction. However, leveraging this first error protection layer requires that all quantum gates preserve the error-bias. Concretely, applying a gate should produce bit-flip errors that are also exponentially suppressed with the cat state photon number. One gate of central importance is the CNOT gate that is used to measure the error syndrome of the repetition code considered to correct the remaining phase-flips errors.

In this work, we present our progress in realizing a bias-preserving CNOT gate between two stabilized cat qubits. This requires both improvement in the performance of the individual cat qubits along with a careful gate design. This work paves the way towards the demonstration of full quantum error correction based on repeated cat qubits.

**Efficient simulations of Lindblad master equations in the stabilized code space of cat qubits**

**Thu. March 9, 5:12 p.m. – 5:24 p.m., Room 412**

*F-M Le Régent, J. Guillaud, P. Rouchon*

We introduce a new method to obtain effective reduced dynamics on the decoherence-free subspace of a dissipative Lindblad dynamics having multiple degenerate steady states.

This method relies on the asymptotic expansion of the perturbative dynamics (usually modelling decoherence channels, or the effect of imperfect gate implementations) in the Heisenberg picture; which is particularly well adapted to the study of composite systems with multiple cat qubits stabilized by a strong two-photon dissipative mechanism.

We illustrate the advantages of this method by explicitly showing how to apply it to the simulation of multi-cat qubit gates; which was a previously intractable numerical problem.

**Passive two-photon dissipation for bit-flip error correction of a cat code**

**Thu. March 9, 8:24 a.m. – 8:36 a.m., Room 406**

*A. Marquet, A. Essig, N. Cottet, A. Murani, E. Albertinale, J. Guillaud, T. Peronnin, S. Jezouin, B. Huard, R. Lescanne*

Bosonic codes offer a resource-efficient method to quantum error correction. Of particular interest, autonomous correction was successfully demonstrated for cat codes, where the logical |0〉 and |1〉 states are coherent states of opposite amplitudes |α〉 and | − α〉 in a superconducting resonator with single-photon loss rates κ1 as low as possible. They correct bit-flip errors by either using the non-linearity of the oscillator or parametrically pumping couplers to produce two-photon dissipation at a rate κ2. The bit-flip time increases exponentially with |α|2 while the phase-flip rate only increases linearly with |α|2. In this work, we introduce and experimentally demonstrate a new superconducting circuit designed to correct for bit-flip errors of cat codes. Crucially, the two-photon dissipation does not require any pump, so that a single drive is required to stabilize the qubit manifold. This is obtained by non-linearly coupling the cat qubit to a buffer mode that resonates at twice the frequency of the cat qubit. We experimentally demonstrate unprecedented ratios κ2/κ1, so that bit flip times well over a ms can be reached with a few photons only. We also demonstrate quantum gates on this corrected cat qubit.

This work was partly supported by the grant ANR-19-QUAN-0006.

**Squeezed Kerr quantum oscillator with multiple spectral degeneracies**

**Thu. March 9, 4:48 p.m. – 5:00 p.m., Room 406**

*D. Ruiz, R. Gautier, J. Guillaud, M. Mirrahimi*

Kerr-nonlinear oscillators driven by a two-photon process have been recently considered as an interesting system to encode quantum information and to ensure a hardware-efficient scaling towards fault-tolerant quantum computation. In this talk, we show that an extra control parameter, the detuning of the two-photon drive with respect to the oscillators resonance, plays a crucial role in the properties of the defined qubit. At specific values of this detuning, we benefit from strong symmetries in the system, leading to multiple degeneracies in the spectrum of the effective confinement Hamiltonian. Overall, these degeneracies lead to a stronger suppression of bit-flip errors. We also study the combination of such Hamiltonian confinement with colored dissipation to suppress leakage outside of the bosonic code space. We show that the additional degeneracies allow us to perform fast and high-fidelity gates while preserving a strong suppression of bit-flip errors.

**Encoding a cat-qubit in a 3D millisecond lifetime superconducting cavity**

**Tue. March 7, 5:12 p.m. – 5:24 p.m., Room 401/402**

*U. Reglade, A. Murani, F. Rautschke, S. Polis, N. Pankratova, E. Albertinale, A. Gras, T. Peronnin, P. Champagne-Ibarcq, R. Lescanne, S. Jezouin, Z. Leghtas*

In this talk on experimental superconducting circuits, we implement a cat-qubit in a millisecond lifetime cavity. The cat-qubit encodes quantum information in an oscillator endowed with a special mechanism that dissipates photons in pairs. This pins down two coherent states of opposite phase that play the role of logical states. Remarkably, as the number of photons in each coherent state is increased, bit-flips between the two are exponentially suppressed. This comes at the cost of a linear increase of the phase flip rate, that is augmented, for each added photon, by twice the oscillator energy dissipation rate. Therefore, minimizing oscillator losses is crucial to maintain low phase-flip rates. The lowest dissipation rates have been reported in 3D superconducting cavities, routinely reaching single photon lifetimes up to several milliseconds. In this experiment, we embed a two-photon dissipation apparatus in a 3D cavity, and address the several technological challenges associated to combining a millisecond lifetime superconducting cavity, flux tunability, and a strongly driven-dissipative mode.

**Assessing phonon trap efficiency through on-chip spatial and energy resolved detection of high energy impacts**

**Tue. March 7, 1:54 p.m. – 2:06 p.m., Room 405**

*A. Murani, F. Valenti, P. Paluch, N. Gosling, T. Reisinger, R. Kruk, R. Gartmann, R. Gebauer, O. Sander, I. Pop*

High energy ionizing impacts (muons, gamma rays, etc.) on a chip convert to high energy phonons which can propagate over large distances in the substrate, breaking Cooper pairs in superconducting devices on their way. These impacts are detrimental for quantum computing as they can produce correlated errors, a critical pitfall for current quantum error correction schemes. Mitigating these impacts can be done e.g. through shielding or on-chip phonon traps. Being able to detect high energy impacts and quantify the efficiency of phonon traps is therefore of paramount importance for superconducting quantum processors.

In this talk I will present on-chip high energy events detection with both spatial and energy resolution in order to assess the efficiency of phonon traps. We fabricated on the same chip six resonators made of granular aluminum, a high kinetic inductance superconductor which maximizes the device’s susceptibility to Cooper pair breaking. Additionally, our chips were designed to host phonon traps made of aluminum, a lower gap superconductor, similarly to Ref. [1]. Using custom made electronics, we performed simultaneous event detection with time resolution at the nanosecond scale, allowing us to reconstruct the location of the impacts. Additionally, the time response of the resonators provides information about the impact’s energy. In light of these results, I will discuss the efficiency of phonon traps in reducing the rate of (correlated) quasiparticle generation from ionizing impacts.

**Alice & Bob team**

Emanuele Albertinale, Danielius Banys, Nicolas Bourdaud, Joachim Cohen, Nathanael P Cottet, Louise Devanz, Antoine Essig, Pierre Fevrier, Adrien Gicquel, Antoine Gras, Jérémie Guillaud, Pierre Guilmin, Sebastien Jezouin, Raphael Lescanne, Paul Magnard, Alexandre May, Anil Murani, Theau Peronnin, Ivana Petkovic, Stephane Polis, Felix Rautschke, Camille Roy, Jeremy Stevens, Jean-Loup Ville