Quantum Feedback Engineering

Project Information

Q-Feedback

Grant agreement ID: 884762

DOI

10.3030/884762

EC signature date 25 November 2020

Start date 1 December 2020

End date 30 September 2026

Funded under

• EXCELLENT SCIENCE - European Research Council (ERC)

Total cost

€ 2 440 125,00

EU contribution

€ 2 440 125,00

Coordinated by

ASSOCIATION POUR LA RECHERCHE ET LE DEVELOPPEMENT DES METHODES ET PROCESSUS INDUSTRIELS
France

Periodic Reporting for period 3 - Q-Feedback (Quantum Feedback Engineering)

Reporting period: 2023-12-01 to 2025-05-31

Summary of the context and overall objectives of the project

Quantum technologies, such as quantum computers and simulators, have the potential of revolutionizing our computational speed, communication security and measurement precision. The power of the quantum relies on two keys but fragile resources: quantum coherence and entanglement. This promising field is facing a major open question: how to design machines which exploit quantum properties on a large scale, and efficiently protect them from external perturbations (decoherence), which tend to suppress the quantum advantage?
Making a system robust and stable to the influence of external perturbations is one of the core problems in control engineering. The goal of this project is to address the above question from the angle of control systems. The fundamental and scientific ambition is to elaborate theoretical control methods to analyse and design feedback schemes for protecting and stabilizing quantum information. Q-Feedback develops mathematical methods to harness the inherently stochastic aspects of quantum measurements. Relying on the development of original mathematical perturbation techniques specific to open quantum systems, Q-Feedback proposes a new hierarchical strategy for quantum feedback modelling, design and analysis.
The building block of a quantum machine is the quantum bit (qubit), a system which can adopt two quantum states. Despite major progress, qubits remain fragile and lose their quantum properties before a meaningful task can be accomplished. For this reason, a qubit must be both protected against external perturbations and manipulated to perform a task. Today, no such qubit has been built.
In collaboration with experimentalists, the practical ambition is to design, relying on the control tools developed here, qubits readily integrable in a quantum processing unit. The physical platform is based on Josephson superconducting circuits where the qubit is encoded in a high-quality single superconducting resonator having thus an infinite dimensional Hilbert space. The stabilization scheme is decomposed into two layers: a fast quantum-controller layer supported mainly by low-quality resonators with non-linear interaction Hamiltonians; a slow classical-controller layer exploiting measurement outcomes to estimate and/or to compensate for slow parameter drifts and low-frequency noises.
Q-Feedback is expected to demonstrate the crucial role of control engineering in emerging quantum technologies.

Work performed from the beginning of the project to the end of the period covered by the report and main results achieved so far

Since the beginning of the project in December 2020, and despite the pandemic that disrupted lab organisation we have:
1.Built a new lab space at ENS Paris to host the experiments from project Q-feedback and equipped a He3 dilution cryostat with necessary RF and DC electronic devices now intensively used for the experimental tasks of Q-feedback.
2.Hired a team of scientists: We have hired a team 5+2 PhD students and 2+2 postdocs working on various aspects of Q-feedback.
3.Contributed with the control-theoretical methods (WP1) developed in Q-feedback to key experiments: two conducted by Z. Leghtas (doi: https://doi.org/10.1103/PRXQuantum.4.020350 and https://arxiv.org/abs/2307.06617) where the bit-flip time of a cat-qubit is increased by many orders of magnitude; one experiment conducted by B. Huard (https://doi.org/10.48550/arXiv.2402.05046) with potential application to quantum error correction protocols on bosonic codes.
4.Published a proposal of a state-of-the-art experimental circuit ensuring autonomous stabilization and generation of GKP-qubits (https://doi.org/10.1103/PhysRevX.15.011011). We developed here a novel approach to stabilize these qubits by dissipation engineering (i.e. quantum controller) in high-impedance circuits. French, European and US patents protect this proposal (FR3133467A1, EP4490674A1, US20250181958A1).
5.Published five papers on adiabatic elimination and efficient numerical simulations for composite open quantum systems encountered in bosonic code (https://doi.org/10.48550/arXiv.2303.04495 https://doi.org/10.1016/j.ifacol.2023.10.1779 https://doi.org/10.48550/arXiv.2303.17308 https://doi.org/10.48550/arXiv.2303.05089 https://doi.org/10.48550/arXiv.2404.01802). The new numerical scheme is protected by European and US patents (EP4428768A1, US20240303519A1).
6.Published control-theoretical results: on GKP-qubit autonomous stabilisation (doi.org/10.1109/CDC51059.2022.9992722 and doi.org/10.1016/j.ifacol.2023.10.1776); on parameter estimation based on stochastic master equation (https://doi.org/10.1016/j.ifacol.2023.10.110 10.1109/LCSYS.2024.3407608); convergence of bipartite open quantum systems stabilized by reservoir engineering (https://doi.org/10.1007/s00023-024-01481-8).
7. Analysed in https://doi.org/10.48550/arXiv.2410.00975 the flux-pump-induced degradation of 1 for dissipative cat qubits. This article combines time-dependent Schrieffer-Wolff perturbation theory with numerically exact Floquet theory.
8.Published an original numerical method to generate quantum gates for open quantum systems via a monotonic algorithm with time optimization (https://www.aimsciences.org/article/id/6708e39b2d4d1a4052cb08cf).
9.Obtained new results submitted for publications:
-on complete-positivity, trace preserving and linear schemes for simulations on classical computers of infinite dimensional open quantum systems including truncation-errors estimation (arXiv:2501.09607 and arXiv:2503.01712).
-on classical parameter estimation of quantum stochastic master equation from standard correlation functions attached to realistic measurement data (arXiv:2410.11955)
-on dynamical models of reduced order for continuously measured quantum systems (arXiv:2503.08296)
-on a prototypical circuit that we designed, fabricated and tested to engineer high-order dissipation channels and investigate sources of residual nonlinearities in the context of Q-feedback (arXiv:2501.05960).

Progress beyond the state of the art and expected potential impact (including the socio-economic impact and the wider societal implications of the project so far)

On the control-theoretical and numerical side of the project we expected progress on:
- efficient estimation algorithms, based on maxlike and smoothing techniques, for process and quantum-state tomography based on binned measurement data and their corresponding stochastic master equations.
- convergence of numerical simulation schemes for infinite dimensional Lindblad master equation combining Galerkin approximation and time discretisation based on exact Kraus maps.
- simplified architecture of super-conducting quantum circuits ensuring autonomous stabilization and generation of GKP-qubits with passive elements and gyrators.
- efficient numerical simulations on classical computer based on tensor-networks methods for bosonic codes.
- on time-averaged continuous quantum measurement and filtering motivated by experimental constraints with binned measurement data.
On the experimental side, we have designed, tested and characterized a circuit allowing to activate high-order dissipation channels in a linear superconducting resonator. Our circuit employs a near Kerr-free Josephson mixer (the Asymetrically Threaded SQUID). Compared to the state-of-the-art, this mixer is embedded in a high-impedance circuit and participates strongly in the target mode embedding the bosonic code to be stabilized. This allows the direct mixing of up to 6-waves. This novel regime led to unexpected complications arising from residual non-linear mechanisms. These mechanisms were characterized in detail and mitigation measures for future experiments were proposed.
In the near-future, we intend to implement these mitigation measures and use our circuit to dynamically stabilize a four-legged cat qubit. In the longer term, we intend to ramp up our circuit impedance and stabilize cat qubits with a larger number of components and eventually GKP qubits.

q-feedback-figure-3.jpg