Periodic Reporting for period 2 - Q-Feedback (Quantum Feedback Engineering)
Okres sprawozdawczy: 2022-06-01 do 2023-11-30
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 key 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 modeling, 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.
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 modeling, 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.
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 in order 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+1 postdocs working on various aspects of Q-feedback
-3- contributed with the control-theoretical methods (WP1) developed in Q-feedback to two key experiments conducted by Z. Leghtas (DOI: 10.1103/PRXQuantum.4.020350 arXiv preprint arXiv:2307.06617) where the bit-flip of a cat-qubit is increased by many orders of magnitude.
-4- published control-theoretical results on GKP-qubit autonomous stabilisation (doi.org/10.1109/CDC51059.2022.9992722 doi.org/10.1016/j.ifacol.2023.10.1776) on parameter estimation based on stochastic master equation (doi.org/10.1016/j.ifacol.2023.10.110) and on adiabatic elimination for open quantum systems (doi.org/10.1016/j.ifacol.2023.10.1779).
-5- obtained new results submitted for publications:
- (WP1, WP2) adiabatic elimination to derive efficient numerical simulations for composite open quantum systems encountered in bosonic code. A patent with the startup Alice&Bob (Application number EP23305313.1) and the arXiv preprint arXiv:2303.05089 have been submitted.
- (WP1, WP2) control-theoretical proof of convergence for infinite dimensional bipartite open quantum systems stabilized by reservoir engineering has been obtained in the preprint arXiv preprint arXiv:2311.10037
- (WP3) proposal of a state-of-the-art experimental circuit ensuring autonomous stabilization and generation of GKP-qubits (arXiv preprint arXiv:2304.03806). We developed here a novel approach to stabilize these qubits by dissipation engineering (i.e. quantum controller) in high-impedance circuits.
-1- Built a new lab space at ENS Paris in order 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+1 postdocs working on various aspects of Q-feedback
-3- contributed with the control-theoretical methods (WP1) developed in Q-feedback to two key experiments conducted by Z. Leghtas (DOI: 10.1103/PRXQuantum.4.020350 arXiv preprint arXiv:2307.06617) where the bit-flip of a cat-qubit is increased by many orders of magnitude.
-4- published control-theoretical results on GKP-qubit autonomous stabilisation (doi.org/10.1109/CDC51059.2022.9992722 doi.org/10.1016/j.ifacol.2023.10.1776) on parameter estimation based on stochastic master equation (doi.org/10.1016/j.ifacol.2023.10.110) and on adiabatic elimination for open quantum systems (doi.org/10.1016/j.ifacol.2023.10.1779).
-5- obtained new results submitted for publications:
- (WP1, WP2) adiabatic elimination to derive efficient numerical simulations for composite open quantum systems encountered in bosonic code. A patent with the startup Alice&Bob (Application number EP23305313.1) and the arXiv preprint arXiv:2303.05089 have been submitted.
- (WP1, WP2) control-theoretical proof of convergence for infinite dimensional bipartite open quantum systems stabilized by reservoir engineering has been obtained in the preprint arXiv preprint arXiv:2311.10037
- (WP3) proposal of a state-of-the-art experimental circuit ensuring autonomous stabilization and generation of GKP-qubits (arXiv preprint arXiv:2304.03806). We developed here a novel approach to stabilize these qubits by dissipation engineering (i.e. quantum controller) in high-impedance circuits.
On the control-theoretical and numerical side of the project we expected progress on:
- time-dependent perturbation theory combined with numerically exact Floquet methods, to quantify parametrically-activated spurious relaxation processes in cat/GKP-qubit circuits when strong drive-amplitudes are used.
- original monotone algorithms based on Lyapunov and optimal-control methods to quantum gate generation in presence of decoherence described by Lindblad master equation.
- efficient numerical algorithm for parameter estimation and quantum-state tomography based on binned measurement data and their corresponding stochastic master equations.
- convergence and precision analysis of numerical simulation schemes for infinite dimensional Lindblad master equation combining Galerkin approximation and time discretisation based on exact Kraus maps.
On the experimental side of the project, we are developing and testing a Josephson circuit hosting a high-impedance resonant mode and enabling parametric pumping of multi-photonic processes. These features lie at the heart of our proposal to autonomously stabilize GKP qubits (arXiv preprint arXiv:2304.03806). As a proof of principle, illustrated by the figure 4 illustrating the ATS circuit for four-legged cat stabilization, we currently aim at stabilizing a four-component Schrödinger cat state in this circuit by engineering a four-photon dissipation channel. The requirements for this experiment are similar to those to stabilize GKP qubits, albeit in a less demanding parameter regime.
Expected experimental results: The next step is to provide experimental demonstration. Preliminary experiments have been conducted to validate the support circuit architectures and key experimental methods. While implementing fully these proposals will require several years of development, we expect several key results before the end of the project, such as the extension of cat/GKP qubits lifetime far beyond the coherence time of the underlying hardware.
- time-dependent perturbation theory combined with numerically exact Floquet methods, to quantify parametrically-activated spurious relaxation processes in cat/GKP-qubit circuits when strong drive-amplitudes are used.
- original monotone algorithms based on Lyapunov and optimal-control methods to quantum gate generation in presence of decoherence described by Lindblad master equation.
- efficient numerical algorithm for parameter estimation and quantum-state tomography based on binned measurement data and their corresponding stochastic master equations.
- convergence and precision analysis of numerical simulation schemes for infinite dimensional Lindblad master equation combining Galerkin approximation and time discretisation based on exact Kraus maps.
On the experimental side of the project, we are developing and testing a Josephson circuit hosting a high-impedance resonant mode and enabling parametric pumping of multi-photonic processes. These features lie at the heart of our proposal to autonomously stabilize GKP qubits (arXiv preprint arXiv:2304.03806). As a proof of principle, illustrated by the figure 4 illustrating the ATS circuit for four-legged cat stabilization, we currently aim at stabilizing a four-component Schrödinger cat state in this circuit by engineering a four-photon dissipation channel. The requirements for this experiment are similar to those to stabilize GKP qubits, albeit in a less demanding parameter regime.
Expected experimental results: The next step is to provide experimental demonstration. Preliminary experiments have been conducted to validate the support circuit architectures and key experimental methods. While implementing fully these proposals will require several years of development, we expect several key results before the end of the project, such as the extension of cat/GKP qubits lifetime far beyond the coherence time of the underlying hardware.