Rouchon group
Mines Paris – PSL, Paris, France
- Tracked papers
- 14 (2009–2024)
Topics
The most frequent field-map topics among the PI' tracked papers.
- Feedback 10
- Bosonic 5
- Superconducting 4
- Photonics 4
- Closed-loop 3
- Reservoir engineering 3
- Open systems 2
Recent papers
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Gate generation for open quantum systems via a monotonic algorithm with time optimization
Abstract
We present a monotonic numerical algorithm including time optimization for generating quantum gates for open systems. Such systems are assumed to be governed by Lindblad master equations for the density operators on a large Hilbert-space whereas the quantum gates are relative to a sub-space of small dimension. Starting from an initial seed of the control input, this algorithm consists in the repetition of the following two steps producing a new control input: (A) backwards integration of adjoint Lindblad-Master equations (in the Heisenberg-picture) from a set of final conditions encoding the quantum gate to generate; (B) forward integration of Lindblad-Master equations in closed-loop where a Lyapunov based control produced the new control input. The numerical stability is ensured by the stability of both the open-loop adjoint backward system and the forward closed-loop system. A clock-control input can be added to the usual control input. The obtained monotonic algorithm allows then to optimise not only the shape of the control imput, but also the gate time. Preliminary numerical implementations indicate that this algorithm is well suited for cat-qubit gates, where Hilbert-space dimensions (2 for the Z-gate and 4 for the CNOT-gate) are much smaller than the dimension of the physical Hilbert-space involving mainly Fock-states (typically 20 or larger for a single cat-qubit). This monotonic algorithm, based on Lyapunov control techniques, is shown to have a straightforward interpretation in terms of optimal control: its stationary conditions coincides with the first-order optimality conditions for a cost depending linearly on the final values of the quantum states.
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Quantum control of a cat-qubit with bit-flip times exceeding ten seconds
Abstract
Quantum bits (qubits) are prone to several types of errors due to uncontrolled interactions with their environment. Common strategies to correct these errors are based on architectures of qubits involving daunting hardware overheads. A hopeful path forward is to build qubits that are inherently protected against certain types of errors, so that the overhead required to correct remaining ones is significantly reduced. However, the foreseen benefit rests on a severe condition: quantum manipulations of the qubit must not break the protection that has been so carefully engineered. A recent qubit - the cat-qubit - is encoded in the manifold of metastable states of a quantum dynamical system, thereby acquiring continuous and autonomous protection against bit-flips. Here, in a superconducting circuit experiment, we implement a cat-qubit with bit-flip times exceeding 10 seconds. This is a four order of magnitude improvement over previous cat-qubit implementations. We prepare and image quantum superposition states, and measure phase-flip times above 490 nanoseconds. Most importantly, we control the phase of these quantum superpositions without breaking bit-flip protection. This experiment demonstrates the compatibility of quantum control and inherent bit-flip protection at an unprecedented level, showing the viability of these dynamical qubits for future quantum technologies.
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Number-resolved photocounter for propagating microwave mode
Abstract
Detectors of propagating microwave photons have recently been realized using superconducting circuits. However a number-resolved photocounter is still missing. In this letter, we demonstrate a single-shot counter for propagating microwave photons that can resolve up to $3$ photons. It is based on a pumped Josephson Ring Modulator that can catch an arbitrary propagating mode by frequency conversion and store its quantum state in a stationary memory mode. A transmon qubit then counts the number of photons in the memory mode using a series of binary questions. Using measurement based feedback, the number of questions is minimal and scales logarithmically with the maximal number of photons. The detector features a detection efficiency of $0.96 \pm 0.04$, and a dark count probability of $0.030 \pm 0.002$ for an average dead time of $4.5~\mathrm{μs}$. To maximize its performance, the device is first used as an \emph{in situ} waveform detector from which an optimal pump is computed and applied. Depending on the number of incoming photons, the detector succeeds with a probability that ranges from $(54 \pm 2)\%$ to $99\%$.
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Continuous-time Quantum Error Correction with Noise-assisted Quantum Feedback
Abstract
We address the standard quantum error correction using the three-qubit bit-flip code, yet in continuous-time. This entails rendering a target manifold of quantum states globally attractive. Previous feedback designs could feature spurious equilibria, or resort to discrete kicks pushing the system away from these equilibria to ensure global asymptotic stability. We present a new approach that consists of introducing controls driven by Brownian motions. Unlike the previous methods, the resulting closed-loop dynamics can be shown to stabilize the target manifold exponentially. We further present a reduced-order filter formulation with classical probabilities. The exponential property is important to quantify the protection induced by the closed-loop error-correction dynamics against disturbances. We study numerically the performance of this control law and of the reduced filter.
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Exponential stochastic stabilization of a two-level quantum system via strict Lyapunov control
Abstract
This article provides a novel continuous-time state feedback control strategy to stabilize an eigenstate of the Hermitian measurement operator of a two-level quantum system. In open loop, such system converges stochastically to one of the eigenstates of the measurement operator. Previous work has proposed state feedback that destabilizes the undesired eigenstates and relies on a probabilistic analysis to prove convergence. In contrast, we here associate the state observer to an adaptive version of so-called Markovian feedback (essentially, proportional control) and we show that this leads to a global exponential convergence property with a strict Lyapunov function. Furthermore, besides the instantaneous measurement output, our controller only depends on the single coordinate along the measurement axis, which opens the way to replacing the full state observer by lower-complexity filters in the future.
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Using Spontaneous Emission of a Qubit as a Resource for Feedback Control
Abstract
Persistent control of a transmon qubit is performed by a feedback protocol based on continuous heterodyne measurement of its fluorescence. By driving the qubit and cavity with microwave signals whose amplitudes depend linearly on the instantaneous values of the quadratures of the measured fluorescence field, we show that it is possible to stabilize permanently the qubit in any targeted state. Using a Josephson mixer as a phase-preserving amplifier, it was possible to reach a total measurement efficiency $η$=35%, leading to a maximum of 59% of excitation and 44% of coherence for the stabilized states. The experiment demonstrates multiple-input multiple-output analog Markovian feedback in the quantum regime.
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Stabilization of photon-number states via single-photon corrections: a first convergence analysis under an ideal set-up
Abstract
This paper presents a first mathematical convergence analysis of a Fock states feedback stabilization scheme via single-photon corrections. This measurement-based feedback has been developed and experimentally tested in 2012 by the cavity quantum electrodynamics group of Serge Haroche and Jean-Michel Raimond. Here, we consider the infinite-dimensional Markov model corresponding to the ideal set-up where detection errors and feedback delays have been disregarded. In this ideal context, we show that any goal Fock state can be stabilized by a Lyapunov-based feedback for any initial quantum state belonging to the dense subset of finite rank density operators with support in a finite photon-number sub-space. Closed-loop simulations illustrate the performance of the feedback law.
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Efficient Quantum Filtering for Quantum Feedback Control
Abstract
We discuss an efficient numerical scheme for the recursive filtering of diffusive quantum stochastic master equations. We show that the resultant quantum trajectory is robust and may be used for feedback based on inefficient measurements. The proposed numerical scheme is amenable to approximation, which can be used to further reduce the computational burden associated with calculating quantum trajectories and may allow real-time quantum filtering. We provide a two-qubit example where feedback control of entanglement may be within the scope of current experimental systems.
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Models and Feedback Stabilization of Open Quantum Systems
Abstract
At the quantum level, feedback-loops have to take into account measurement back-action. We present here the structure of the Markovian models including such back-action and sketch two stabilization methods: measurement-based feedback where an open quantum system is stabilized by a classical controller; coherent or autonomous feedback where a quantum system is stabilized by a quantum controller with decoherence (reservoir engineering). We begin to explain these models and methods for the photon box experiments realized in the group of Serge Haroche (Nobel Prize 2012). We present then these models and methods for general open quantum systems.
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Design and Stability of Discrete-Time Quantum Filters with Measurement Imperfections
Abstract
This work considers the theory underlying a discrete-time quantum filter recently used in a quantum feedback experiment. It proves that this filter taking into account decoherence and measurement errors is optimal and stable. We present the general framework underlying this filter and show that it corresponds to a recursive expression of the least-square optimal estimation of the density operator in the presence of measurement imperfections. By measurement imperfections, we mean in a very general sense unread measurement performed by the environment (decoherence) and active measurement performed by non-ideal detectors. However, we assume to know precisely all the Kraus operators and also the detection error rates. Such recursive expressions combine well known methods from quantum filtering theory and classical probability theory (Bayes' law). We then demonstrate that such a recursive filter is always stable with respect to its initial condition: the fidelity between the optimal filter state (when the initial filter state coincides with the real quantum state) and the filter state (when the initial filter state is arbitrary) is a sub-martingale.