arXiv subjects

Frédéric Sauvage

Publications and source records attributed to Frédéric Sauvage.

9 recordsLinked to original sources

arXiv2026

Unbiased Hamiltonian Simulation by Reversing Trotter Error Dynamics

Owing to their simplicity and low overhead, Suzuki-Trotter formulas remain the de facto Hamiltonian simulation methods on current quantum computing platforms. Systematic Trotter errors, however, will quickly become limiting when scaling to larger problems and aiming for higher accuracy. We present a mechanism that removes the systematic error of any $k$-th order Suzuki-Trotter simulation, at the cost of a constant sampling overhead. The key insight is that the Trotter error is itself a coherent dynamics to be reversed, rather than a deviation to be bounded. By identifying the structure of this error in closed form, we carry out that reversal through quasi-probabilistic decompositions. The resulting algorithm, called Probabilistic Trotter Error Reversal (PTER), is unbiased and still improves the gate-count scaling of Suzuki-Trotter formulas while retaining their simplicity. Numerical simulations of a Heisenberg spin chain support the predicted resource advantage already at modest system sizes.

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arXiv2026

Quantum machine learning models for graphs

Geometric Machine Learning (GML) successes have been achieved through the thorough study and design of new equivariant neural networks. In comparison, geometric quantum machine learning (GQML) models lack such a detailed understanding and, despite already several proposals, a unifying perspective on their design remains elusive. In this work, we focus on GQML models for graph problems that showcase a lot of structure and still remain frontier in machine learning. For the case when n-node graphs are encoded in n-qubit states, we provide a comprehensive characterization of their constituents. Taken together, these furnish us with a toolbox for the design of quantum graph models, and we further probe its benefits including the natural integration with classical models, generalization of known GQML models (sometimes extending their expressivity at virtually no cost), and straightforward classical pre-training strategies. The latter two features are demonstrated in dedicated numerical experiments.

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arXiv2026

Exact log-depth preparation of highly entangled matrix product states

Preparing matrix product states (MPS) on a quantum device is a key subroutine in many quantum algorithms. The most competitive methods, based on the renormalisation group, prepare translationally invariant MPS of size $L$ and bond dimension $χ$, up to an error $\varepsilon$, in circuit depth $\tilde O(χ^{4}\log(L/\varepsilon))$ or $\tilde O(χ^{6}\log\log(L/\varepsilon))$. We improve multiple aspects of these methods. First, using block-encoded correction maps, whose post-selection succeeds with constant probability, we render the preparation exact without sacrificing the scaling in $L$. Second, through a generalisation of oblivious amplitude amplification to isometries, we reduce the bond-dimension dependence, improving the depth to $\tilde O(χ^{2}\log L + χ^{4})$ or $\tilde O(χ^{2}\log\log L + χ^{4})$, and even to $\tilde O(χ^{3}\log L)$ for incoherent preparations. Finally, we extend the framework to non-translationally invariant MPS and prove logarithmic-depth exact preparation for independent and identically distributed random tensor sequences. Confirmed by numerical studies, these results constitute, to the best of our knowledge, the most efficient exact MPS preparation protocols in the relevant parameter regimes.

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arXiv2025

More buck-per-shot: Why learning trumps mitigation in noisy quantum sensing

Quantum sensing is one of the most promising applications for quantum technologies. However, reaching the ultimate sensitivities enabled by the laws of quantum mechanics can be a challenging task in realistic scenarios where noise is present. While several strategies have been proposed to deal with the detrimental effects of noise, these come at the cost of an extra shot budget. Given that shots are a precious resource for sensing -- as infinite measurements could lead to infinite precision -- care must be taken to truly guarantee that any shot not being used for sensing is actually leading to some metrological improvement. In this work, we study whether investing shots in error-mitigation, inference techniques, or combinations thereof, can improve the sensitivity of a noisy quantum sensor on a (shot) budget. We present a detailed bias-variance error analysis for various sensing protocols. Our results show that the costs of zero-noise extrapolation techniques outweigh their benefits. We also find that pre-characterizing a quantum sensor via inference techniques leads to the best performance, under the assumption that the sensor is sufficiently stable.

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arXiv2025

Lie-algebraic classical simulations for quantum computing

The classical simulation of quantum dynamics plays an important role in our understanding of quantum complexity, and in the development of quantum technologies. Efficient techniques such as those based on the Gottesman-Knill theorem for Clifford circuits, tensor networks for low entanglement-generating circuits, or Wick's theorem for fermionic Gaussian states, have become central tools in quantum computing. In this work, we contribute to this body of knowledge by presenting a framework for classical simulations, dubbed "$\mathfrak{g}$-sim", which is based on the underlying Lie algebraic structure of the dynamical process. When the dimension of the algebra grows at most polynomially in the system size, there exists observables for which the simulation is efficient. Indeed, we show that $\mathfrak{g}$-sim enables new regimes for classical simulations, is able to deal with certain forms of noise in the evolution, as well as can be used to tackle several paradigmatic variational and non-variational quantum computing tasks. For the former, we perform Lie-algebraic simulations to train and optimize parametrized quantum circuits (thus effectively showing that some variational models can be dequantized), design enhanced parameter initialization strategies, solve tasks of quantum circuit synthesis, and train a quantum-phase classifier. For the latter, we report large-scale noiseless and noisy simulations on benchmark problems. By comparing the limitations of $\mathfrak{g}$-sim and certain Wick's theorem-based simulations, we find that the two methods become inefficient for different types of states or observables, hinting at the existence of distinct, non-equivalent, resources for classical simulation.

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arXiv2024

Bayesian optimization of non-classical optomechanical correlations

Nonclassical correlations provide a resource for many applications in quantum technology as well as providing strong evidence that a system is indeed operating in the quantum regime. Optomechanical systems can be arranged to generate nonclassical correlations (such as quantum entanglement) between the mechanical mode and a mode of travelling light. Here we propose automated optimization of the production of quantum correlations in such a system, beyond what can be achieved through analytical methods, by applying Bayesian optimization to the control parameters. A two-mode optomechanical squeezing experiment is simulated using a detailed theoretical model of the system and the measurable outputs fed to the Bayesian optimization process. This then modifies the controllable parameters in order to maximize the non-classical two-mode squeezing and its detection, independently of the inner workings of the model. We focus on a levitated nano-sphere system, but the techniques described are broadly applicable in optomechanical experiments, and also more widely, especially where no detailed theoretical treatment is available. We find that in the experimentally relevant thermal regimes, the ability to vary and optimize a broad array of control parameters provides access to large values of two-mode squeezing that would otherwise be difficult or intractable to discover via analytical or trial and error methods. In particular we observe that modulation of the driving frequency around the resonant sideband allows for stronger nonclassical correlations. We also observe that our optimization approach finds parameters that allow significant squeezing in the high temperature regime. This extends the range of experimental setups in which non-classical correlations could be generated beyond the region of high quantum cooperativity.

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arXiv2024

A Lie Algebraic Theory of Barren Plateaus for Deep Parameterized Quantum Circuits

Variational quantum computing schemes train a loss function by sending an initial state through a parametrized quantum circuit, and measuring the expectation value of some operator. Despite their promise, the trainability of these algorithms is hindered by barren plateaus (BPs) induced by the expressiveness of the circuit, the entanglement of the input data, the locality of the observable, or the presence of noise. Up to this point, these sources of BPs have been regarded as independent. In this work, we present a general Lie algebraic theory that provides an exact expression for the variance of the loss function of sufficiently deep parametrized quantum circuits, even in the presence of certain noise models. Our results allow us to understand under one framework all aforementioned sources of BPs. This theoretical leap resolves a standing conjecture about a connection between loss concentration and the dimension of the Lie algebra of the circuit's generators.

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arXiv2022

Diabatic Quantum Annealing for the Frustrated Ring Model

Quantum annealing is a continuous-time heuristic quantum algorithm for solving or approximately solving classical optimization problems. The algorithm uses a schedule to interpolate between a driver Hamiltonian with an easy-to-prepare ground state and a problem Hamiltonian whose ground state encodes solutions to an optimization problem. The standard implementation relies on the evolution being adiabatic: keeping the system in the instantaneous ground state with high probability and requiring a time scale inversely related to the minimum energy gap between the instantaneous ground and excited states. However, adiabatic evolution can lead to evolution times that scale exponentially with the system size, even for computationally simple problems. Here, we study whether non-adiabatic evolutions with optimized annealing schedules can bypass this exponential slowdown for one such class of problems called the frustrated ring model. For sufficiently optimized annealing schedules and system sizes of up to 39 qubits, we provide numerical evidence that we can avoid the exponential slowdown. Our work highlights the potential of highly-controllable quantum annealing to circumvent bottlenecks associated with the standard implementation of quantum annealing.

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arXiv2021

Efficient Assessment of Process Fidelity

The accurate implementation of quantum gates is essential for the realisation of quantum algorithms and digital quantum simulations. This accuracy may be increased on noisy hardware through the variational optimisation of gates, however the experimental realisation of such a protocol is impeded by the large effort required to estimate the fidelity of an implemented gate. With a hierarchy of approximations we find a faithful approximation to the quantum process fidelity that can be estimated experimentally with reduced effort. Its practical use is demonstrated with the optimisation of a three-qubit quantum gate on a commercially available quantum processor.

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