Advanced Quantum Algorithms for Many-body systems (AQAM-2025)

Nov 18, 2025, 8:15 AM → Nov 21, 2025, 4:35 PM Europe/Paris

Montpellier

The advent of quantum computers, enabled by the second quantum revolution, could greatly improve our understanding of problems that are hard or impossible to tackle on classical computers. Among these problems, quantum many-body systems appear as perfect test benches for novel quantum technologies --- which are themselves artificial interacting quantum systems. 

In recent years, the development of quantum computing techniques for many-body problems has gained significant momentum, and communities of experts have emerged in different fields of physics and chemistry.     

This workshop aims to overview the most recent developments and facilitate the exchange between field experts, with applications ranging from atomic nuclei, neutrinos, atomic and condensed matter, and quantum chemistry. Recent works and progress in treating many-body systems with quantum computers and related quantum information aspects will be presented. Another objective will be to discuss future avenues and challenges for quantum computers to describe many-body systems.

 

Organizers:

Thomas Ayral (Eviden)

François Jamet (Alice & Bob)

Denis Lacroix (IJCLab, Paris-Saclay University)

Bruno Senjean (ICGM, Montpellier University)

For support, please contact:

bruno.senjean@umontpellier.fr
and
denis.lacroix@ijclab.in2p3.fr

 

Tue, November 18

8:30 AM Welcome

1 introductory speech

2 Towards quantum simulations of nuclear reactions

With the recent experimental realization of quantum computing devices containing tens to hundreds of qubits and fully controllable operations, the theoretical effort in designing efficient quantum algorithms for a variety of problems has seen a tremendous growth worldwide. In this talk I will discuss the prospects of describing nuclear reactions on digital quantum computers using a low energy effective interaction. I will in particular highlight recent progress in formulating these processes in first quantization.

Speaker: Prof. Alessandro Roggero (University of Trento)

slides_montpellier.pdf

10:30 AM Coffee-break

3 Turning qubit noise into an advantage: automatic state preparation and long-time dynamics for impurity models on quantum computers

Noise is often regarded as a limitation of quantum computers.
In this work, we show that in the dynamical mean field theory (DMFT) approach to strongly-correlated systems, it can actually be harnessed to our advantage.
Indeed, DMFT maps a lattice model onto an impurity model, namely a finite system coupled to a dissipative bath.
While standard approaches require a large number of high-quality qubits,
we propose a circuit that harvests qubit noise (amplitude damping) to reproduce the dynamics of this model with a blend of noisy and noiseless qubits.
We find compelling advantages with this approach: a substantial reduction in the number of qubits, the ability to reach longer time dynamics, and no need for ground state search and preparation.
This method would naturally fit in a partial quantum error correction framework.

Speaker: Corentin Bertrand (Eviden Quantum Lab)

4 Quantum Simulations of Chemistry in First Quantization with any Basis Set

Quantum computation of the energy of molecules and materials is one of the most promising applications of fault-tolerant quantum computers. Practical applications require development of quantum algorithms with reduced resource requirements. Previous work has mainly focused on quantum algorithms where the Hamiltonian is represented in second quantization with compact basis sets while existing methods in first quantization are limited to a grid-based basis. In this work, we present a new method to solve the generic ground-state chemistry problem in first quantization using any basis set. We achieve asymptotic speedup in Toffoli count for molecular orbitals, and orders of magnitude improvement using dual plane waves as compared to the second quantization counterparts. In some instances, our approach provides similar or even lower resources compared to previous first quantization plane wave algorithms that, unlike our approach, avoids the loading of the classical data. The developed methodology can be applied to variety of applications, where the matrix elements of a first quantized Hamiltonian lack simple circuit representation.

Speaker: Aleksei V. Ivanov (Riverlane)

12:30 PM Lunch break

5 Pauli and Majorana Propagation methods for classically simulating quantum circuits

Simulating quantum circuits classically is in general a hard task. However, certain families of quantum circuits may be practically or even provably efficiently simulable by use of specialized classical algorithms. In this talk, we will cover "Pauli propagation" which has recently been shown to enable efficient classical simulation of expectation values in quantum circuits and a wide range of noise-free quantum circuits. Appreciating the strengths and weaknesses of this simulation method, and how it can be efficiently combined with other classical and quantum subroutines, will help point towards promising applications of quantum devices. We will end by discussing a generalization of this approach to Fermionic systems opening up new applications in quantum chemistry and material science. This talk will give an overview of the following works: arxiv:2308.09109, arXiv:2408.12739, arXiv:2409.01706, arXiv:2411.19896, arXiv:2501.13101, arXiv:2503.18939.

Speaker: Prof. Zoë Holmes (EPFL)

6 Off-diagonal Pauli Weight truncation and equilibration temperature dependence for simulating local dynamics in quantum systems

The complexity of simulating the out-of-equilibrium evolution of local operators in the Heisenberg picture is governed by the operator entanglement, which grows linearly in time for generic nonintegrable systems, leading to an exponential increase in computational resources. A promising approach to simplify this challenge involves discarding parts of the operator and focusing on a subspace formed by “light” Pauli strings—strings with few Pauli matrices—as proposed by Rakovszki et al. [Phys. Rev. B 105, 07513 (2022)] for infinite temperature settings.
In our recent works [Phys. Rev. B 111, 094301(2025), In preparation], we investigated whether this strategy can be applied to quenches starting from homogeneous product states, end extend it to handle arbitrary temperatures, since the evolution of ergodic Hamiltonians combined with these initial states grant access to a wide range of equilibration regimes.
By concentrating on the required matrix elements and retaining only the portion of the operator that contains Pauli strings parallel to the initial state, we uncover a complex scenario. For intermediate simulation times, in some cases the light Pauli strings suffice to describe the dynamics, enabling efficient simulation with current algorithms; however, for other cases heavier strings become necessary, pushing computational demands beyond our current capabilities.
For long simulation times, we detect that complexity is intimately correlated with the equilibration temperature, and that our modified method agrees with the state-of-the art transverse contraction simulations. In the process, we found that the transverse light-cone algorithm also displays a complexity correlated with temperature, which can be explained by a careful reinterpretation of our results in [Phys. Rev. Research 6, 033021(2024)].

Speaker: Carlos Ramos-Marimón (Quobly)

7 Ab Initio Polaritonic Chemistry on Diverse Quantum Computing Platforms: Qubit, Qudit, and Hybrid Qubit-Qumode Architectures

Describing polaritonic systems at the ab initio level is computationally demanding, as it requires a high-level representation of the interaction between confined electromagnetic fields and the electronic structure of a molecule. Capturing these effects accurately necessitates efficient encoding schemes that can handle both electronic and photonic degrees of freedom within a quantum computational framework [1, 2].

In this work [3], we address this challenge using a quantum algorithm, specifically, the ensemble-VQE [4–6], which enables the calculation of both ground and excited states. This algorithm is initially formulated on a qubit-based architecture. While fermionic degrees of freedom are naturally well-suited to qubit encoding, the same does not hold for bosonic modes. Although the number of qubits required scales linearly with the number of fermionic modes, it typically scales with the product of the number of bosons and bosonic modes. Furthermore, standard boson-to-qubit mappings often introduce unphysical states, artificially increasing the size of the Hamiltonian and making quantum computations significantly more difficult.

These limitations motivated us to ask a broader question:

• Should hybrid fermionic-bosonic quantum simulations remain confined to a qubit-only framework?
• Or could we leverage the intrinsic properties of alternative quantum devices/platforms to better encode bosonic degrees of freedom?

To explore these questions, we go beyond the conventional qubit-based architecture and investigate two other approaches for modeling cavity quantum electrodynamics systems: a qudit-based [7–11] architecture and a hybrid qubit–qumode framework [12–15].

Qudit-based approach

A qudit is a generalization of a qubit with a dimension $d > 2$, meaning that the possible states are:

$$ \{|0\rangle, |1\rangle, |2\rangle, \ldots, |d-1\rangle\} $$ and any linear combination of them. Quantum computing with qudits is a young field, and the availability of standard gate sets remains limited. However, the motivation for using them is to take advantage of the $d$ discrete levels to encode a bosonic Fock space directly, up to a given truncation. ### Qumode-based approach Qumodes refer to genuine quantum harmonic oscillators, either mechanical or electromagnetic, that naturally behave as bosonic modes. They are described using continuous-variable representations, which are inherently better suited to bosonic systems than the discrete-variable representations used by qubits and qudits. As with qudits, qumodes aim to encode the bosonic Fock space, with the added benefit that hardware implementations are often more direct. # Benchmark and results We benchmark all three strategies on a cavity-embedded H₂ molecule, resolving the three lowest-energy polaritonic states using noiseless quantum circuit simulations [16, 17]. All platforms yield comparable accuracy in predicting polaritonic eigenenergies and eigenstates, with energy errors below $10^{-4}$ Ha and eigenstate fidelities exceeding $99.99\%$ overlap with the QED-FCI reference solutions. In terms of quantum resource requirements (e.g., number of entangling gates and quantum information units), the hybrid qubit–qumode approach offers the best trade-off between efficiency and accuracy, followed closely by the qudit-based method — both outperform the standard qubit-only architecture.

References

1. T. W. Ebbesen, Acc. Chem. Res. 49, 2403 (2016)
2. U. Mordovina et al., Phys. Rev. Res. 2, 023262 (2020)
3. E. Chiari et al., arXiv:2506.12504 (2025)
4. F. Pavosevic & J. Flick, J. Phys. Chem. Lett. 12, 9100 (2021)
5. M. Hassan et al., J. Phys. Chem. Lett. 15, 1373 (2024)
6. A. Peruzzo et al., Nat. Commun. 5, 4213 (2014)
7. M. Howard & J. Vala, Phys. Rev. A 86, 022316 (2012)
8. J. Daboul et al., J. Phys. A 36, 2525 (2003)
9. X. Gao et al., Phys. Rev. Lett. 125, 050501 (2020)
10. L. Ermann et al., Phys. Rev. A 102, 033729 (2020)
11. S. S. Ivanov et al., Phys. Rev. A 85, 062321 (2012)
12. J. Casanova et al., Phys. Rev. Lett. 107, 260501 (2011)
13. A. Mezzacapo et al., Phys. Rev. Lett. 109, 200501 (2012)
14. L. Lamata et al., EPJ Quantum Technol. 1, 1 (2014)
15. A. Macridin et al., Phys. Rev. A 98, 042312 (2018)
16. J. R. McClean et al., Quantum Sci. Technol. 5, 034014 (2020)
17. T. J. Stavenger et al., IEEE HPEC, pp. 1–8 (2022)

Speaker: Even Chiari;Chiari (Université de Strasbourg)

3:50 PM Tea-break

8 Error mitigation and circuit division for early fault-tolerant quantum phase estimation

As fully fault-tolerant quantum computers capable of solving useful problems remain a distant goal, we anticipate an era of early fault tolerance where limited error correction is available.
We propose a framework for designing early fault-tolerant algorithms by trading between error correction overhead and residual logical noise, and apply it to quantum phase estimation (QPE).
We develop a quantum-Fourier-transform (QFT)-based QPE technique that is robust to global depolarising noise and outperforms the previous state of the art at low and moderate noise rates.
We further introduce the Explicitly Unbiased Maximum Likelihood Estimation (EUMLE), a data processing technique that mitigates arbitrary errors in QFT-based QPE schemes. EUMLE provides consistent, asymptotically normal error-mitigated estimates, addressing the open problem of extending error mitigation beyond expectation value estimation.
Applying this scheme to the ground state problem of the two-dimensional Hubbard model and various molecular Hamiltonians, we find we can roughly halve the number of physical qubits with a $\sim 10\times$ wall-clock time overhead, but further reduction causes a steep runtime increase.
This work provides an end-to-end analysis of early fault-tolerance cost reductions and space-time trade-offs, and identifies areas for future improvement.

Speaker: Stefano Polla (Leiden University)

251118-Montpellier.pdf

9 Quantum Algorithm for Real-Space Chemistry on Adaptive Molecular Grids

First-quantized, real-space formulations of quantum chemistry on quantum computers are appealing: qubit count scales logarithmically with spatial resolution, and the two-body Coulomb term achieve quadratic scaling, rather than usual quartic scaling in orbital-based approaches. However, existing schemes employ uniform discretizations whose resolution is imposed by the electron‑nuclear cusps of the wave functions in high‑density regions, thereby oversampling low-density regions and wasting computational resources. To address this, we repurpose the non‑uniform, molecule‑adaptive grids long used for DFT integration, which concentrate points where the electronic density is highest, to discretize the molecular Hamiltonian. Once encoded as a quantum operation, its ground state can be obtained with standard Quantum Phase Estimation. We further derive a transcorrelated, non‑Hermitian yet isospectral Hamiltonian that removes Coulomb singularities and associated cusps in its eigenfunctions, whose ground‑state energy is accessible through the recent generalized Quantum Eigenvalue Estimation protocol. Numerical validation on benchmark systems confirms this ab initio framework paves a promising route to ground‑state chemistry on quantum hardware.

Speaker: César Feniou

5:50 PM Wine & Cheese

Wed, November 19

10 A framework for spin-adapted quantum chemistry on quantum computers

Quantum computers promise to transform molecular simulation, but many existing algorithms overlook the powerful role of spin symmetry in chemistry. The Quantum Paldus Transform provides a new framework that makes spin adaptation a built-in feature of quantum computation.

At its core, the transform connects two representations of electronic states: the conventional occupation-number basis used in quantum chemistry, and a symmetry-adapted basis that organises states by total spin, particle number, and orbital symmetries. This shift, grounded in mathematical structure known as Paldus duality, allows quantum devices to work directly with spin-pure states - the natural language of chemistry.

The benefits are considerable. Spin-free Hamiltonians reduce to block-diagonal, sparser forms, enabling more efficient simulations. The transform itself admits polynomial-cost implementations and even highly compact circuit constructions. Beyond simulation, the framework facilitates efficient preparation of Configuration State Functions (CSFs) and naturally embeds quantum information in decoherence-free subsystems, offering potential protection against certain noise channels.

By extending the quantum Schur transform into the fermionic setting, the Quantum Paldus Transform establishes a principled and practical route for exploiting spin symmetry in quantum algorithms. This framework opens new directions for scalable, accurate, and symmetry-aware quantum chemistry algorithms on quantum computers

Speaker: Prof. Nathan Fitzpatrick (Cambridge Quantum)

10:00 AM Coffee-break

11 Learning Density Functionals from Noisy Quantum Data

The search for useful applications of noisy intermediate-scale quantum (NISQ) devices in quantum simulation has been hindered by their intrinsic noise and the high costs associated with achieving high accuracy.
A promising approach to finding utility despite these challenges involves using quantum devices to generate training data for classical machine learning (ML) models.
In this study, we explore the use of noisy data generated by quantum algorithms in training an ML model to learn a density functional for the Fermi-Hubbard model.
We benchmark various ML models against exact solutions, demonstrating that a neural-network ML model can successfully generalize from small datasets subject to noise typical of NISQ algorithms.
The learning procedure can effectively filter out unbiased sampling noise, resulting in a trained model that outperforms any individual training data point.
Conversely, when trained on data with expressibility and optimization error typical of the variational quantum eigensolver, the model replicates the biases present in the training data.
The trained models can be applied to solving new problem instances in a Kohn-Sham-like density optimization scheme, benefiting from automatic differentiability and achieving reasonably accurate solutions on most problem instances.
Our findings suggest a promising pathway for leveraging NISQ devices in practical quantum simulations, highlighting both the potential benefits and the challenges that need to be addressed for successful integration of quantum computing and ML techniques.
This work is recently published in Machine Learning Science & Technology.

[Emiel Koridon et al 2025 Mach. Learn.: Sci. Technol. 6 025020]

Speaker: Emiel Koridon;Koridon (Leiden University)

251119-AQAM2025_pdfsplit.pdf

12 Hybrid quantum-classical analog simulation of two-dimensional Fermi-Hubbard models with neutral atoms

In this work, we implement a hybrid quantum-classical algorithm on a Rydberg-based analog quantum processor to simulate the two-dimensional Fermi-Hubbard model (FHM) which relies on a recent proposal. The latter exploits a $Z_2$ slave spin reformulation of the original interacting fermions in terms of self-correlated auxiliary spin degrees of freedom (naturally encoded in the Rydberg atom Quantum Processor Unit QPU), and noninteracting fermionic degrees of freedom (efficiently solvable classically).
To demonstrate the feasibility and utility of this approach, we experimentally realize the proposed hybrid quantum-classical algorithm to study the anisotropic Fermi-Hubbard model in the square lattice and its anisotropic version in the rectangular lattice with a qubit-based neutral-atom quantum processing unit. On the one hand, we study the Mott transition in an anisotropic Fermi-Hubbard model consisting of 36 electron sites at equilibrium. On the other hand, we also consider the nonequilibrium properties of the isotropic Fermi-Hubbard model in the square lattice after a sudden quench of the on-site interaction, for systems consisting of 36 and 64 electronic sites. We observe the expected collapsed oscillations of the quasiparticle weight in the Mott phase.

Speaker: Antoine Michel (EDF R&D)

12:00 PM Lunch break

13 Quantum Simulations driven by Many-Body Complexity

Understanding how many-body phenomena are rooted in quantum information is key to building quantum simulation algorithms that faithfully capture their complexity while optimally distributing computation across classical and quantum resources.

I will explore aspects of multipartite entanglement and non-stabilizerness in strongly-correlated systems in relation with emergent collective phenomena, and will discuss efforts towards leveraging these concepts to develop resource-efficient quantum simulations with both NISQ and fault-tolerant quantum computers.

Speaker: Prof. Caroline Robin (Universität Bielefeld)

AQAM-Robin.pdf

14 Double-bracket quantum algorithms for ground-state preparation via cooling

Preparing ground-states of Hamiltonians is a fundamental task in quantum computation with wide-ranging applications. While efficiently preparing approximate ground-states of large, strongly-correlated systems on quantum hardware is challenging, nature is innately adept at this. This has motivated the study of thermodynamically-inspired approaches to ground-state preparation that aim to replicate cooling, such as imaginary-time evolution (ITE). However, synthesizing quantum circuits that efficiently implement such cooling methods is itself difficult. In this work, we propose quantum algorithms for preparing ground-states of many-body systems by exploiting recently-established Double-Bracket Quantum Algorithms (DBQA). More specifically, we propose a new algorithm called Double-Bracket Quantum Imaginary-Time Evolution (DB-QITE) that compiles quantum circuits for ITE without requiring measurements. We then provide rigorous guarantees that DB-QITE systematically lowers the energy of a state and increases its fidelity with the ground-state. Moreover, we develop a more general framework called Double-Bracket Quantum Signal Processing (DB QSP), which realizes quantum circuits for ground state preparation and extends to broader tasks involving polynomial transformations of Hamiltonians. We expect our algorithm to be used as a standalone method in the early fault-tolerant era, as well as in conjunction with more established and heuristic approaches to ground-state preparation for many-body systems.

Speaker: Yudai Suzuki (EPFL)

3:15 PM Tea-break

15 Phase-space approximation for three-flavor neutrino oscillations: challenging quantum algorithms

The simulation of collective neutrino oscillations represents a paradigmatic many-body quantum problem, where the exponential complexity of the Hilbert space severely limits classical approaches. We present an algorithmic framework for simulating three-flavor neutrino oscillations, based on the recently developed Phase-Space Approximation (PSA). Originally formulated for two-flavor systems, the PSA is here generalized to the full SU(3) case, enabling an efficient representation of the many-body dynamics of interacting neutrinos (M. Mangin-Brinet et al., "Three-flavor neutrino oscillations using the Phase Space Approach'' [arXiv:2507.18482 [hep-ph]]). By reformulating the problem in terms of coupled mean-field–like equations, the PSA avoids the exponential growth of Hilbert space, while achieving an excellent reproduction of the exact dynamics for small ensembles -- up to eight neutrinos -- and scaling to systems of hundreds of particles on standard classical hardware. Such scalability, unattainable with brute-force diagonalization, highlights the potential of PSA as both an efficient approximation scheme and a serious competitor for quantum simulations. In addition, the parallelizable nature of the equations makes the method particularly relevant both for the development of quantum algorithms strategies, and for the benchmarking of quantum simulators. We will present the theoretical derivation, algorithmic principles, numerical validation, and discuss its embedding into the broader context of quantum algorithms for many-body physics, with an emphasis on applications to astrophysical neutrino flavor conversions.

Speaker: Mariane MANGIN BRINET (LPSC/CNRS)

MMB_PresentationAQAM2025.pdf

16 Quantum simulations of Green’s functions for small superfluid systems

Quantum computing offers a promising approach to reduce the computational cost of quantum many-body problems. In this context, it is important to test quantum algorithms on simple, yet nontrivial models, with the goal of assessing their efficiency and benchmarking them. Focusing on the pairing Hamiltonian, a model for the strong many-body correlations arising in nuclear systems, this work [1] addresses the computation of odd systems and Green’s functions. Hybrid quantum-classical computations are compared to exact results and standard BCS techniques.

[1] S. Aychet Claisse, D. Lacroix, V. Somà and J. Zhang, in preparation.

Speaker: Samuel Aychet-Claisse (CEA Saclay)

4:55 PM Poster session and cocktail (apéritif)

Thu, November 20

17 QPE Resource Reduction for Chemistry

Quantum phase estimation (QPE) is a leading route to chemically accurate ground-state energies, but its practicality hinges on quantum resource costs. In this talk I present concrete strategies to lower those costs. First, I show how orbital optimization improves initial-state overlap with the exact ground state, boosting QPE's success probability. Second, I detail how the Hamiltonian one-norm can be lowered using symmetry-compressed double factorization. Finally, I discuss how dynamic correlation can be included by enlarging the active space while controlling growth of the one-norm through careful basis-set selection. Together, these techniques (and follow-on methods) yield substantially lower resource estimates for running QPE on fault-tolerant hardware.

Speaker: Prof. Pauline Ollitrault (QC Ware)

10:00 AM Coffee-break

18 Quantum algorithms for the nuclear shell model

Quantum simulations offer a promising path toward understanding fermionic quantum many-body systems without the limitations of exponential scaling. In this talk, I will present ongoing efforts to simulate various quantum algorithms designed to address nuclear systems within the shell model framework.

I will begin by discussing hybrid variational algorithms, highlighting our estimates of the quantum resources required for a range of nuclear systems [1,2]. I will then explore predictions for nuclear entanglement properties [3] and how these can be leveraged in quantum computing applications [4].

Finally, I may introduce our recent proposal for an adiabatic quantum algorithm tailored to solving the nuclear shell model [5].

[1] A. Pérez-Obiol et al., Sci. Rep. 13, 12291 (2023), arXiv:2302.03641.
[2] M. Carrasco-Codina et al., arXiv:2507.13819.
[3] A. Pérez-Obiol et al., Eur. Phys. J. A 59, 240 (2023), arXiv:2307.05197.
[4] A. Pérez-Obiol et al., arXiv:2409.04510.
[5] E. Costa et al., arXiv:2411.06954 (accepted in SciPost).

Speaker: Arnau Rios Huguet (Institute of Cosmos Sciences, University of Barcelona)

rios_Montpellier25.pdf

19 Quantum Circuit Optimization with Differentiable Projected Entangled Pair States for Ground State Preparation

The interplay between quantum computers and tensor networks have been increasingly popular, and can provide pathways to overcome difficult problems inherent to quantum algorithms, such as preparing relevant initial states for further computations. In this work, we utilize tensor networks to optimize quantum circuits for ground state preparation. Specifically, we employ differentiable Projected Entangled Pair States (PEPS) across various topologies to simulate and optimize parameterized quantum circuits for model Hamiltonians. Our approach enables the preparation of ground states with high energy accuracy, even for large qubit systems and connectivities that are beyond one dimension. Furthermore, by analyzing the energy landscape around the optimized parameters, we demonstrate that PEPS-based optimization may help mitigate the barren plateau phenomenon by providing a warm-start initialization with enhanced gradient magnitudes. Finally, we examined the classical simulation costs of this strategy and identified cases where quantum computers exhibit favorable scaling. We believe this work pushes the potential of quantum computing by leveraging classical pre-processing for both NISQ experiments and FT algorithms and helps to identify which tasks are best suited for classical or quantum resources.

Speaker: Baptiste ANSELME MARTIN (Eviden Quantum Lab)

12:00 PM Lunch break

20 Rethinking measurements by coupling quantum algorithms to classical heuristics in electronic structure

Finding an algorithm to prepare a desired quantum state of a correlated ab initio electronic system on a quantum computer is not the end of the story – we still need to extract out arbitrary properties from this state. This is where a significant and unsolved ‘variance problem’ emerges for arbitrary observables, across both near-term and fault-tolerant algorithms in this field, due to the large number of shots required to reach a statistical uncertainty suitable for chemical and materials science applications. We combine classical heuristic methods with partial shadow tomography to enable an efficient protocol to dramatically reduce this variance and extract information for ab initio systems. We propose using a correlation energy functional and sampling excitation amplitudes to demonstrate an almost two order of magnitude reduction in required number of shots for a given statistical error in the energy estimate, as well as observing a linear scaling to accessible system sizes. Furthermore, we find a high-degree of noise resilience of these estimators on real quantum devices, with up to an order of magnitude increase in the tolerated noise compared to traditional techniques. While these approaches are expected to break down asymptotically, we find strong evidence that these large system arguments do not prevent algorithmic advantage from these simple protocols in many systems of interest. We further extend this to consider the extraction of beyond-energetic properties by mapping to a coupled cluster surrogate model, as well as a natural combination within a quantum embedding framework. This embedding framework avoids the unstable self-consistent requirements of previous quantum embedding approaches interfaced with quantum solvers, enabling application to realistic correlated materials science, where we demonstrate the volume-dependence of the spin gap of Nickel Oxide.

Ref: Lenihan et. al, ArXiv:2506.15438 (2025)

Speaker: Prof. George Booth (King's College - London)

21 Measurement of the Lindbladian of quantum computers with randomised Pauli measurements

In the work, we propose a scalable Lindbladian measurement protocol for quantum computers. We will show both numerical and experimental results on systems of 10 and 51 1D chains of trapped ions, subject to XY power law interactions.

A generic characterization protocol for the Lindbladian, i.e. one that does not rely on strong assumptions about its form, is crucial in quantum computing and simulation platforms to certify the generated data.
To overcome the task's complexity, we prepare the qubits in a random Pauli state [1], time-evolve under a Lindbladian (Hamiltonian and additional
dissipation), and measure in a random Pauli basis. We repeat the experiment multiples times, for various random configurations (set of initial states and measurement basis) and evolution times.
Using the randomness of the data [2], we reconstruct the time evolution of Pauli observables, $\langle O\rangle(t)=\textrm{tr}[\rho O(t)]$, where $\rho$ is a product of Pauli states [1]. We then extract the derivatives at t = 0 via polynomial interpolation.
By choosing particular states $\rho$, we can isolate a few parameters in the Lindbladian and construct a small linear system of equations to determine them. Following the “Divide and Conquer” algorithmic ideas, we learn the full Lindbladian parts by parts, which makes the protocol scalable with the system size.

Ref:
[1] Efficient and robust estimation of many-qubit Hamiltonians, Daniel Stilck França, 2024
Nature Communications https://doi.org/10.1038/s41467-023-44012-5

[2] Elben, A., Flammia, S.T., Huang, HY. et al. The randomized measurement toolbox. Nat Rev Phys 5, 9–24 (2023). https://doi.org/10.1038/s42254-022-00535-2

Speaker: William LAM (LPMMC UGA CNRS)

22 How Equi-ensemble Systematically Outperforms Weighted-ensemble Variational Quantum Eigensolver

Calculating excited states in chemistry is crucial to provide insight into molecular behavior beyond the ground state, enabling innovations in spectroscopy, material sciences, and drug design. While several approaches have been developed to compute excited-state properties, finding the best ratio between computational cost and accuracy remains challenging. The advent of quantum computers brings new perspectives, with the development of quantum algorithms that promise an advantage over classical ones. Most of these new algorithms are inspired from previous classical ones, but with different pros and cons. In this work, we focus on the generalization of the variational principle for many-body excited-states that led to the ensemble variational quantum eigensolver (VQE). We compare the performance of two ensemble VQE approaches, the equi-ensemble1 and weighted-ensemble2 one, and conclude that the equi-ensemble is the way to go.

References:
1. E.K.U Gross, L.N. Oliveira and W. Kohn, Phys. Rev. A. 37, 2805 (1988)
2. Nakanishi, Ken M. , Mitarai, Kosuke and Fujii, Keisuke, Phys. Rev. Res. 1, 033062 (2019).

Speaker: Akilan Rajamani (ICGM, Université de Montpellier, CNRS, ENSCM, Montpellier, France)

3:20 PM Tea-break

23 Molecular property simulations on quantum computers: Derivation, implementation, and hardware experiments

Molecular simulation has been identified as one of the first practical applications where quantum computers could demonstrate utility, prompting extensive research into quantum algorithms for chemistry. Here, we go beyond ground state energy simulation and present various works related to obtaining molecular properties on quantum computers. These works are inspired by classical quantum chemistry knowledge, formulated in a hybrid quantum/classical algorithm framework, and go beyond “ideal simulator” studies, investigating shot and device noise. Crucially, we present first proof-of-concept hardware experiments of our algorithms on real quantum devices.
First, we present quantum algorithms for modelling spectroscopic properties by studying the response of matter to light. Classical linear response theory in a multi-configurational self-consistent field framework is reformulated for quantum computing. We explore different qLR formalisms, leveraging reduced density matrices, subspace approaches, and polarizable embedding. We showcase ideal simulator and noise study results of absorption spectra and electronic circular dichroism.[1-4]
Second, our in-house developed quantum computational software is introduced.[5] Here, we combine implementation of common wave function Ansätze with our property algorithm development. We use qubit-wise commutativity, on-the-fly Pauli savings, circuit grouping, Ansatz-based read-out and error mitigation, Pauli twirling, and dynamic decoupling. The software interfaces directly to Qiskit and IBM Quantum allowing shot and device noise simulations as well as cloud-based quantum hardware access. To showcase these developments, we present experimental results of absorption spectrum calculated on IBM quantum hardware using our in-house developed software to run qLR with novel error mitigation techniques.[6]
Third, we introduce a proof-of-concept study of electron spin resonance isotropic hyperfine coupling constants using unrestricted oo-qubit-ADAPT. We present hardware results using a combination of error suppression, mitigation, and post-selection schemes.[7]

[1] Ziems, Kjellgren, Reinholdt, Jensen, Sauer, Kongsted, Coriani, J. Chem. Theory Comput. 2024, 20, 3551
[2] Buchwald, Ziems, Kjellgren, Sauer, Kongsted, Coriani, J. Chem. Theory Comput. 2024, 20, 7093
[3] Reinholdt, Kjellgren, Fuglsbjerg, Ziems, Coriani, Sauer, Kongsted, J. Chem. Theory Comput. 2024, 20, 3729
[4] Reinholdt, Kjellgren, Ziems, Coriani, Sauer, Kongsted, J. Phys. Chem. A 2025, 129, 1504
[5] Kjellgren and Ziems. SlowQuant, https://github.com/erikkjellgren/SlowQuant
[6] Ziems, Kjellgren, Sauer, Kongsted, Coriani, Chem. Sci., 2025, 16, 4456
[7] Jensen, Hedemark, Ziems, Kjellgren, Reinholdt, Knecht, Coriani, Kongsted, Sauer, arXiv:2503.09214

Speaker: Karl Michael Ziems (University of Southampton)

24 Efficient Molecular Spectroscopy via Hybrid Subspace Methods

We propose a hybrid classical–quantum protocol for zero-temperature dynamical correlation functions and excitation spectra of interacting molecular systems. A classical ansatz (MPS or NQS) prepares an approximate ground state; after applying a probe operator, we sample configurations from the perturbed state. Short-time, shallow-circuit evolutions on quantum hardware identify small, dynamically relevant subspaces; projecting the Hamiltonian onto these subspaces enables accurate long-time classical propagation and high-resolution spectra without ground-state preparation on hardware. To tackle sharply peaked wavefunctions in ab-initio quantum chemistry, we introduce an adaptive sampling scheme for NQS that stabilizes and accelerates the variational optimization underlying the classical ground-state preparation.

Speaker: Alessandro Santini (CPHT école polytechnique)

Alessandro Santini - AQAM - 20:11:2025.pdf

5:20 PM Free time

7:30 PM Social dinner

Fri, November 21

25 Hybrid algorithms for the simulation of fermionic systems on near-term quantum hardware.

In this talk, I will explore the potential of hybrid quantum–classical algorithms for addressing fermionic problems in condensed matter physics and quantum chemistry on near-term quantum computers. For condensed matter applications, I will focus on the Quantum Selected Configuration Interaction (QSCI) method, in which a Hamiltonian is diagonalized in a basis of CI states obtained by sampling a quantum trial state. In particular, QSCI is employed as an impurity solver within the Ghost-Gutzwiller Ansatz (GGut) embedding framework to study the metal–insulator transition in the half-filled Anderson Impurity Model (AIM), as revealed by the density of states and computed using IQM’s superconducting quantum hardware. For quantum chemistry, I will discuss the Quantum-Assisted Auxiliary-Field Quantum Monte Carlo (QC-AFQMC) method, which uses a quantum trial state to guide the classical QMC process. I will show how efficient compact trial states can be constructed within contextual subspaces and present algorithmic advances that reduce the classical scaling of QC-AFQMC by several orders of magnitude.

Speaker: Dr Fedor Šimkovic (IQM)

10:00 AM Coffee-break

26 Variational Quantum Subspace Construction via Symmetry-Preserving Cost Functions

Determining low-lying eigenstates in correlated quantum systems is a central challenge in quantum chemistry and condensed matter physics. We propose the Variational Quantum Subspace Method (VQSM), a hybrid quantum-classical algorithm that iteratively constructs an orthonormal variational subspace from optimized trial states, in which the Hamiltonian is diagonalized classically. By employing symmetry-preserving cost functions, VQSM maintains shallow quantum circuits while ensuring rapid and robust convergence toward low-energy eigenvalues, closely resembling classical Lanczos-type methods. Benchmark calculations on hydrogen chain and ring models (H₄) demonstrate that VQSM achieves chemical accuracy with limited circuit depth and efficiently captures both ground-state energies and excited-state properties such as charge and spin gaps. These results establish VQSM as a promising and noise-resilient strategy for low-energy spectrum calculations on noisy intermediate-scale quantum (NISQ) devices.

Speaker: Alexandre Perrin (LOMA (CNRS))

27 Mapping Nuclear Shell Model Hamiltonians on Quantum Simulators: a quasiparticle pairing approach

Quantum computing is emerging as a powerful tool in Nuclear Physics, with a growing number of algorithms and applications developed. However, the high cost of encoding fermionic operators makes the algorithms challenging for NISQ devices. In this work, we introduce an encoding scheme based on pairing nucleon modes with opposite magnetic quantum number m. This approach reduces the complexity of the encoding, while
maintaining good accuracy, in systems where pairing interaction dominates. Furthermore, we demonstrate a computational advantage of up to three orders of magnitude in CNOT gate count using a Trotterized Quantum Adiabatic evolution, compared to standard Jordan-Wigner encoding. Our approach paves the way for more efficient quantum simulations of nuclear structure in both digital and hybrid quantum computing platforms.

Speaker: Emanuele Costa (University of Barcelona)

12:00 PM Lunch break

28 Towards benchmarking quantum computers for applications in many-body systems

To verify the performance of quantum computers and guide their progress toward scalable implementations achieving quantum advantage for many-body systems, one needs to evaluate performance metrics from the individual sources of noise in qubit hardware to full applications, and one needs to compare the quantum algorithms with the most efficient classical methods. Here we present the QCMet benchmarking software package [1], which implements a comprehensive collection of performance metrics allowing holistic evaluation of quantum computing performance. It is linked to a systematic and consistent set of definitions across all metrics, including a transparent description of the methodology and of the main assumptions and limitations. We then present a hybrid classical/quantum algorithm for the evaluation of Green’s functions of correlated materials, which integrates tensor networks for preparing ground states on classical computers with quantum computers for evaluation of dynamics [2]. For these simulations we use our recently released python tree tensor networks simulation package pyTTN [3]. We conclude by discussing the required development of metrics to address a number of open challenges for quantum computers towards achievement of quantum advantage [1,4].

[1] D. Lall et al., A Review and Collection of Metrics and Benchmarks for Quantum
Computers: Definitions, Methodologies and Software, arXiv:2502.06717;
https://qcmet.npl.co.uk.
[2] F. Jamet et al, Anderson impurity solver integrating tensor network methods with quantum computing, APL Quantum 2, 016121 (2025).
[3] L. P. Lindoy et al., pyTTN: An Open Source Toolbox for Open and Closed System Quantum Dynamics Simulations Using Tree Tensor Networks, arXiv:2503.15460;
https://gitlab.npl.co.uk/qsm/pyttn.
[4] J. Tilly et al., The Variational Quantum Eigensolver: A review of methods and best practices, Phys. Rep. 986, 1 (2022).

Speaker: Dr Ivan Rungger (National Physical Laboratory - UK)

29 Time-delayed collective dynamics in waveguide QED and bosonic quantum networks

This work introduces a theoretical framework to model the collective dynamics of quantum emitters in highly non-Markovian environments, interacting through the exchange of photons with significant retardations [1]. The formalism consists on a set of coupled delay differential equations for the emitter's polarizations, supplemented by input-output relations that describe the field mediating the interactions. These equations capture the dynamics of both linear (bosonic) and nonlinear (two-level) emitter arrays. It is exact in some limitse.g., bosonic emitters or generic systems with up to one collective excitationand can be integrated to provide accurate results for larger numbers of photons. These equations support a study of collective spontaneous emission of emitter arrays in open waveguide-QED environments. This study uncovers an effect we term cascaded super- and sub-radiance, characterized by light-cone-limited propagation and increasingly correlated photon emission across distant emitters. The collective nature of this dynamics for two-level systems is evident both in the enhancement of collective emission rates, as well as in a superradiant burst with a faster than linear growth. While these effects should be observable in existing circuit QED devices or slight generalizations thereof, the formalism put forward in this work can be extended to model other systems such as network of quantum emitters or the generation of correlated photon states.

[1] arXiv:2505.02642 [quant-ph] (2025)

Speaker: Alan COSTA DOS SANTOS (Instituto de Física Fundamental)

30 Vibrational structure study: from qubit-based to photonic simulations

The vibrational structure is a challenging problem, which has been little explored compared to the electronic structure one [1,2]. For a qubit representation, one cannot directly map the bosonic states to two-level qubits [3]. Still, encodings of second-quantized bosonic operators to qubits have been determined previously [4,5]. If one can obtain a finite polynomial Taylor expansion of the potential, it is convenient to use a harmonic oscillator basis set for the analytic integrals of the position and momentum operators. Nevertheless, the latter basis set contains an infinite number of functions and must be truncated. Here, we highlight the crucial importance of the ordering of the second quantization bosonic operators, which is a consequence of the basis truncation. We illustrate the ordering effect on the spectrum of a system with a one-mode double-well potential using the aforementioned basis set. The model is chosen to describe a large-amplitude motion exhibiting fine splitting of its eigenvalues due to deep tunneling [6]. Another question at stake is: what is the optimal choice, for a simulation based on a quantum algorithm, of the origin of the basis for this prototypical Hamiltonian? To answer that, we compare the scaling of the 1-norm with respect to the number of qubits of the two Hamiltonians. We inspect as well the convergences of the low-lying eigenvalues and their corresponding eigenstates with respect to the number of basis functions. Because mapping bosonic states to qubits is either inefficient or leads to complex circuits, we then explore the representation and computation of bosonic systems using photonic operations. We focus on the vibrational spectrum of the stretching mode in the water molecule. To do so, we use an ansatz that is boson-number-preserving to work with polyads as done in the Harmonically Coupled Anharmonic Oscillators (HCAO) approximation [7]. To this end, we run the State Average Variational Quantum Eigensolver (SAVQE) to target all the eigenvalues in a polyad and show the importance of a physically inspired guess for the initial wave function with respect to different anharmonicity and mode-coupling regimes. We also implement a way to estimate the dipole-dipole term of the extended model in a noisy sampling scheme.

[1] Sawaya, N. P. D. and Paesani, F. and Tabor, D. P., PhysRevA, 104 (2021), 15
[2] Ollitrault, P. J., Baiardi, A., Tavernelli, I., Reiher, M., Chem. Sci., 11 (2020), 6842
[3] Batista, C. D. and Ortiz, G., Advances in Physics, 53, (2004), 1
[4] Somma, R. D., Ortiz, G., Knill, E. H., Gubernatis, J., Quantum Information and Computation, 1, (2003), 189
[5] X. Huang et al., Progress in High Energy Physics, 2025, (2025), 1
[6] Letelier, R. J.; Utreras-Díaz, C. A., Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy, 53, (1997), 247
[7] M. S. Child; R. T. Lawton, Faraday Discuss. Chem. Soc., 71, (1981), 273

Speaker: Mr Joachim Knapik (Institut Charles Gerhardt Montpellier)

abstractAQAM2025V2.pdf

3:20 PM Concluding words