publications

2025

1. QM Intell

   Exploiting symmetries in nuclear Hamiltonians for ground state preparation

   Joe Gibbs, Zoë Holmes, and Paul Stevenson

   Quantum Machine Intelligence, 2025

   Abs

   The Lipkin and Agassi models are simplified nuclear models that provide natural test beds for quantum simulation methods. Prior work has investigated the suitability of the variational quantum eigensolver (VQE) to find the ground state of these models. There is a growing awareness that if VQE is to prove viable, we will need problem inspired ansätze that take into account the symmetry properties of the problem and use clever initialisation strategies. Here, by focusing on the Lipkin and Agassi models, we investigate how to do this in the context of nuclear physics ground state problems. We further use our observations to discus the potential of new classical, but quantum-inspired, approaches to learning ground states in nuclear problems.

2. QM Intell

   On fundamental aspects of quantum extreme learning machines

   Weijie Xiong, Giorgio Facelli, Mehrad Sahebi, and 4 more authors

   Quantum Machine Intelligence, 2025

   Abs

   Quantum extreme learning machines (QELMs) have emerged as a promising framework for quantum machine learning. Their appeal lies in the rich feature map induced by the dynamics of a quantum substrate—the quantum reservoir—and the efficient post-measurement training via linear regression. Here, we study the expressivity of QELMs by decomposing the prediction of QELMs into a Fourier series. We show that the achievable Fourier frequencies are determined by the data encoding scheme, while Fourier coefficients depend on both the reservoir and the measurement. Notably, the expressivity of QELMs is fundamentally limited by the number of Fourier frequencies and the number of observables, while the complexity of the prediction hinges on the reservoir. As a cautionary note on scalability, we identify four sources that can lead to the exponential concentration of the observables as the system size grows (randomness, hardware noise, entanglement, and global measurements) and show how this can turn QELMs into useless input-agnostic oracles. In particular, our result on the reservoir-induced concentration strongly indicates that quantum reservoirs drawn from a highly random ensemble make QELM models unscalable. Our analysis elucidates the potential and fundamental limitations of QELMs and lays the groundwork for systematically exploring quantum reservoir systems for other machine learning tasks.

3. arXiv preprint

   Double-bracket algorithm for quantum signal processing without post-selection

   Yudai Suzuki, Bi Hong Tiang, Jeongrak Son, and 3 more authors

   2025
4. arXiv preprint

   A unifying account of warm start guarantees for patches of quantum landscapes

   Hela Mhiri, Ricard Puig, Sacha Lerch, and 4 more authors

   2025
5. PRX Quantum

   Variational Quantum Simulation: A Case Study for Understanding Warm Starts

   Ricard Puig, Marc Drudis, Supanut Thanasilp, and 1 more author

   PRX Quantum, Jan 2025
6. arXiv preprint

   Simulating quantum circuits with arbitrary local noise using Pauli Propagation

   Armando Angrisani, Antonio A. Mele, Manuel S. Rudolph, and 2 more authors

   Jan 2025
7. Nat. Rev. Phys.

   Barren plateaus in variational quantum computing

   Martı́n Larocca, Supanut Thanasilp, Samson Wang, and 7 more authors

   Nature Reviews Physics, Jan 2025

   Abs

   Variational quantum computing offers a flexible computational approach with a broad range of applications. However, a key obstacle to realizing their potential is the barren plateau (BP) phenomenon. When a model exhibits a BP, its parameter optimization landscape becomes exponentially flat and featureless as the problem size increases. Importantly, all the moving pieces of an algorithm —choices of ansatz, initial state, observable, loss function and hardware noise —can lead to BPs if they are ill-suited. As BPs strongly impact on trainability, researchers have dedicated considerable effort to develop theoretical and heuristic methods to understand and mitigate their effects. As a result, the study of BPs has become a thriving area of research, influencing and exchanging ideas with other fields such as quantum optimal control, tensor networks and learning theory. This article provides a review of the current understanding of the BP phenomenon.

8. arXiv preprint

   Role of scrambling and noise in temporal information processing with quantum systems

   Weijie Xiong, Zoë Holmes, Armando Angrisani, and 3 more authors

   Jan 2025
9. arXiv preprint

   On Dequantization of Supervised Quantum Machine Learning via Random Fourier Features

   Mehrad Sahebi, Alice Barthe, Yudai Suzuki, and 2 more authors

   Jan 2025
10. arXiv preprint

    Pauli Propagation: A Computational Framework for Simulating Quantum Systems

    Manuel S. Rudolph, Tyson Jones, Yanting Teng, and 2 more authors

    Jan 2025
11. QM Intell

    On fundamental aspects of quantum extreme learning machines

    Weijie Xiong, Giorgio Facelli, Mehrad Sahebi, and 4 more authors

    Quantum Machine Intelligence, Jan 2025

    Abs

    Quantum extreme learning machines (QELMs) have emerged as a promising framework for quantum machine learning. Their appeal lies in the rich feature map induced by the dynamics of a quantum substrate—the quantum reservoir—and the efficient post-measurement training via linear regression. Here, we study the expressivity of QELMs by decomposing the prediction of QELMs into a Fourier series. We show that the achievable Fourier frequencies are determined by the data encoding scheme, while Fourier coefficients depend on both the reservoir and the measurement. Notably, the expressivity of QELMs is fundamentally limited by the number of Fourier frequencies and the number of observables, while the complexity of the prediction hinges on the reservoir. As a cautionary note on scalability, we identify four sources that can lead to the exponential concentration of the observables as the system size grows (randomness, hardware noise, entanglement, and global measurements) and show how this can turn QELMs into useless input-agnostic oracles. In particular, our result on the reservoir-induced concentration strongly indicates that quantum reservoirs drawn from a highly random ensemble make QELM models unscalable. Our analysis elucidates the potential and fundamental limitations of QELMs and lays the groundwork for systematically exploring quantum reservoir systems for other machine learning tasks.

12. QM Intell

    Exploiting symmetries in nuclear Hamiltonians for ground state preparation

    Joe Gibbs, Zoë Holmes, and Paul Stevenson

    Quantum Machine Intelligence, Jan 2025

    Abs

    The Lipkin and Agassi models are simplified nuclear models that provide natural test beds for quantum simulation methods. Prior work has investigated the suitability of the variational quantum eigensolver (VQE) to find the ground state of these models. There is a growing awareness that if VQE is to prove viable, we will need problem inspired ansätze that take into account the symmetry properties of the problem and use clever initialisation strategies. Here, by focusing on the Lipkin and Agassi models, we investigate how to do this in the context of nuclear physics ground state problems. We further use our observations to discus the potential of new classical, but quantum-inspired, approaches to learning ground states in nuclear problems.

13. arXiv preprint

    Pitfalls when tackling the exponential concentration of parameterized quantum models

    Reyhaneh Aghaei Saem, Behrang Tafreshi, Zoë Holmes, and 1 more author

    Jan 2025
14. arXiv preprint

    Grover’s algorithm is an approximation of imaginary-time evolution

    Yudai Suzuki, Marek Gluza, Jeongrak Son, and 3 more authors

    Jan 2025
15. arXiv preprint

    Resource-Efficient Simulations of Particle Scattering on a Digital Quantum Computer

    Yahui Chai, Joe Gibbs, Vincent R. Pascuzzi, and 4 more authors

    Jan 2025
16. arXiv preprint

    On the Complexity of Quantum States and Circuits from the Orthogonal and Symplectic Groups

    Oxana Shaya, Zoë Holmes, Christoph Hirche, and 1 more author

    Jan 2025
17. arXiv preprint

    Advantage for Discrete Variational Quantum Algorithms in Circuit Recompilation

    Oleksandr Kyriienko, Chukwudubem Umeano, and Zoë Holmes

    Jan 2025
18. arXiv preprint

    When quantum resources backfire: Non-gaussianity and symplectic coherence in noisy bosonic circuits

    Varun Upreti, Ulysse Chabaud, Zoë Holmes, and 1 more author

    Jan 2025
19. arXiv preprint

    Classically estimating observables of noiseless quantum circuits

    Armando Angrisani, Alexander Schmidhuber, Manuel S. Rudolph, and 3 more authors

    Jan 2025

2024

1. arXiv preprint

   Classically estimating observables of noiseless quantum circuits

   Armando Angrisani, Alexander Schmidhuber, Manuel S Rudolph, and 3 more authors

   arXiv preprint arXiv:2409.01706, Jan 2024
2. Nat. Commun

   Exponential concentration in quantum kernel methods

   Supanut Thanasilp, Samson Wang, M. Cerezo, and 1 more author

   Nature Communications, Jan 2024
3. arXiv preprint

   Efficient quantum-enhanced classical simulation for patches of quantum landscapes

   Sacha Lerch, Ricard Puig, Manuel S. Rudolph, and 5 more authors

   Jan 2024
4. npj Quantum Inf

   Trainability barriers and opportunities in quantum generative modeling

   Manuel S. Rudolph, Sacha Lerch, Supanut Thanasilp, and 5 more authors

   npj Quantum Information, Jan 2024

   Abs

   Quantum generative models provide inherently efficient sampling strategies and thus show promise for achieving an advantage using quantum hardware. In this work, we investigate the barriers to the trainability of quantum generative models posed by barren plateaus and exponential loss concentration. We explore the interplay between explicit and implicit models and losses, and show that using quantum generative models with explicit losses such as the KL divergence leads to a new flavor of barren plateaus. In contrast, the implicit Maximum Mean Discrepancy loss can be viewed as the expectation value of an observable that is either low-bodied and provably trainable, or global and untrainable depending on the choice of kernel. In parallel, we find that solely low-bodied implicit losses cannot in general distinguish high-order correlations in the target data, while some quantum loss estimation strategies can. We validate our findings by comparing different loss functions for modeling data from High-Energy-Physics.

5. npj Quantum Inf

   Large-scale simulations of Floquet physics on near-term quantum computers

   Timo Eckstein, Refik Mansuroglu, Piotr Czarnik, and 5 more authors

   npj Quantum Information, Jan 2024

   Abs

   Periodically driven quantum systems exhibit a diverse set of phenomena but are more challenging to simulate than their equilibrium counterparts. Here, we introduce the Quantum High-Frequency Floquet Simulation (QHiFFS) algorithm as a method to simulate fast-driven quantum systems on quantum hardware. Central to QHiFFS is the concept of a kick operator which transforms the system into a basis where the dynamics is governed by a time-independent effective Hamiltonian. This allows prior methods for time-independent simulation to be lifted to simulate Floquet systems. We use the periodically driven biaxial next-nearest neighbor Ising (BNNNI) model, a natural test bed for quantum frustrated magnetism and criticality, as a case study to illustrate our algorithm. We implemented a 20-qubit simulation of the driven two-dimensional BNNNI model on Quantinuum’s trapped ion quantum computer. Our error analysis shows that QHiFFS exhibits not only a cubic advantage in driving frequency ωbut also a linear advantage in simulation time t compared to Trotterization.

6. arXiv preprint

   Classically estimating observables of noiseless quantum circuits

   Armando Angrisani, Alexander Schmidhuber, Manuel S. Rudolph, and 3 more authors

   Jan 2024
7. Nat. Commun

   Exponential concentration in quantum kernel methods

   Supanut Thanasilp, Samson Wang, M. Cerezo, and 1 more author

   Nature Communications, Jan 2024

   Abs

   Kernel methods in Quantum Machine Learning (QML) have recently gained significant attention as a potential candidate for achieving a quantum advantage in data analysis. Among other attractive properties, when training a kernel-based model one is guaranteed to find the optimal model’s parameters due to the convexity of the training landscape. However, this is based on the assumption that the quantum kernel can be efficiently obtained from quantum hardware. In this work we study the performance of quantum kernel models from the perspective of the resources needed to accurately estimate kernel values. We show that, under certain conditions, values of quantum kernels over different input data can be exponentially concentrated (in the number of qubits) towards some fixed value. Thus on training with a polynomial number of measurements, one ends up with a trivial model where the predictions on unseen inputs are independent of the input data. We identify four sources that can lead to concentration including expressivity of data embedding, global measurements, entanglement and noise. For each source, an associated concentration bound of quantum kernels is analytically derived. Lastly, we show that when dealing with classical data, training a parametrized data embedding with a kernel alignment method is also susceptible to exponential concentration. Our results are verified through numerical simulations for several QML tasks. Altogether, we provide guidelines indicating that certain features should be avoided to ensure the efficient evaluation of quantum kernels and so the performance of quantum kernel methods.

8. Phys. Rev. Res.

   Dynamical simulation via quantum machine learning with provable generalization

   Joe Gibbs, Zoë Holmes, Matthias C. Caro, and 5 more authors

   Phys. Rev. Res., Mar 2024
9. npj Quantum Inf

   Trainability barriers and opportunities in quantum generative modeling

   Manuel S. Rudolph, Sacha Lerch, Supanut Thanasilp, and 5 more authors

   npj Quantum Information, Mar 2024

   Abs

   Quantum generative models provide inherently efficient sampling strategies and thus show promise for achieving an advantage using quantum hardware. In this work, we investigate the barriers to the trainability of quantum generative models posed by barren plateaus and exponential loss concentration. We explore the interplay between explicit and implicit models and losses, and show that using quantum generative models with explicit losses such as the KL divergence leads to a new flavor of barren plateaus. In contrast, the implicit Maximum Mean Discrepancy loss can be viewed as the expectation value of an observable that is either low-bodied and provably trainable, or global and untrainable depending on the choice of kernel. In parallel, we find that solely low-bodied implicit losses cannot in general distinguish high-order correlations in the target data, while some quantum loss estimation strategies can. We validate our findings by comparing different loss functions for modeling data from High-Energy-Physics.

10. npj Quantum Inf

    Large-scale simulations of Floquet physics on near-term quantum computers

    Timo Eckstein, Refik Mansuroglu, Piotr Czarnik, and 5 more authors

    npj Quantum Information, Mar 2024

    Abs

    Periodically driven quantum systems exhibit a diverse set of phenomena but are more challenging to simulate than their equilibrium counterparts. Here, we introduce the Quantum High-Frequency Floquet Simulation (QHiFFS) algorithm as a method to simulate fast-driven quantum systems on quantum hardware. Central to QHiFFS is the concept of a kick operator which transforms the system into a basis where the dynamics is governed by a time-independent effective Hamiltonian. This allows prior methods for time-independent simulation to be lifted to simulate Floquet systems. We use the periodically driven biaxial next-nearest neighbor Ising (BNNNI) model, a natural test bed for quantum frustrated magnetism and criticality, as a case study to illustrate our algorithm. We implemented a 20-qubit simulation of the driven two-dimensional BNNNI model on Quantinuum’s trapped ion quantum computer. Our error analysis shows that QHiFFS exhibits not only a cubic advantage in driving frequency ωbut also a linear advantage in simulation time t compared to Trotterization.

11. Nat. Commun

    Exponential concentration in quantum kernel methods

    Supanut Thanasilp, Samson Wang, M. Cerezo, and 1 more author

    Nature Communications, Mar 2024

    Abs

    Kernel methods in Quantum Machine Learning (QML) have recently gained significant attention as a potential candidate for achieving a quantum advantage in data analysis. Among other attractive properties, when training a kernel-based model one is guaranteed to find the optimal model’s parameters due to the convexity of the training landscape. However, this is based on the assumption that the quantum kernel can be efficiently obtained from quantum hardware. In this work we study the performance of quantum kernel models from the perspective of the resources needed to accurately estimate kernel values. We show that, under certain conditions, values of quantum kernels over different input data can be exponentially concentrated (in the number of qubits) towards some fixed value. Thus on training with a polynomial number of measurements, one ends up with a trivial model where the predictions on unseen inputs are independent of the input data. We identify four sources that can lead to concentration including expressivity of data embedding, global measurements, entanglement and noise. For each source, an associated concentration bound of quantum kernels is analytically derived. Lastly, we show that when dealing with classical data, training a parametrized data embedding with a kernel alignment method is also susceptible to exponential concentration. Our results are verified through numerical simulations for several QML tasks. Altogether, we provide guidelines indicating that certain features should be avoided to ensure the efficient evaluation of quantum kernels and so the performance of quantum kernel methods.

2023

1. arXiv preprint

   On fundamental aspects of quantum extreme learning machines

   Weijie Xiong, Giorgio Facelli, Mehrad Sahebi, and 4 more authors

   arXiv preprint arXiv:2312.15124, Mar 2023

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2. arXiv preprint

   Does provable absence of barren plateaus imply classical simulability? Or, why we need to rethink variational quantum computing

   M Cerezo, Martin Larocca, Diego Garcı́a-Martı́n, and 8 more authors

   arXiv preprint arXiv:2312.09121, Mar 2023

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3. arXiv preprint

   Classical surrogate simulation of quantum systems with LOWESA

   Manuel S. Rudolph, Enrico Fontana, Zoë Holmes, and 1 more author

   Aug 2023

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4. arXiv preprint

   Trainability barriers and opportunities in quantum generative modeling

   Manuel S. Rudolph, Sacha Lerch, Supanut Thanasilp, and 4 more authors

   May 2023

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5. arXiv preprint

   Large-scale simulations of Floquet physics on near-term quantum computers

   Timo Eckstein, Refik Mansuroglu, Piotr Czarnik, and 5 more authors

   arXiv preprint arXiv:2303.02209, Mar 2023

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6. Nat. Commun

   Out-of-distribution generalization for learning quantum dynamics

   Matthias C. Caro, Hsin-Yuan Huang, Nicholas Ezzell, and 5 more authors

   NatComms, May 2023

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7. arXiv preprint

   The power and limitations of learning quantum dynamics incoherently

   Sofiene Jerbi, Joe Gibbs, Manuel S. Rudolph, and 4 more authors

   May 2023

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8. arXiv preprint

   Classical surrogate simulation of quantum systems with LOWESA

   Manuel S. Rudolph, Enrico Fontana, Zoë Holmes, and 1 more author

   May 2023
9. Phys. Rev. Res.

   Nonlinear transformations in quantum computation

   Phys. Rev. Res., Feb 2023

2022

1. npj

   Long-time simulations with high fidelity on quantum hardware

   Joe Gibbs, Kaitlin Gili, Zoë Holmes, and 5 more authors

   Nov 2022

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2. prx-quantum

   Connecting Ansatz Expressibility to Gradient Magnitudes and Barren Plateaus

   Zoë Holmes, Kunal Sharma, M. Cerezo, and 1 more author

   PRX Quantum, Jan 2022

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3. Quantum

   Quantum algorithms from fluctuation theorems: Thermal-state preparation

   Zoe Holmes, Gopikrishnan Muraleedharan, Rolando D. Somma, and 2 more authors

   Quantum, Oct 2022

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4. arXiv preprint

   Dynamical simulation via quantum machine learning with provable generalization

   Joe Gibbs, Zoë Holmes, Matthias C. Caro, and 5 more authors

   Apr 2022

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5. Quantum

   Quantum algorithms from fluctuation theorems: Thermal-state preparation

   Zoe Holmes, Gopikrishnan Muraleedharan, Rolando D. Somma, and 2 more authors

   Quantum, Oct 2022
6. PRX Quantum

   Connecting Ansatz Expressibility to Gradient Magnitudes and Barren Plateaus

   Zoë Holmes, Kunal Sharma, M. Cerezo, and 1 more author

   PRX Quantum, Jan 2022

2021

1. arXiv preprint

   Long-time simulations with high fidelity on quantum hardware

   Joe Gibbs, Kaitlin Gili, Zoë Holmes, and 5 more authors

   Jan 2021
2. Phys. Rev. Lett.

   Barren Plateaus Preclude Learning Scramblers

   Zoë Holmes, Andrew Arrasmith, Bin Yan, and 3 more authors

   Phys. Rev. Lett., May 2021

2020

1. New J. Phys

   Gibbs mixing of partially distinguishable photons with a polarising beamsplitter membrane

   Zoë Holmes, Florian Mintert, and Janet Anders

   New Journal of Physics, Nov 2020
2. Phys. Rev. Lett.

   Enhanced Energy Transfer to an Optomechanical Piston from Indistinguishable Photons

   Zoë Holmes, Janet Anders, and Florian Mintert

   Phys. Rev. Lett., May 2020
3. Entropy

   Quantifying Athermality and Quantum Induced Deviations from Classical Fluctuation Relations

   Zoë Holmes, Erick Hinds Mingo, Calvin Y.-R. Chen, and 1 more author

   Entropy, May 2020

2019

1. Quantum

   Coherent fluctuation relations: from the abstract to the concrete

   Zoë Holmes, Sebastian Weidt, David Jennings, and 2 more authors

   Quantum, Feb 2019