Importance sampling for stochastic quantum simulations

Simulating complex quantum systems is a promising task for digital quantum computers. However, the depth of popular product formulas scales with the number of summands in the Hamiltonian, which can therefore be challenging to implement on near-term as well as fault-tolerant devices. An efficient solution is given by the stochastic compilation protocol known as qDrift, which builds random product formulas by sampling from the Hamiltonian according to the magnitude of their coefficients. In this work, we unify the qDrift protocol with importance sampling, allowing us to sample from arbitrary distributions while controlling both the bias as well as the statistical fluctuations. We show that the simulation cost can be reduced while achieving the same accuracy by considering the individual simulation cost during the sampling stage. Moreover, we incorporate recent work on composite channel and compute rigorous bounds on the bias and variance showing how to choose the number of samples, experiments, and time steps for a given target accuracy. These results lead to a more efficient implementation of the qDrift protocol, both with and without the use of composite channels. Theoretical results are confirmed by numerical simulations performed on a lattice nuclear effective field theory.Comment: 15 pages, 10 pages supplemental materia

Importance sampling for stochastic quantum simulations

Simulating many-body quantum systems is a promising task for quantum computers. However, the depth of most algorithms, such as product formulas, scales with the number of terms in the Hamiltonian, and can therefore be challenging to implement on near-term, as well as early fault-tolerant quantum devices. An efficient solution is given by the stochastic compilation protocol known as qDrift, which builds random product formulas by sampling from the Hamiltonian according to the coefficients. In this work, we unify the qDrift protocol with importance sampling, allowing us to sample from arbitrary probability distributions, while controlling both the bias, as well as the statistical fluctuations. We show that the simulation cost can be reduced while achieving the same accuracy, by considering the individual simulation cost during the sampling stage. Moreover, we incorporate recent work on composite channel and compute rigorous bounds on the bias and variance, showing how to choose the number of samples, experiments, and time steps for a given target accuracy. These results lead to a more efficient implementation of the qDrift protocol, both with and without the use of composite channels. Theoretical results are confirmed by numerical simulations performed on a lattice nuclear effective field theory

Symmetry-invariant quantum machine learning force fields

Machine learning techniques are essential tools to compute efficient, yet accurate, force fields for atomistic simulations. This approach has recently been extended to incorporate quantum computational methods, making use of variational quantum learning models to predict potential energy surfaces and atomic forces from ab initio training data. However, the trainability and scalability of such models are still limited, due to both theoretical and practical barriers. Inspired by recent developments in geometric classical and quantum machine learning, here we design quantum neural networks that explicitly incorporate, as a data-inspired prior, an extensive set of physically relevant symmetries. We find that our invariant quantum learning models outperform their more generic counterparts on individual molecules of growing complexity. Furthermore, we study a water dimer as a minimal example of a system with multiple components, showcasing the versatility of our proposed approach and opening the way towards larger simulations. Our results suggest that molecular force fields generation can significantly profit from leveraging the framework of geometric quantum machine learning, and that chemical systems represent, in fact, an interesting and rich playground for the development and application of advanced quantum machine learning tools.Comment: 12 pages, 8 figure

Finite-size criticality in fully connected spin models on superconducting quantum hardware

The emergence of a collective behavior in a many-body system is responsible of the quantum criticality separating different phases of matter. Interacting spin systems in a magnetic field offer a tantalizing opportunity to test different approaches to study quantum phase transitions. In this work, we exploit the new resources offered by quantum algorithms to detect the quantum critical behaviour of fully connected spin$-1/2$ models. We define a suitable Hamiltonian depending on an internal anisotropy parameter $\gamma,$ that allows us to examine three paradigmatic examples of spin models, whose lattice is a fully connected graph. We propose a method based on variational algorithms run on superconducting transmon qubits to detect the critical behavior for systems of finite size. We evaluate the energy gap between the first excited state and the ground state, the magnetization along the easy-axis of the system, and the spin-spin correlations. We finally report a discussion about the feasibility of scaling such approach on a real quantum device for a system having a dimension such that classical simulations start requiring significant resources.Comment: 11 pages, 9 figures. Comments are welcom

Bayesian Optimization for machine learning algorithms in the context of Higgs searches at the CMS experiment

Machine Learning algorithms, such as Boosted Decisions Trees and Deep Neural Network, are widely used in High-Energy-Physics. The aim of this study is to apply Bayesian Optimization to tune the hyperparameters used in a machine learning algorithm. This algorithm performs an energy regression process on photons and electrons detected in the electromagnetic calorimeter at the Compact Muon Solenoid experiment operating at the Large Hadron Collider at CERN. The goal of this algorithm is to estimate the energy of photons and electrons created during the collisions in the Compact Muon Solenoid, from the measured energy.Comment: arXiv admin note: This version has been removed as the user did not have the right to agree to the license at the time of submissio

Stochastic quantum simulations for scattering experiments

NEW START TIME: 14:00Simulating many-body quantum systems is a promising task for quantum computers. However, early fault-tolerant devices are not expected to correct arbitrary amounts of error, making the quest for better algorithms an important task. &nbsp;We concentrate on random product formulas, such as qDrift, and unify this framework with importance sampling, allowing us to sample from arbitrary distributions while controlling both the bias, as well as the statistical fluctuations. We show that the simulation cost can be reduced while achieving the same accuracy by considering the individual simulation cost during the sampling stage. We hope this work to pave the way for tailored qDrift implementations on specific problems and hardware.&nbsp;As a bonus, we will also discuss how to compute linear response functions from nuclear scattering experiments using quantum hardware. We will cover circuit design optimization, different purification-based error mitigation protocols, and some hardware results.&nbsp;About the speakerOriel Moira Kiss obtained his Master's degree in Physics from ETH Zürich in 2021. He is now PhD student at University of Geneva, collaborating in the CERN QTI.&nbsp;Collaborators: Michele Grossi (CERN) &amp; Alessandro Roggero (INFN)</p

Quantum neural networks force fields generation

Accurate molecular force fields are of paramount importance for the efficient implementation of molecular dynamics techniques at large scales. In the last decade, machine learning (ML) methods have demonstrated impressive performances in predicting accurate values for energy and forces when trained on finite size ensembles generated with ab initio techniques. At the same time, quantum computers have recently started to offer new viable computational paradigms to tackle such problems. On the one hand, quantum algorithms may notably be used to extend the reach of electronic structure calculations. On the other hand, quantum ML is also emerging as an alternative and promising path to quantum advantage. Here we follow this second route and establish a direct connection between classical and quantum solutions for learning neural network (NN) potentials. To this end, we design a quantum NN architecture and apply it successfully to different molecules of growing complexity. The quantum models exhibit larger effective dimension with respect to classical counterparts and can reach competitive performances, thus pointing towards potential quantum advantages in natural science applications via quantum ML.ISSN:2632-215

Conditional Born machine for Monte Carlo event generation

Generative modeling is a promising task for near-term quantum devices, which can use the stochastic nature of quantum measurements as a random source. So-called Born machines are purely quantum models and promise to generate probability distributions in a quantum way, inaccessible to classical computers. This paper presents an application of Born machines to Monte Carlo simulations and extends their reach to multivariate and conditional distributions. Models are run on (noisy) simulators and IBM Quantum superconducting quantum hardware. More specifically, Born machines are used to generate muonic force carrier (MFC) events resulting from scattering processes between muons and the detector material in high-energy physics collider experiments. MFCs are bosons appearing in beyond-the-standard-model theoretical frameworks, which are candidates for dark matter. Empirical evidence suggests that Born machines can reproduce the marginal distributions and correlations of data sets from Monte Carlo simulations.Generative modeling is a promising task for near-term quantum devices, which can use the stochastic nature of quantum measurements as a random source. So called Born machines are purely quantum models and promise to generate probability distributions in a quantum way, inaccessible to classical computers. This paper presents an application of Born machines to Monte Carlo simulations and extends their reach to multivariate and conditional distributions. Models are run on (noisy) simulators and IBM Quantum superconducting quantum hardware. More specifically, Born machines are used to generate muonic force carrier (MFC) events resulting from scattering processes between muons and the detector material in high-energy physics colliders experiments. MFCs are bosons appearing in beyond-the-standard-model theoretical frameworks, which are candidates for dark matter. Empirical evidence suggests that Born machines can reproduce the marginal distributions and correlations of data sets from Monte Carlo simulations

Quantum phase detection generalization from marginal quantum neural network models

Quantum machine learning offers a promising advantage in extracting information about quantum states, e.g., phase diagram. However, access to training labels is a major bottleneck for any supervised approach, preventing getting insights about new physics. In this Letter, using quantum convolutional neural networks, we overcome this limit by determining the phase diagram of a model where analytical solutions are lacking, by training only on marginal points of the phase diagram, where integrable models are represented. More specifically, we consider the axial next-nearest-neighbor Ising Hamiltonian, which possesses a ferromagnetic, paramagnetic, and antiphase, showing that the whole phase diagram can be reproduced.Quantum machine learning offers a promising advantage in extracting information about quantum states, e.g. phase diagram. However, access to training labels is a major bottleneck for any supervised approach, preventing getting insights about new physics. In this Letter, using quantum convolutional neural networks, we overcome this limit by determining the phase diagram of a model where analytical solutions are lacking, by training only on marginal points of the phase diagram, where integrable models are represented. More specifically, we consider the axial next-nearest-neighbor Ising (ANNNI) Hamiltonian, which possesses a ferromagnetic, paramagnetic and antiphase, showing that the whole phase diagram can be reproduced

Counterdiabatic optimized driving in quantum phase sensitive models

State preparation plays a pivotal role in numerous quantum algorithms, including quantum phase estimation. This paper extends and benchmarks counterdiabatic driving protocols across three one-dimensional spin systems characterized by phase transitions: the axial next-nearest neighbor Ising (ANNNI), XXZ, and Haldane-Shastry (HS) models. We perform quantum optimal control protocols by optimizing the energy cost function, which can always be evaluated as opposed to the fidelity one requiring the exact state. Moreover, we incorporate Bayesian optimization within a code package for computing various adiabatic gauge potentials. This protocol consistently surpasses standard annealing schedules, often achieving performance improvements of several orders of magnitude. Notably, the ANNNI model stands out as a notable example, where fidelities exceeding 0.5 are attainable in most cases. Furthermore, the optimized paths exhibits promising generalization capabilities to higher-dimensional systems, allowing for the extension of parameters from smaller models. This opens up possibilities for applying the protocol to higher-dimensional systems. However, our investigations reveal limitations in the case of the XXZ and HS models, particularly when transitioning away from the ferromagnetic phase. This suggests that finding optimal diabatic gauge potentials for specific systems remains an important research direction