Searcharxiv⌕ Search

arXiv subjects

Denis Lacroix

Publications and source records attributed to Denis Lacroix.

At least 37 records · Page 2Linked to original sources
arXiv2023

Quantum Information Science and Technology for Nuclear Physics. Input into U.S. Long-Range Planning, 2023

In preparation for the 2023 NSAC Long Range Plan (LRP), members of the Nuclear Science community gathered to discuss the current state of, and plans for further leveraging opportunities in, QIST in NP research at the Quantum Information Science for U.S. Nuclear Physics Long Range Planning workshop, held in Santa Fe, New Mexico on January 31 - February 1, 2023. The workshop included 45 in-person participants and 53 remote attendees. The outcome of the workshop identified strategic plans and requirements for the next 5-10 years to advance quantum sensing and quantum simulations within NP, and to develop a diverse quantum-ready workforce. The plans include resolutions endorsed by the participants to address the compelling scientific opportunities at the intersections of NP and QIST. These endorsements are aligned with similar affirmations by the LRP Computational Nuclear Physics and AI/ML Workshop, the Nuclear Structure, Reactions, and Astrophysics LRP Town Hall, and the Fundamental Symmetries, Neutrons, and Neutrinos LRP Town Hall communities.

nucl-ex↗
arXiv2022

Symmetry breaking/symmetry preserving circuits and symmetry restoration on quantum computers: A quantum many-body perspective

We discuss here some aspects related to the symmetries of a quantum many-body problem when trying to treat it on a quantum computer. Several features related to symmetry conservation, symmetry breaking, and possible symmetry restoration are reviewed. After briefly discussing some of the standard symmetries relevant for many-particle systems, we discuss the advantage of encoding some symmetries directly in quantum ansätze, especially to reduce the quantum register size. It is, however, well-known that the use of symmetry-breaking states can also be a unique way to incorporate specific internal correlations when a spontaneous symmetry breaking occurs. These aspects are discussed in the quantum computing context. Ultimately, an accurate description of quantum systems can be achieved only when the initially broken symmetries are properly restored. We review several methods explored previously to perform symmetry restoration on a quantum computer, for instance, the ones based on symmetry filtering by quantum phase estimation and by an iterative independent set of Hadamard tests. We propose novel methods that pave the new directions to perform symmetry restoration, like those based on the purification of the state employing the linear combination of unitaries (LCU) approach.

quant-ph↗
arXiv2022

Role of non-gaussian quantum fluctuations in neutrino entanglement

The flavor evolution of neutrinos in environments with large neutrino number densities is an open problem at the nexus of astrophysics and neutrino flavor physics. Among the many unanswered questions pertaining to this problem, it remains to be determined whether neutrino-neutrino coherent scattering can give rise to nontrivial quantum entanglement among neutrinos, and whether this can affect the flavor evolution in a meaningful way. To gain further insight into this question, here we study a simple system of two interacting neutrino beams, and obtain the exact phase-space explored by this system using the Husimi quasi-probability distribution. We observe that the entanglement induced by the coupling leads to strong delocalization in phase-space with largely non-Gaussian quantum fluctuations. The link between the neutrino entanglement and quantum fluctuations is illustrated using the one- and two-neutrino entropy. In addition, we propose an approximate phase-space method to describe the interacting neutrinos problem, where the exact evolution is replaced by a set of independent mean-field evolutions with a statistical sampling of the initial conditions. The phase-space approach provides a simple and accurate method to describe the gross features of the neutrino entanglement problem. Applications are shown using time-independent and time-dependent Hamiltonians in the non-adiabatic regime.

nucl-th↗
arXiv2022

Restoring broken symmetries using oracles

We present a new method to perform variation after projection in many-body systems on quantum computers that does not require performing explicit projection. The technique employs the notion of ``oracle'', generally used in quantum search algorithms. We show how to construct the oracle and the projector associated with a symmetry operator. The procedure is illustrated for the parity, particle number, and total spin symmetries. The oracle is used to restore symmetry by indirect measurements using a single ancillary qubit. An Illustration of the technique is made to obtain the approximate ground state energy for the pairing model Hamiltonian.

quant-ph↗
arXiv2022

Simulating excited states of the Lipkin model on a quantum computer

We simulate the excited states of the Lipkin model using the recently proposed Quantum Equation of Motion (qEOM) method. The qEOM generalizes the EOM on classical computers and gives access to collective excitations based on quasi-boson operators $\hat{O}^\dagger_n(α)$ of increasing configuration complexity $α$. We show, in particular, that the accuracy strongly depends on the fermion to qubit encoding. Standard encoding leads to large errors, but the use of symmetries and the Gray code reduces the quantum resources and improves significantly the results on current noisy quantum devices. With this encoding scheme, we use IBM quantum machines to compute the energy spectrum for a system of $N=2, 3$ and $4$ particles and compare the accuracy against the exact solution. We found that the results of the approach with $α= 2$, an analog of the second random phase approximation (SRPA), are, in principle, more accurate than with $α= 1$, which corresponds to the random phase approximation (RPA), but the SRPA is more amenable to noise for large coupling strengths. Thus, the proposed scheme shows potential for achieving higher spectroscopic accuracy by implementations with higher configuration complexity, if a proper error mitigation method is applied.

nucl-th↗
arXiv2021

Calculation of generating function in many-body systems with quantum computers: technical challenges and use in hybrid quantum-classical methods

The generating function of a Hamiltonian $H$ is defined as $F(t)=\langle e^{-itH}\rangle$, where $t$ is the time and where the expectation value is taken on a given initial quantum state. This function gives access to the different moments of the Hamiltonian $\langle H^{K}\rangle$ at various orders $K$. The real and imaginary parts of $F(t)$ can be respectively evaluated on quantum computers using one extra ancillary qubit with a set of measurement for each value of the time $t$. The low cost in terms of qubits renders it very attractive in the near term period where the number of qubits is limited. Assuming that the generating function can be precisely computed using quantum devices, we show how the information content of this function can be used a posteriori on classical computers to solve quantum many-body problems. Several methods of classical post-processing are illustrated with the aim to predict approximate ground or excited state energies and/or approximate long-time evolutions. This post-processing can be achieved using methods based on the Krylov space and/or on the $t$-expansion approach that is closely related to the imaginary time evolution. Hybrid quantum-classical calculations are illustrated in many-body interacting systems using the pairing and Fermi-Hubbard models.

quant-ph↗
arXiv2021

Filtering states with total spin on a quantum computer

Starting from a general wave function described on a set of spins/qubits, we propose several quantum algorithms to extract the components of this state on eigenstates of the total spin ${\bf S}^2$ and its azimuthal projection $S_z$. The method plays the role of total spin projection and gives access to the amplitudes of the initial state on a total spin basis. The different algorithms have various degrees of sophistication depending on the requested tasks. They can either solely project onto the subspace with good total spin or completely uplift the degeneracy in this subspace. After each measurement, the state collapses to one of the spin eigenstates that could be used for post-processing. For this reason, we call the method Total Quantum Spin filtering (TQSf). Possible applications ranging from many-body physics to random number generators are discussed.

quant-ph↗
arXiv2020

Future of Nuclear Fission Theory

There has been much recent interest in nuclear fission, due in part to a new appreciation of its relevance to astrophysics, stability of superheavy elements, and fundamental theory of neutrino interactions. At the same time, there have been important developments on a conceptual and computational level for the theory. The promising new theoretical avenues were the subject of a workshop held at the University of York in October 2019; this report summarises its findings and recommendations.

nucl-th↗
arXiv2020

Non-Markovian modeling of Fermi-Bose systems coupled to one or several Fermi-Bose thermal baths

A method is proposed to describe Fermi or Bose systems coupled to one or several heat baths composed of fermions and/or bosons. The method, called Coupled Equations of Motion method, properly includes non-Markovian effects. The approach is exact in the Full-Coupling approximation when only bosonic particles are present in the system and baths. The approach provides an approximate treatment when fermions are present either in the system and/or in one or several environments. The new approach has the advantage to properly respect the Pauli exclusion principle for fermions during the evolution. We illustrate the approach for the single Fermi or Bose two-level system coupled to one or two heat-baths assuming different types of quantum statistics (Fermion or Bosons) for them. The cases of Fermi system coupled to fermion or boson heat baths or a mixture of both are analyzed in details. With the future goal to treat Fermi systems formed of increasing number of two-level systems (Qubits), we discuss possible simplifications that could be made in the equations of motion and their limits of validity in terms of the system--baths coupling or of the initial heat baths temperatures.

quant-ph↗
arXiv2020

Lee-Yang-inspired energy-density functional including contributions from $p$-wave scattering

The ELYO functional proposed in [M. Grasso, D. Lacroix, and C. J. Yang, Phys. Rev. C \textbf{95}, 054327 (2017)] belongs to the family of energy-density functionals (EDFs) inspired by effective-field theories (EFTs) and constrained by \textit{ab--initio} pseudo-data. We present here an extension of this EDF which also accounts for the first $p$-wave term appearing in the low-density expansion from which it derives. It is shown that this enrichment of the ansatz on which the functional is based leads to a significant improvement of the description of neutronic systems, especially in regimes besides the pseudo--data set employed to adjust the parameters. As an illustrative application, the mass-radius relation of neutron stars is considered. In contrast to its initial version, the new functional predicts values which are qualitatively consistent with recent observations.

nucl-th↗
arXiv2019

Combining phase-space and time-dependent reduced density matrix approach to describe the dynamics of interacting fermions

The possibility to apply phase-space methods to many-body interacting systems might provide accurate descriptions of correlations with a reduced numerical cost. For instance, the so--called stochastic mean-field phase-space approach, where the complex dynamics of interacting fermions is replaced by a statistical average of mean-field like trajectories is able to grasp some correlations beyond the mean-field. We explore the possibility to use alternative equations of motion in the phase-space approach. Guided by the BBGKY hierarchy, equations of motion that already incorporate part of the correlations beyond mean-field are employed along each trajectory. The method is called Hybrid Phase-Space (HPS) because it mixes phase-space techniques and the time-dependent reduced density matrix approach. The novel approach is applied to the one-dimensional Fermi-Hubbard model. We show that the predictive power is improved compared to the original stochastic mean-field method. In particular, in the weak-coupling regime, the results of the HPS theory can hardly be distinguished from the exact solution even for long time.

nucl-th↗
arXiv2019

Impact of the initial fluctuations on the dissipative dynamics of interacting Fermi systems: A model case study

Standard methods used for computing the dynamics of a quantum many-body system are the mean-field (MF) approximations such as the time-dependent Hartree-Fock (TDHF) approach. Even though MF approaches are quite successful, they suffer some well-known shortcomings, one of which is insufficient dissipation of collective motion. The stochastic mean-field approach (SMF), where a set of MF trajectories with random initial conditions are considered, is a good candidate to include dissipative effects beyond mean field. In this approach, the one-body density matrix elements are treated initially as a set of stochastic Gaussian c numbers that are adjusted to reproduce first and second moments of collective one-body observables. It is shown that the predictive power of the SMF approach can be further improved by relaxing the Gaussian assumption for the initial probabilities. More precisely, using Gaussian or uniform distributions for the matrix elements generally leads to overdamping for long times, whereas distributions with smaller kurtosis lead to much better reproduction of the long time evolution.

nucl-th↗
arXiv2019

Counting statistics in finite Fermi systems: illustrations with the atomic nucleus

We analyze here in details the probability to find a given number of particles in a finite volume inside a normal or superfluid finite system. This probability, also known as counting statistics, is obtained using projection operator techniques directly linked to the characteristic function of the probability distribution. The method is illustrated in atomic nuclei. The nature of the particle number fluctuations from small to large volumes compared to the system size are carefully analyzed in three cases: normal systems, superfluid systems and superfluid systems with total particle number restoration. The transition from Poissonian distribution in the small volume limit to Gaussian fluctuations as the number of particles participating to the fluctuations increases, is analyzed both in the interior and at the surface of the system. While the restoration of total number of particles is not necessary for small volume, we show that it affects the counting statistics as soon as more than very few particles are involved.

nucl-th↗
arXiv2019

Approximate self-energy for Fermi systems with large s-wave scattering length: a step towards density functional theory

In the present work, we start from a minimal Hamiltonian for Fermi systems where the s-wave scattering is the only low energy constant at play. Many-Body Perturbative approach that is usually valid at rather low density is first discussed. We then use the resummation technique with the ladder approximation to obtain compact expressions for both the energy and/or the on-shell self-energy in infinite spin-degenerated systems. Diagrammatic resummation technique has the advantage in general to be predictive in a region of density larger compared to many-body perturbation theory. It also leads to non-diverging limit as $|a_s| \rightarrow + \infty$. Still, the obtained expressions are rather complex functional of the Fermi momentum $k_F$. We introduce the full phase-space average or the partial phase-space methods respectively applied to the energy or to the self-energy to simplify their dependences in terms of $(a_s k_F)$ while keeping the correct limit at low density and the non-diverging property at large $|a_s k_F|$. Quasi-particle properties of Fermi system in various regime of density and scattering length are then illustrated. Our conclusion is that such simplified expressions where the direct link is made with the low energy constant without fine-tuning can provide a clear guidance to obtain density functional theory beyond the perturbative regime. However, quasi-particle properties close or near unitary cannot be reproduced unless this limit is explicitly used as a constraint. We finally discuss how such approximate treatment of quasi-particle can guide the development of density functional theory for strongly interacting Fermi systems.

nucl-th↗
arXiv2018

Energy-density functionals inspired by effective-field theories: Applications to neutron drops

New energy-density functionals (EDFs) inspired by effective-field theories (EFTs) have been recently proposed. The present work focuses on three of such functionals which were developed to produce satisfactory equations of state for nuclear matter. We aim to extend these functionals to treat finite systems including a spin-orbit contribution and pairing correlations. We illustrate here a first step towards this direction, namely a generalization of such functionals tailored to perform applications to neutron gases confined in harmonic traps. Sets of available \textit{ab initio} results are used as benchmark pseudo-data for adjusting the additional parameters (with respect to the nuclear matter case) that have to be introduced for finite-size systems. Several quantities are predicted and compared to \textit{ab initio} and other EDF results such as, for instance, total energies, potentials, and density profiles. The associated effective masses are also analyzed. In cases where \textit{ab initio} results are available, two of these functionals globally provide predictions which are close one to the other as well as to \textit{ab initio} values. It is shown that, in general, this is not the case for several currently used Skyrme functionals. Directions for improving the third functional are discussed.

nucl-th↗
arXiv2018

Microscopic description of pair transfer between two superfluid Fermi systems: combining phase-space averaging and combinatorial techniques

In a mean-field description of superfluidity, particle number and gauge angle are treated as quasi-classical conjugated variables. This level of description was recently used to describe nuclear reactions around the Coulomb barrier. Important effects of the relative gauge angle between two identical superfluid nuclei (symmetric collisions) on transfer probabilities and fusion barrier have been uncovered. A theory making contact with experiments should at least average over different initial relative gauge-angles. In the present work, we propose a new approach to obtain the multiple pair transfer probabilities between superfluid systems. This method, called Phase-Space combinatorial (PSC) technique, relies both on phase-space averaging and combinatorial arguments to infer the full pair transfer probability distribution at the cost of multiple mean-field calculations only. After benchmarking this approach in a schematic model, we apply it to the collision $^{20}$O+$^{20}$O at various energies below the Coulomb barrier. The predictions for one pair transfer are similar to results obtained with an approximated projection method whereas significant differences are found for two pairs transfer. Finally, we investigated the applicability of the PSC method to the contact between non-identical superfluid systems. [...] The applicability of the PSC method to asymmetric nuclear collisions is investigated for the $^{14}$O+$^{20}$O collision and it turns out that unrealistically small single- and multiple-pair transfer probabilities are obtained. [...] We conclude that the best ground for probing gauge-angle effects in nuclear reaction and/or for applying the proposed PSC approach on pair transfer is the collisions of identical open-shell spherical nuclei.

nucl-th↗
arXiv2018

Static response, collective frequencies and ground state thermodynamical properties of spin saturated two-component cold atoms and neutron matter

The thermodynamical ground-state properties and static response in both cold atoms at or close to unitarity and neutron matter are determined using a recently proposed Density Functional Theory (DFT) based on the s-wave scattering length $a_s$, effective range $r_e$, and unitary gas limit. In cold atoms, when the effective range may be neglected, we show that the pressure, chemical potential, compressibility modulus and sound velocity obtained with the DFT are compatible with experimental observations or exact theoretical estimates. The static response in homogeneous infinite systems is also obtained and a possible influence of the effective range on the response is analyzed. The neutron matter differs from unitary gas due to the non infinite scattering length and to a significant influence of effective range which affects all thermodynamical quantities as well as the static response. In particular, we show for neutron matter that the latter response recently obtained in Auxiliary-Field Diffusion Monte-Carlo (AFDMC) can be qualitatively reproduced when the p-wave contribution is added to the functional. Our study indicates that the close similarity between the exact AFDMC static response and the free gas response might stems from the compensation of the $a_s$ effect by the effective range and p-wave contributions. We finally consider the dynamical response of both atoms or neutron droplets in anisotropic traps. Assuming the hydrodynamical regime and a polytropic equation of state, a reasonable description of the radial and axial collective frequencies in cold atoms is obtained. Following a similar strategy, we estimate the equivalent collective frequencies of neutron drops in anisotropic traps.

nucl-th↗