Quantum Many-Body Physics and Quantum Information Research at Bielefeld University

We are working on the development of methods for solving the quantum many-body problem, in order to describe the structure and dynamics of strongly-interacting systems, in particular atomic nuclei.

We are particularly interested in studying the role of entanglement in nuclear structure and nuclear processes, and in the development of entanglement-driven methods and algorithms for classical and quantum simulations of nuclei.

This involves borrowing and adapting tools of quantum information, as well as techniques developed in others fields of quantum many-body physics, such as quantum chemistry and condensed matter physics. In turn, the findings of made in the area of nuclear physics may be beneficial for these other areas of many-body physics.

Indeed, atomic nuclei are prime examples of mesoscopic systems, at the frontiers between microscopic and macroscopic worlds. They display properties common to other such systems, as, for example, collective behaviours (superfluidity, deformation, vibrations or rotations), single-particle features (shell structure, clustering), as well as a strong interplay between the two. Atomic nuclei are thus great laboratories that can serve to learn about mesoscopic systems in general.

At the same time, nuclei exhibit specificities due, in part, to the presence of two types of particles (protons and neutrons) which are themselves non-elementary, to the non-perturbative character of the strong nuclear force (long-range residue of the strong interaction between internal quarks and gluons), and to the various types of excitation and decay modes via strong, electromagnetic or weak-interaction processes. Their study can thus also contribute to answering some of the most important questions in science, such as: What is the origin of the elements? How does matter organize and how do collective phenomena emerge from fundamental constituents? What are the fundamental symmetries of nature?


Multi-Body Entanglement and Information Rearrangement in Nuclear Many-Body Systems

S. Momme Hengstenberg, Caroline Robin , Martin Savage | arXiv:2306.16535 [nucl-th], Eur.Phys.J. A 59, 231 (2023)

The present work examines how effective-model-space calculations of nuclear many-body systems are able to rearrange and converge information and multi-particle entanglement. To this aim we considered the LMG model as a demonstration, which allowed us to understand and shed light on the accelerated convergence of classical and quantum simulations found in our previous study in terms of entanglement point of view. The method is based on a truncation of the Hilbert space together with a variational rotation of the relevant elementary degrees of freedom (qubits in this model), thereby defining an effective Hamiltonian. The rotated qubits were found to provide effective DoF exhibiting strongly-suppressed and fast-converging bi- and multi-partite entanglement measures, such as entanglement entropy, mutual information and n-tangles, while largely capturing the exact results with small model spaces.

This work provides insights motivating future studies in nuclear many-body systems that are closer to nature, and future developments of entanglement-driven descriptions of nuclei.

Quantum Simulations of SO(5) Many-Fermion Systems using Qudits

Marc Illa, Caroline Robin, Martin Savage | arXiv:2305.11941 [quant-ph]

The structure and dynamics of quantum many-body systems are the result of a delicate interplay between underlying interactions, which leads to intricate entanglement structures. Despite this apparent complexity, symmetries emerge and have long been used to determine the relevant degrees of freedom and simplify classical descriptions of these systems. In this paper, we explore the potential utility of quantum computers with arrays of qudits (d-level quantum systems) in simulating interacting fermionic systems with underlying symmetries, when the qudits can naturally map these relevant degrees of freedom. As an example, we consider the Agassi model of fermions which is based on an underlying so(5) algebra, with subsystems which can be partitioned into pairs of modes with five basis states, naturally embedding in arrays of d=5 qudits (qu5its). Classical noiseless simulations of the time evolution of systems of fermions embedded in up to twelve qu5its are performed using Google's cirq software. We find advantages in using qudits, as opposed to qubits. specifically in lowering the required quantum resources and reducing anticipated errors that take the simulation out of the physical space. A previously unrecognized sign problem has been identified from Trotterization errors in time evolving high-energy excitations. This has implications for quantum simulations in high-energy and nuclear physics, specifically of fragmentation and highly inelastic, multi-channel processes.

Quantum Simulations in Effective Model Spaces (I): Hamiltonian Learning-VQE using Digital Quantum Computers and Application to the Lipkin-Meshkov-Glick Model

Caroline Robin, Martin Savage | arXiv:2301.05976 [quant-ph], Phys.Rev.C 108, 024313 (2023).

In this work we explored the utility of effective model spaces in quantum simulations of non-relativistic quantum many-body systems, considering the Lipkin-Meshkov-Glick model of interacting fermions as an example. We introduced a new iterative hybrid-classical-quantum algorithm, Hamiltonian learning variational quantum eigensolver (HL-VQE), that simultaneously optimizes an effective Hamiltonian and the associated ground-state wavefunction. HL-VQE is found to provide an exponential improvement in Lipkin-Meshkov-Glick model calculations, compared to a naive truncation without Hamiltonian learning, throughout a significant fraction of the Hilbert space. Quantum simulations are performed to demonstrate the HL-VQE algorithm, using an efficient mapping where the number of qubits scales with the log of the size of the effective model space, rather than the particle number, allowing for the description of large systems with small quantum circuits. Implementations on IBM's QExperience quantum computers and simulators for 1- and 2-qubit effective model spaces are shown to provide accurate and precise results, reproducing classical predictions.

This work constitutes a step in the development of entanglement-driven quantum algorithms for the description of nuclear systems, that leverages the potential of noisy intermediate-scale quantum (NISQ) devices.

Entanglement Rearrangement in Self-Consistent Nuclear Structure Calculations

Caroline Robin, Martin J. Savage, Nathalie Pillet | arXiv:2007.09157 [nucl-th], Phys.Rev.C 103, 034325 (2021). Entanglement Rearrangement in 6He

The goal of this work was to begin investigating the entanglement properties of nuclei from first-principle nuclear many-body calculations. We studied entanglement features of single-particle orbitals within the nuclear ground state of 4He and 6He using a chiral two-body interaction. The patterns of entanglement emerging from different single-particle bases were compared, and possible links with the convergence of ground state energies were explored. Overall we found that orbitals derived from a variational principle (applied to the correlated ground state) display much more localized structures of entanglement within the basis, as compared to, for example, harmonic oscillator or Hartree-Fock orbitals. In particular, a core-valence structure clearly emerges from the full no-core calculation of 6He using the variational basis. The two-nucleon mutual information showed that this basis, which typically exhibits good convergence properties, effectively decouples the active and inactive spaces. In the future, such studies may be useful to develop more efficient entanglement-based many-body schemes, and may have benefits for designing hybrid classical-quantum computations of nuclei.