Quantum ManyBody Physics and Quantum Computing Research at Bielefeld University
We are working on the development of methods for solving the quantum manybody problem, in order to describe the structure and dynamics of stronglyinteracting 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 entanglementdriven 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 manybody 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 manybody 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), singleparticle 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 nonelementary, to the nonperturbative character of the strong nuclear force (longrange residue of the strong interaction between internal quarks and gluons), and to the various types of excitation and decay modes via strong, electromagnetic or weakinteraction 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?
RECENT RESEARCH WORKS:
The Magic in Nuclear and Hypernuclear Forces
Caroline Robin and Martin Savage 
arXiv:2405.10268 [nuclth] (2024)
Toward an improved understanding of the role of quantum information in nuclei and exotic matter, we examine the magic (nonstabilizerness) in lowenergy strong interaction processes. As stabilizer states can be prepared efficiently using classical computers, and include classes of entangled states, it is magic and fluctuations in magic, along with entanglement, that determine resource requirements for quantum simulations. As a measure of fluctuations in magic induced by scattering, the "magic power" of the Smatrix is introduced. Using experimentallydetermined scattering phase shifts and mixing parameters, the magic power in nucleonnucleon and hyperonnucleon scattering, along with the magic in the deuteron, are found to exhibit interesting features. The Σ baryon is identified as a potential candidate catalyst for enhanced spreading of magic and entanglement in dense matter, depending on inmedium decoherence.
Qu8its for Quantum Simulations of Lattice Quantum Chromodynamics
Marc Illa, Caroline E. P. Robin, Martin J. Savage 
arXiv:2403.14537 [quantph]
We explore the utility of d = 8 qudits, qu8its, for quantum simulations of the dynamics of 1+1D
SU(3) lattice quantum chromodynamics, including a mapping for arbitrary numbers of flavors and
lattice size and a reorganization of the Hamiltonian for efficient timeevolution. Recent advances
in parallel gate applications, along with the shorter application times of singlequdit operations
compared with twoqudit operations, lead to significant projected advantages in quantum simulation
fidelities and circuit depths using qu8its rather than qubits. The number of twoqudit entangling
gates required for time evolution using qu8its is found to be more than a factor of five fewer than for
qubits. We anticipate that the developments presented in this work will enable improved quantum
simulations to be performed using emerging quantum hardware.
MultiBody Entanglement and Information Rearrangement in Nuclear ManyBody Systems
S. Momme Hengstenberg, Caroline E. P. Robin, Martin J. Savage 
arXiv:2306.16535 [nuclth], Eur. Phys. J. A 59, 231 (2023)
The present work examines how effectivemodelspace calculations of nuclear manybody systems are able to rearrange and converge information and multiparticle 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 stronglysuppressed and fastconverging bi and multipartite entanglement measures, such as entanglement entropy, mutual information and ntangles, while largely capturing the exact results with small model spaces.
This work provides insights motivating future studies in nuclear manybody systems that are closer to nature, and future developments of entanglementdriven descriptions of nuclei.
Quantum Simulations of SO(5) ManyFermion Systems using Qudits
Marc Illa, Caroline E. P. Robin, Martin J. Savage 
arXiv:2305.11941 [quantph], Phys. Rev. C 108, 064306 (2023)
The structure and dynamics of quantum manybody 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 (dlevel 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 highenergy excitations. This has implications for quantum simulations in highenergy and nuclear physics, specifically of fragmentation and highly inelastic, multichannel processes.
Quantum Simulations in Effective Model Spaces (I): Hamiltonian LearningVQE using Digital Quantum Computers and Application to the LipkinMeshkovGlick Model
Caroline Robin, Martin J. Savage 
arXiv:2301.05976 [quantph], Phys.Rev.C 108, 024313 (2023).
In this work we explored the utility of effective model spaces in quantum simulations of nonrelativistic quantum manybody systems, considering the LipkinMeshkovGlick model of interacting fermions as an example.
We introduced a new iterative hybridclassicalquantum algorithm, Hamiltonian learning variational quantum eigensolver (HLVQE), that simultaneously optimizes an effective Hamiltonian and the associated groundstate wavefunction.
HLVQE is found to provide an exponential improvement in LipkinMeshkovGlick 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 HLVQE 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 2qubit effective model spaces are shown to provide accurate and precise results, reproducing classical predictions.
This work constitutes a step in the development of entanglementdriven quantum algorithms for the description of nuclear systems, that leverages the potential of noisy intermediatescale quantum (NISQ) devices.
Entanglement Rearrangement in SelfConsistent Nuclear Structure Calculations
Caroline Robin, Martin J. Savage, Nathalie Pillet 
arXiv:2007.09157 [nuclth], Phys.Rev.C 103, 034325 (2021).
The goal of this work was to begin investigating the entanglement properties of nuclei from firstprinciple nuclear manybody calculations. We studied entanglement features of singleparticle orbitals within the nuclear ground state of 4He and 6He using a chiral twobody interaction. The patterns of entanglement emerging from different singleparticle 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 HartreeFock orbitals. In particular, a corevalence structure clearly emerges from the full nocore calculation of 6He using the variational basis. The twonucleon 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 entanglementbased manybody schemes, and may have benefits for designing hybrid classicalquantum computations of nuclei.
TEACHING:
Teaching at Bielefeld University:
More information can be found here

Summer 22, 23 & 24: Quantum Computing

Winter 20/21: Nuclear Physics

Summer 20 and Winter 20/21: Quantum Information for Nuclear Physics (student seminar)
Schools:
Euroschool for exotic beams 2021 Three lectures on The Nuclear ManyBody Problem Beyond Mean Field