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arxiv: 2604.26376 · v1 · submitted 2026-04-29 · 🪐 quant-ph · hep-lat· hep-ph· nucl-th

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Quantum Complexity and New Directions in Nuclear Physics and High-Energy Physics Phenomenology

Caroline E. P. Robin , Martin J. Savage
Authors on Pith no claims yet

Pith reviewed 2026-05-07 13:20 UTC · model grok-4.3

classification 🪐 quant-ph hep-lathep-phnucl-th
keywords quantum information sciencenuclear physicshigh-energy physicsquantum simulationsmany-body systemshadronsnucleiphenomenology
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The pith

Quantum information science is defining new frontiers in nuclear and high-energy physics through complexity insights into many-body systems.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper examines how advances in quantum information science offer new ways to analyze the complexity of quantum many-body systems in nuclear and high-energy physics. It describes the development of analytic frameworks and algorithms, both classical and quantum, that aim to overcome current obstacles in these fields. These methods are expected to illuminate the structure and dynamics of particles and nuclei, and to guide the use of quantum simulations on large scales. Readers would be interested because this integration could lead to breakthroughs in simulating systems that are currently computationally challenging.

Core claim

Advances in quantum information science are providing transformative insights into the complexity of quantum many-body systems, defining new frontiers in nuclear and high-energy physics. QIS-derived techniques are fostering new analytic frameworks and algorithms to tackle barriers to discovery, shedding light on hadrons, nuclei, and matter in extreme conditions, and playing an essential role in large-scale quantum simulations by balancing quantum and classical resources.

What carries the argument

QIS techniques for analyzing quantum complexity in many-body systems, applied to create new frameworks and algorithms for nuclear and high-energy physics phenomenology.

If this is right

  • New analytic frameworks and algorithms from QIS will address barriers in fundamental physics.
  • Insights will emerge on the structure and dynamics of hadrons, nuclei, and extreme matter.
  • Large-scale quantum simulations will be developed with an optimal balance of quantum and classical resources.
  • The techniques will apply to other science domains beyond physics.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Such approaches might allow simulations of nuclear reactions under conditions impossible to replicate in labs.
  • Cross-pollination could accelerate progress in related areas like quantum chemistry or materials science.
  • Future work may focus on identifying specific QIS algorithms most suited to particular nuclear physics problems.

Load-bearing premise

That techniques from quantum information science will successfully create new frameworks and algorithms able to overcome the current barriers in nuclear and high-energy physics research.

What would settle it

Computational tests or experiments showing that QIS-based methods fail to improve simulation accuracy or yield new physical insights for hadrons and nuclei beyond existing classical approaches.

Figures

Figures reproduced from arXiv: 2604.26376 by Caroline E. P. Robin, Martin J. Savage.

Figure 1
Figure 1. Figure 1: Left: 8-qubit graph (LC equivalent to a stabilizer) state with volume-law entanglement entropy. The vertices represent the qubits and edges represent entanglement between them created by the CZ gates in Eq. (5). Right: Arbitrary 8-qubit state (schematic) with entanglement and magic. The magic creates complex (non-regular) patterns of entanglement view at source ↗
Figure 2
Figure 2. Figure 2: Artist view of the lattice of stabilizer states mapping a finite many-body Hilbert space. distribution [106–108]. For qudit systems with dimension equal to the power of a prime number, stabilizer states form a 2-design, reproducing Haar averages up to second order only [107]. In order to attain non-stabilizer states, and fill the gaps in the Hilbert space, it is necessary to introduce some amount of non-st… view at source ↗
Figure 3
Figure 3. Figure 3: Entanglement-magic diagram (schematic) and hardness of classical simulations. The light blue regions denote regions of the Hilbert space that are easy to represent, while the darker regions represent states with higher complexity. States with low (area law) entanglement (near the y axis) may be described efficiently with tensor networks (TNs) while states with low magic and arbitrary entanglement entropy (… view at source ↗
Figure 4
Figure 4. Figure 4: Pauli distribution of a 12-qubit stabilizer state (left) and an arbitrarily selected state with non-zero magic (right). Only non-zero Pauli string expectation values are shown view at source ↗
Figure 5
Figure 5. Figure 5: (a) M2(∣ψ⟩) of a single qubit state ∣ψ⟩ = cos (θ/2) ∣0⟩+ e iϕ sin(θ/2) ∣1⟩ on the Bloch sphere. (b) Special states on the Bloch sphere: Stabilizer states ∣0⟩, ∣1⟩, ∣+⟩, ∣−⟩, ∣+i⟩, ∣−i⟩ (blue points) occupy the vertices of an octahedron, T-type states ∣T⟩ (red points) possess maximal magic M2 = log2 (3/2) ≃ 0.585, while H-type states ∣H⟩ are associated with the most probable value of M2 = log2 (4/3) ≃ 0.415… view at source ↗
Figure 6
Figure 6. Figure 6: Flat (left) versus non-flat (right) bipartite entanglement spectra. Both spectra yields the same von Neumann entangle￾ment entropy S ≃ 3.322 (calculated here with log2 ). The total linear magic Mlin, with M2 = −log(1−Mlin), is directly proportional to the anti-flatness averaged over Clifford orbits [186] ⟨FA(Γˆ ∣ψ⟩AB)⟩C = c(d, dA) Mlin(∣ψ⟩AB) , (30) where the left-hand side is the anti-flatness of Γˆ ∣ψ⟩AB… view at source ↗
Figure 7
Figure 7. Figure 7: GSE per qudit as a function of the qudit T-gate doping rate q, for different qudit local dimensions (dloc = 3, 5, 11) and system sizes N. The value qc(dloc) denotes the critical doping rate, at which the GSE density saturates. For N → ∞ the GSE saturates to the Haar value log(dloc). [Figure from Ref. [188] used with permission from the authors under Creative Commons Attribution 4.0 International license [1… view at source ↗
Figure 8
Figure 8. Figure 8: The upper panel shows (a): phase transitions in en￾tanglement; and (b): possible phase transitions in entangle￾ment and nonstabilizerness. The lower panel shows the magic￾entanglement phase diagram observed in Ref. [192], with the new transition between regions II and III. [Figure adapted from Ref. [192] with permission from the authors under Creative Commons Attribution 4.0 International license [175].] T… view at source ↗
Figure 9
Figure 9. Figure 9: The renormalization flow of non-local linear magic, anti-flatness and entanglement entropy for Gaussian (upper panel) and Hadamard (lower panel) smearing. A set of 200 6- qubit Haar-random states was selected and flowed by successive Gaussian smearing (from 0 to 2 6 applications of a width=1 Gaussian profile) or Hadamard transform truncations over a finite interval (by subtracting 2, 4, 8, 16, 32 and 55 st… view at source ↗
Figure 10
Figure 10. Figure 10: Resources characterizing the computational complexity of quantum many-body states: entanglement, non-stabilizerness (magic), and non-Gaussianity. Figure inspired by Ref. [211]. Characterizing the detailed structures of entanglement, magic and/or non-Gaussian features of physical states of interest reveals how far they lie from easy, classically￾tractable states, and allows for locating them relative to di… view at source ↗
Figure 13
Figure 13. Figure 13: Magic power M(Sˆ) (left panel) and entanglement power E(Sˆ) (right panel) in Σ −n and Λp scattering, obtained us￾ing N2LO-χEFT phase shifts from Ref. [252]. Isospin symmetry between Σ + p and Σ −n has been assumed, and Coulomb inter￾actions have been neglected. The uncertainty bands represent the maximum and minimum values in magic and entanglement derived from the N2LO phase-shift uncertainty bands [252]… view at source ↗
Figure 12
Figure 12. Figure 12: Entanglement power E(Sˆ) (turquoise), total magic power M(Sˆ) (pink), and non-local magic power M(NL)(Sˆ) (orange), for low-energy s-wave nucleon-nucleon scattering as a function of momentum in the laboratory [52,53], obtained from Nijmegen phase shifts [250, 251] view at source ↗
Figure 14
Figure 14. Figure 14: Entanglement powers for the np (upper panel a)) and nn (lower panel b)) systems as a function of the scattering angle θc.m. and momentum p in the center-of-mass frame. The displayed results are obtained using the WPC potential from Ref. [265] at different orders in the chiral expansion, and using the phenomenological NijmI potential from Ref. [250]. [Figure adapted from Ref. [245] with permission from the… view at source ↗
Figure 15
Figure 15. Figure 15: Singular value spectra of the neutron-proton 1S0 partial wave for the SRG-evolved (a) Entem-Machleidt (EM) interaction derived from χEFT [271] and (b) phenomenological AV18 interaction [272] at different resolution scales λ. [Figure reproduced from Ref. [266] with permission from the authors and the American Physical Society.] 3.2 Many-Body Nuclear Structure As prime example of mesoscopic systems, atomic … view at source ↗
Figure 17
Figure 17. Figure 17: Proton-neutron entanglement entropy in N = Z sd￾shell nuclei as a function of total nucleon number A= N + Z. The entropies are calculated with the natural logarithm Spn ≡ Sentangled = −Tr (ρν lnρν). The black curve shows the maximum possible entanglement entropy S max pn based on dimensionalities. The left panel shows the entanglement Spn for the high-quality empirical interaction USDB [276], as well as f… view at source ↗
Figure 16
Figure 16. Figure 16: Singular values sj (eigenvalues of ρν) for ground states of a few nuclei in the sd and pf shells. The dimension of the proton many-body space is denoted dp, which corresponds to dπ in the main text. Note that 20Ne, 24Mg and 28Si have N = Z. [Figure reproduced from Ref. [55] with permission from the authors and the American Physical Society.] as somewhat surprising, as nuclei with similar numbers of proton… view at source ↗
Figure 18
Figure 18. Figure 18: for the Mg isotopic chain, and attributed to the spreading of neutron occupation number, thus fragmenting the many-body wave function and increasing entanglement entropies. The correlations reflected in the fractional oc￾cupations number indeed signal information sharing with other components of the system, which appears to be facil￾itated in the proton-neutron channel. Intuitively, this can be understood… view at source ↗
Figure 19
Figure 19. Figure 19: The proton-neutron interaction unlocks more com￾munication channels than in the proton-proton and neutron￾neutron sector. Orbital entanglement: from few to many, towards the emergence of collectivity The bipartite proton-neutron entanglement studied above has allowed for connections between tra￾ditional concepts in nuclear structure and entanglement properties of shell-model nuclei, which in turn has moti… view at source ↗
Figure 20
Figure 20. Figure 20: Left: Total one-orbital neutron entropies I ν tot = ∑ Mν i=1 Si where Si = −Tr (ρi lnρi), from valence-space DMRG calculations for the oxygen chain (Z = 8). The low entropy reveals the emergence of the shell closure at N = 16, indicated by the dashed vertical line. To a lesser extent, the sub-shell closure at N = 14 also appears. The lighter symbols show the results for odd-mass nuclei. Right: Total proto… view at source ↗
Figure 21
Figure 21. Figure 21: Upper: Network representations of 8-orbital entangle￾ment in the ground state of 26Ne (Z = 10, N = 16) and 24Mg (Z = 12, N = 12), known to be spherical and prolate, respec￾tively. The nodes show the proton (red) and neutron (blue) orbitals. The values of the edges, representing the entanglement, are given by e (8) i1i2 = ∑i3<i4<i5<i6<i7<i8 τ (8) (i1,i2,i3,i4,i5,i6,i7,i8) and are indicated by both the dark… view at source ↗
Figure 22
Figure 22. Figure 22: Non-stabilizerness (magic) M2, n = 4, 6, 8-tangles τ¯ (n) πν in the proton-neutron sector, and axial deformation parameter β, in even-even Mg nuclear ground states, as a function of total nucleon number A. The values of β were taken from Summary Tables [297] reproduced at the website [298]. Each quantity has been normalized to its maximum value in the chain. [Figure adapted from Ref. [69] used with permis… view at source ↗
Figure 23
Figure 23. Figure 23: Full-state magic M2 and bi-partite proton-neutron non-local magic Mpn,NL 2 of sd-shell nuclear ground states. The calculations are performed using the minimum value of the angular momentum projection Jz = Jz,min for a given ground state [178]. As mentioned in section 2.3, the concept of non-local (NL) magic has been recently introduced in Ref. [34] in order to capture the interplay between entanglement an… view at source ↗
Figure 24
Figure 24. Figure 24: Complexity diagram of the LMG model. The red curve shows the magic quantified by 2-SRE density, the plain black and dashed gray curves display the single spin (or one-orbital) entropy and N-tangle, respectively. The darker shaded area corresponds the the region of high complexity, with both high￾entanglement and extensive magic, while the lighter regions correspond to low-complexity ground states: unentan… view at source ↗
Figure 25
Figure 25. Figure 25: One-body entanglement entropy in the fission process of 235U(n, f) induced by a low-energy neutron, as a function of time. The solid (resp. dashed) curves correspond to entropies evaluated without (resp. with) projection onto particle number of the total many-body wave function. The black and red curves differ in their treatment of the initial state of the compound nucleus. See Ref. [293] for more details… view at source ↗
Figure 26
Figure 26. Figure 26: The two-neutron-orbital mutual information in 6He using a harmonic oscillator basis (bottom) and natural orbitals self-consistently optimized with two-body correlations (top). The calculations are performed in an ab-initio framework, in an active space with all particles active (no frozen core). As the basis is optimized, information is rearranged into a small number of orbitals. The figure is adapted fro… view at source ↗
Figure 27
Figure 27. Figure 27: Absolute error in the binding energy from the PANASh algorithm, as a function of the relative proton-neutron entangle￾ment entropy (ratio of the calculated entropy over the maximal value allowed by dimensional considerations). States with higher excitation energy are shaded darker. The even-even nuclei 78Ge and 60Ni are deformed and spherical, respectively, while 70As is odd-odd and deformed, and 79Rb is … view at source ↗
Figure 28
Figure 28. Figure 28: This trend was present independently of the width view at source ↗
Figure 30
Figure 30. Figure 30: A depiction of high-energy gluon-gluon elastic scatter￾ing. The indices are color, momentum and Lorentz, respectively. the Yang-Mills Lagrange density, LYM = − 1 4 8 ∑ a=1 G a µνG a,µν , G a µν = ∂µA a ν − ∂νA a µ + gf abcA b µA c ν , (61) where f abc are SU(3) structure constants, g is the QCD coupling constant and A d α is the gluon field. The two helic￾ity states of a gluon, being massless vector parti… view at source ↗
Figure 31
Figure 31. Figure 31: The concurrence and M2 magic of gluon-gluon scattering from an initial helicity state ∣+,−⟩ as a function of center-of-momentum scattering angle, θ [415], from Eq. (62). Non-local magic generation in these processes has been recently considered [416], motivated by the desire for ba￾sis independent measures of quantum complexity. It was found that the helicity basis is optimal for considering the quantum c… view at source ↗
Figure 32
Figure 32. Figure 32: A summary of the results of simulations of non￾separability in the spins of τ + τ − produced in pp → τ + τ −X [424] for the LHC. [Figure from Ref. [424] used with permission from the authors under Creative Commons Attribution 4.0 International license [175].] 300−400 400−600 600−800 > 800 m(tt) [GeV] 0 0.2 0.4 0.6 0.8 1 1.2 1.4 2 ~M Data stat, total unc. Powheg+P8 Powheg+H7 MG5+P8 MiNNLO+P8 (13 TeV) -1 13… view at source ↗
Figure 33
Figure 33. Figure 33: shows the experimentally determined mixed￾15 For a more general discussion of separability in mixed (Werner) states, see Ref. [421]. 16 Machine learning played an important role in neutrino reconstruction in the numerical simulations view at source ↗
Figure 34
Figure 34. Figure 34: A schematic of the partitioning between valence and sea quarks comprising a hadron [437, 438]. The solid lines denote correlations between hadrons that have been partitioned between valence and sea spaces, denoted by Regions A and B. where the correspondence between the qubit states and the chiral multiplets can be found in Ref. [437]. The valence￾quark contribution to the nucleon spin, 1 2∆Σ, the axial￾c… view at source ↗
Figure 35
Figure 35. Figure 35: The real-time evolution of entanglement entropy and anti-flatness [62] of a two-plaquette subsystem of an asymmetric seven-plaquette system with jmax = 1 for a highly excited initial state chosen at random that lies 19.17 l.u. above the ground state. [Figure reproduced from Ref. [62] with permission from the authors.] the presence of complexity barriers during time evolution of a general out-of-equilibriu… view at source ↗
Figure 37
Figure 37. Figure 37: The vacuum-subtracted total (left) and non-local (right) RoM among the e − and e + in the Schwinger model as a function of separation between static background charges, d, between a spatial site at the center of the string and a site at distance r [67]. The parameters of the (classical) simulations were such that both lattice-spacing artifacts and finite-volume effects are estimated to be small. The dashe… view at source ↗
Figure 38
Figure 38. Figure 38: A schematic of a post off-axis collision of two high￾energy (Lorentz contracted) heavy-ions (red and blue regions). Hard and co-linear partons continue down the beam-line (par￾tition Region-B), while (some of) the soft central modes, trans￾verse to the beam axis) enter the detection regions (partition Region-A) [511]. It has been suggested, using simple 1+1D models, that quantum correlations in particular… view at source ↗
Figure 39
Figure 39. Figure 39: shows the results of this evolution, for the magic M2 and 4-tangle for an initial pure state of ∣νe⟩ ⊗5 and multi-flavored state ∣ντ νµνeντ νµ⟩ (assuming the normal mass hierarchy). It is particularly interesting to examine the behavior of the magic per neutrino asymptotically in time, with increasing system size for different initial conditions view at source ↗
Figure 40
Figure 40. Figure 40: The asymptotic magic per neutrino as a function of the number of neutrinos for initial states with only νe, and for initial states with all three flavors, determined from multi￾qutrit simulations [68]. The dotted horizontal lines denotes maximum magic density that can be supported by a tensor￾product state. [Image adapted from from Ref. [68] used under Creative Commons Attribution 4.0 International licens… view at source ↗
Figure 41
Figure 41. Figure 41: The upper panel shows the total linear magic as a function of the entanglement entropy (points) in 2-qubit wavefunctions from 4K random samples from the SU(4) Haar measure, and the curve corresponds to the non-local linear magic. The lower panel shows the linear magic as a function of the non-local linear magic (points), along with a straight line with unit slope. magic, which provides a lower bound to th… view at source ↗
Figure 42
Figure 42. Figure 42: The upper panel shows the 2-tangle (same as the concurrence) versus the entanglement entropy for 10K two￾qutrit states randomly selected from the SU(9) Haar measure. The lower panel shows the generalized concurrence versus the 2-tangle (the concurrence and the 2-tangle are found to be equal). Thirty-six of these states are tensor products formed from one-qubit stabilizers, while the remaining twenty-four … view at source ↗
Figure 43
Figure 43. Figure 43: The upper panel shows the anti-flatness versus the non￾local linear magic for 10K two-qutrit states randomly selected from the SU(9) Haar measure. The lower panel shows the total linear versus the non-local linear magic view at source ↗
Figure 44
Figure 44. Figure 44: The total and non-local linear magic versus the en￾tanglement entropy for 10K two-qutrit states randomly selected from the SU(9) Haar measure view at source ↗
read the original abstract

Advances in quantum information science (QIS) are providing transformative insights into the complexity of quantum many-body systems, potentially defining new frontiers in nuclear and high-energy physics. This review explores how QIS-derived techniques are fostering new analytic frameworks and algorithms - both classical and quantum - to tackle (some of the) present barriers to discovery in fundamental physics, with applicability to other science domains. We highlight how these techniques are shedding new light on the structure and dynamics of hadrons, nuclei, matter in extreme conditions, and beyond. Importantly, they are expected to play an essential role in the development of large-scale quantum simulations of such systems, particularly in setting the balance among quantum and classical computational resources.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

0 major / 1 minor

Summary. This review article surveys the emerging intersections between quantum information science (QIS) and nuclear/high-energy physics phenomenology. It claims that QIS advances are supplying transformative insights into the complexity of quantum many-body systems, thereby fostering new analytic frameworks and both classical and quantum algorithms to address longstanding barriers in fundamental physics. The manuscript highlights applications to hadron and nuclear structure, dynamics under extreme conditions, and the anticipated role of QIS methods in large-scale quantum simulations that optimally balance quantum and classical resources.

Significance. If the synthesis is accurate, the paper offers a timely, high-level map of how QIS concepts are being imported into nuclear and HEP phenomenology. Its value lies in collating disparate literature strands into a coherent narrative that could guide experimentalists and theorists toward productive cross-disciplinary questions. The explicitly cautious language (advances are 'providing transformative insights' and 'potentially defining new frontiers'; techniques are 'expected to play an essential role') is a strength, as it avoids overstating current capabilities while still identifying plausible future directions.

minor comments (1)
  1. The abstract states that QIS techniques are 'shedding new light on the structure and dynamics of hadrons, nuclei, matter in extreme conditions, and beyond,' yet the manuscript would benefit from a short table or bulleted list in the introduction that explicitly maps the QIS concepts (e.g., entanglement measures, variational quantum algorithms) to the specific nuclear/HEP observables discussed later.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive and insightful review of our manuscript. We are pleased that the synthesis of QIS advances with nuclear and high-energy physics phenomenology was found timely and valuable, and we appreciate the recognition of our cautious language regarding current capabilities and future directions.

Circularity Check

0 steps flagged

No significant circularity in review synthesis

full rationale

This is a review article synthesizing QIS literature for applications in nuclear and HEP phenomenology. It advances no derivations, equations, predictions, fitted parameters, or new theorems. Claims use explicitly forward-looking and cautious phrasing (e.g., 'potentially defining new frontiers', 'expected to play an essential role') rather than asserting demonstrated results. No load-bearing steps reduce by construction to inputs or self-citations; the content rests on external benchmarks and existing work. This is the standard honest non-finding for a synthesis paper with no internal derivation chain.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

As a review paper, the content rests on cited literature in quantum information science and nuclear/high-energy physics rather than introducing new free parameters, axioms, or invented entities.

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Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. The nonlocal magic of a holographic Schwinger pair

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    Holographic Schwinger pair creation generates nonlocal magic for spacetime dimensions d>2, as shown by a non-flat entanglement spectrum that can be read from the probe brane free energy.

Reference graph

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