Quantum Complexity Fluctuations from Nuclear and Hypernuclear Forces

TL;DR

This paper introduces the concept of quantum magic (non-stabilizerness) and defines the magic power of the S-matrix, $\overline{\mathcal{M}}(\hat{\mathbf S})$, as a resource diagnostic for fault-tolerant quantum simulations of nuclei and dense matter. By mapping NN and YN scattering channels to one- and two-qubit systems and using experimental phase shifts (e.g., Nijm93, N2LO χEFT), it quantifies how tensor and spin interactions generate or suppress magic and entanglement across energy. Key findings include a tensor-driven magic in the deuteron allowing $\mathcal{M}\approx0.17$ (with potential up to $0.25$ in idealized cases), and a striking, energy-stable maximum of magic in $\Sigma^-n$ scattering suggesting possible catalysis of entanglement growth in dense exotic matter, contrasted by suppressed magic in $\Lambda p$. The results connect nuclear physics data to quantum resource theory, offering a framework to estimate the classical versus quantum computational costs of simulating nuclei and dense hadronic matter in a fault-tolerant regime.

Abstract

Toward an improved understanding of the role of quantum information in nuclei and exotic matter, we examine the quantum magic (non-stabilizerness) in low-energy strong interaction processes. As stabilizer states can be prepared efficiently using classical computers, and include classes of entangled states, it is quantum magic and fluctuations in quantum magic, together with entanglement, that determine computational resource requirements. As a measure of fluctuations in quantum magic, and hence the severity of the exponentially-scaling classical computing resource requirements, induced by scattering, the "magic power" of the S-matrix is introduced. This provides indirect experimental constraints on quantum resources required to model nuclei and dense matter using fault-tolerant quantum computers. Using experimentally-determined scattering phase shifts and mixing parameters, the magic power in nucleon-nucleon and hyperon-nucleon scattering, along with the magic in the deuteron, are found to exhibit interesting and distinct features. The $Σ^-$-baryon is identified as a potential candidate catalyst for enhanced spreading of magic and entanglement in dense matter, depending on in-medium decoherence.

Figures (6)

• Figure 1: The magic power $\overline{\mathcal{M}}({\hat{\bf S}}_{(J=1)})$ in $np$ scattering in the ${}^3 S_1$-${}^3 D_1$ coupled channels determined using Eq. \ref{['eq:Magic_Power']}, as a function of laboratory momentum p$_{\rm lab}$. The blue curve shows the full result using the Nijm93 phase-shift analysis PhysRevC.49.2950NNonline, while the orange curve corresponds to the limit $\overline{\epsilon}_1 =\overline{\delta}_2=0$.
• Figure 2: The magic power $\overline{\mathcal{M}}(\hat{\bf S})$ (left panel) and entanglement power $\overline{\mathcal{E}}(\hat{\bf S})$ (right panel) of the S-matrix in the spin degrees of freedom in $np$ scattering as a function of the momentum p$_{\rm lab}$ in the laboratory frame. The phase shifts are those from the Nijm93 parametrization PhysRevC.49.2950, obtained from Ref. NNonline. The groups $i'$ are restricted to the tensor-product states of groups $i$, respectively.
• Figure 3: Magic power $\overline{\mathcal{M}}(\hat{\bf S})$ (left panel) and entanglement power $\overline{\mathcal{E}}(\hat{\bf S})$ (right panel) in $\Sigma^-n$ and $\Lambda$p scattering, obtained using N2LO-$\chi$EFT phase shifts from Ref. Haidenbauer:2023qhf. We have assumed isospin symmetry between $\Sigma^+p$ and $\Sigma^-n$, and neglected Coulomb interactions. The uncertainty bands represent the maximum and minimum values in magic and entanglement derived from the N2LO phase-shift uncertainty bands Haidenbauer:2023qhf.
• Figure 4: Contributions of the six one-qubit stabilizer states to the magic power $\overline{\mathcal{M}}({\hat{\bf S}}_{(J=1)})$ in $np$ scattering in the $J=1$ coupled ${}^3 S_1$-${}^3 D_1$ channels as a function of laboratory momentum p$_{\rm lab}$, obtained with the Nijm93 phase shifts PhysRevC.49.2950NNonline.
• Figure 5: Contributions of different stabilizers states to the magic power $\overline{\mathcal{M}}(\hat{\bf S})$ and entanglement power $\overline{\mathcal{E}}(\hat{\bf S})$ of the S-matrix in $\Sigma^- n$ scattering (top two panels) and $\Lambda p$ scattering (bottom two panels). These results have been obtained using N2LO-$\chi$EFT phase shifts from Ref. Haidenbauer:2023qhf. For the magic power, group-1 contains 16 states, group-2 contains 12 states and group-3 contains 32 states. For the entangling power, only the tensor-product stabilizer states of each group are included, (denoted with a prime). Thus, group-1$'$ contains 6 states, group-2$'$ contains 6 states and group-3$'$ contains 24 states. We have assumed isospin symmetry between $\Sigma^+p$ and $\Sigma^-n$, and neglected Coulomb interactions. The uncertainty bands represent the maximum and minimum values in magic and entanglement derived from the N2LO phase-shift uncertainty bands Haidenbauer:2023qhf.