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Physical review. D/Physical review. D.

Three-flavor collective neutrino oscillation simulations on a qubit quantum annealer

Ivan A. Chernyshev

Published Feb 7, 2025• 5 citations
Publisher

Abstract

In extreme environments such as core-collapse supernovae, neutron-star mergers, and the early Universe, neutrinos are dense enough that their self-interactions significantly affect, if not dominate, their flavor dynamics. In order to develop techniques for characterizing the resulting quantum entanglement, I present the results of simulations of Dirac neutrino-neutrino interactions that include all three physical neutrino flavors and were performed on D-Wave Inc.'s Advantage $5000+$ qubit quantum annealer. These results are checked against those from exact classical simulations, which are also used to compare the Dirac neutrino-neutrino interactions to neutrino-antineutrino and Majorana neutrino-neutrino interactions. The D-Wave Advantage annealer is shown to be able to reproduce time evolution with the precision of a classical machine for small numbers of neutrinos and to do so without Trotter errors. However, it suffers from poor scaling in qubit-count with the number of neutrinos.

DOI
10.1103/physrevd.111.043017

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In extreme environments such as core-collapse supernovae, neutron-star mergers, and the early Universe, neutrinos are dense enough that their self-interactions significantly affect, if not dominate, their flavor dynamics. In order to develop techniques for characterizing the resulting quantum entanglement, I present the results of simulations of Dirac neutrino-neutrino interactions that include all three physical neutrino flavors and were performed on D-Wave Inc.'s Advantage 5000+5000+5000+ qubit quantum annealer. These results are checked against those from exact classical simulations, which are also used to compare the Dirac neutrino-neutrino interactions to neutrino-antineutrino and Majorana neutrino-neutrino interactions. The D-Wave Advantage annealer is shown to be able to reproduce time evolution with the precision of a classical machine for small numbers of neutrinos and to do so without Trotter errors. However, it suffers from poor scaling in qubit-count with the number of neutrinos.
In extreme environments such as core-collapse supernovae, neutron-star mergers, and the early Universe, neutrinos are dense enough that their self-interactions significantly affect, if not dominate, their flavor dynamics. In order to develop techniques for characterizing the resulting quantum entanglement, I present the results of simulations of Dirac neutrino-neutrino interactions that include all three physical neutrino flavors and were performed on D-Wave Inc.'s {\tt Advantage} 5000+ qubit quantum annealer. These results are checked against those from exact classical simulations, which are also used to compare the Dirac neutrino-neutrino interactions to neutrino-antineutrino and Majorana neutrino-neutrino interactions. The D-Wave {\tt Advantage} annealer is shown to be able to reproduce time evolution with the precision of a classical machine for small numbers of neutrinos and to do so without Trotter errors. However, it suffers from poor scaling in qubit-count with the number of neutrinos.
Collective neutrino flavor oscillations are of primary importance in understanding the dynamic evolution of core-collapse supernovae and subsequent terrestrial detection, but also among the most challenging aspects of numerical simulations. This situation is complicated by the quantum many-body nature of the problem due to neutrino-neutrino interactions which demands a quantum treatment. An additional complication is the presence of three flavors, which often is approximated by the electron flavor and a heavy lepton flavor. In this work, we provide both qubit and qutrit encodings for all three flavors, and develop optimized quantum circuits for the time evolution and analyze the Trotter error. We conclude our study with a hardware experiment of a system of two neutrinos with superconducting hardware: the IBM Torino device for qubits and AQT device for qutrits. We find that error mitigation greatly helps in obtaining a signal consistent with simulations. While hardware results are comparable at this stage, we expect the qutrit setup to be more convenient for large-scale simulations since it does not suffer from probability leakage into nonphsycial qubit space, unlike the qubit setup.
We simulate a self-interacting three-flavor neutrino system within a core-collapse supernova using a hybrid classical-quantum algorithm on a qutrit computer. Based on the Dirac-Frenkel evolution equations, we employ a variation of the quantum-assisted simulator to calculate the system's time evolution operator by performing qutrit Hadamard tests to find expectation values of unitary operators in the Hamiltonian. The time evolution simulation is then done classically. We find that the hybrid algorithm produces results comparable to an exact numerical integration out to times of t≈30 ω0−1t \approx 30 \,ω_0^{-1}t≈30ω0−1​ with time step δt=0.005 ω0−1δt = 0.005 \,ω_0^{-1}δt=0.005ω0−1​, where ω0ω_0ω0​ is the energy scale of the single neutrino vacuum oscillations. We discuss the lessons learned in simulating neutrino systems using this hybrid quantum-classical algorithm, along with the advantages it offers over quantum Trotterization.
In astrophysical scenarios with large neutrino density, like supernovae and the early universe, the presence of neutrino-neutrino interactions can give rise to collective flavor oscillations in the out-of-equilibrium collective dynamics of a neutrino cloud. The role of quantum correlations in these phenomena is not yet well understood, in large part due to complications in solving for the real-time evolution of the strongly coupled many-body system. Future fault-tolerant quantum computers hold the promise to overcome much of these limitations and provide direct access to the correlated neutrino dynamic. In this work, we present the first simulation of a small system of interacting neutrinos using current generation quantum devices. We introduce a strategy to overcome limitations in the natural connectivity of the qubits and use it to track the evolution of entanglement in real-time. The results show the critical importance of error-mitigation techniques to extract meaningful results for entanglement measures using noisy, near term, quantum devices.
We explore the utility of qutrits and qubits for simulating the flavor dynamics of dense neutrino systems. The evolution of such systems impacts some important astrophysical processes, such as core-collapse supernovae and the nucleosynthesis of heavy nuclei. Many-body simulations require classical resources beyond current computing capabilities for physically relevant system sizes. Quantum computers are therefore a promising candidate to efficiently simulate the many-body dynamics of collective neutrino oscillations. Previous quantum simulation efforts have primarily focused on properties of the two-flavor approximation due to their direct mapping to qubits. Here, we present new quantum circuits for simulating three-flavor neutrino systems on qutrit- and qubit-based platforms, and demonstrate their feasibility by simulating systems of two, four, and eight neutrinos on IBM and Quantinuum quantum computers.
We simulate three-flavor neutrino oscillations on two-qubit quantum circuits. The flavor space is embedded as ∣00⟩=νe\ket{00}=ν_e∣00⟩=νe​, ∣01⟩=νμ\ket{01}=ν_μ∣01⟩=νμ​, ∣10⟩=ντ\ket{10}=ν_τ∣10⟩=ντ​ with the ∣11⟩\ket{11}∣11⟩ channel kept inert, and the input mixing parameters (NuFIT~5.3, normal ordering, with SK-atm) follow the global fit. We verify three physical settings against analytic or exact references: vacuum propagation, reproduced by a mass-eigenstate phase circuit to ∼10−16\sim 10^{-16}∼10−16; constant-density Mikheev--Smirnov--Wolfenstein (MSW) matter effects, showing resonant flavor conversion when the matter potential AAA crosses Δm312Δm^2_{31}Δm312​; and varying-density (supernova shock-shell) propagation by slicing plus second-order Suzuki--Trotter splitting, with per-slice Trotter error ∼10−6\sim 10^{-6}∼10−6 and total accuracy ∼10−4\sim 10^{-4}∼10−4 against the continuous profile. We report a Suzuki--Trotter precision--resource calibration varying order, step number, and matrix/probability error. It delimits brute-force Trotterization on solar baselines: we quantify both standard alternatives, coherence averaging and adiabatic MSW. We also compute quantum-information diagnostics from the same model parameters, namely mode entanglement and the CP asymmetry. Finally, we extend the framework to open quantum systems via a Lindblad master equation with dephasing and absorptive channels. These results provide a reproducible link between low-energy oscillation observables and quantum-information measures.