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arXiv:2207.03189 · Physical review. D/Physical review. D.

Trapped-ion quantum simulation of collective neutrino oscillations

Valentina Amitrano, Alessandro Roggero, Piero Luchi, Francesco Turro, Luca Vespucci, Francesco Pederiva

Published Jan 13, 2023• 41 citations
arXivHTMLPDF

Abstract

It is well known that the neutrino flavor in extreme astrophysical environments changes under the effect of three contributions: the vacuum oscillation, the interaction with the surrounding matter, and the collective oscillations due to interactions between different neutrinos. The latter adds a nonlinear contribution to the equations of motion, making the description of their dynamics complex. In this work we study various strategies to simulate the coherent collective oscillations of a system of $N$ neutrinos in the two-flavor approximation using quantum computation. This was achieved by using a pair-neutrino decomposition designed to account for the fact that the flavor Hamiltonian, in the presence of the neutrino-neutrino term, presents an all-to-all interaction that makes the implementation of the evolution dependent on the qubit topology. We analyze the Trotter error caused by the decomposition demonstrating that the complexity of the implementation of time evolution scales polynomially with the number of neutrinos and that the noise from near-term quantum device simulation can be reduced by optimizing the quantum circuit decomposition and exploiting a full-qubit connectivity. We find that the gate complexity using second order Trotter-Suzuki formulas scales better with system size than with other decomposition methods such as quantum signal processing. We finally present the application and the results of our algorithm on a real quantum device based on trapped-ion qubits.

DOI
10.1103/physrevd.107.023007

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It is well known that the neutrino flavor in extreme astrophysical environments changes under the effect of three contributions: the vacuum oscillation, the interaction with the surrounding matter, and the collective oscillations due to interactions between different neutrinos. The latter adds a nonlinear contribution to the equations of motion, making the description of their dynamics complex. In this work we study various strategies to simulate the coherent collective oscillations of a system of NNN neutrinos in the two-flavor approximation using quantum computation. This was achieved by using a pair-neutrino decomposition designed to account for the fact that the flavor Hamiltonian, in the presence of the neutrino-neutrino term, presents an all-to-all interaction that makes the implementation of the evolution dependent on the qubit topology. We analyze the Trotter error caused by the decomposition demonstrating that the complexity of the implementation of time evolution scales polynomially with the number of neutrinos and that the noise from near-term quantum device simulation can be reduced by optimizing the quantum circuit decomposition and exploiting a full-qubit connectivity. We find that the gate complexity using second order Trotter-Suzuki formulas scales better with system size than with other decomposition methods such as quantum signal processing. We finally present the application and the results of our algorithm on a real quantum device based on trapped-ion qubits.
We simulate the time evolution of collective neutrino oscillations in two-flavor settings on a quantum computer. We explore the generalization of Trotter-Suzuki approximation to time-dependent Hamiltonian dynamics. The trotterization steps are further optimized using the Cartan decomposition of two-qubit unitary gates $U\ensuremath{\in}SU(4)$ in the minimum number of controlled-NOT (CNOT) gates making the algorithm more resilient to the hardware noise. A more efficient hybrid quantum-classical algorithm is also explored to solve the problem on noisy intermediate-scale quantum devices.
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.
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 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.
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.
Neutrino evolution in dense astrophysical environments is typically described either within a quantum kinetic framework, which neglects the build-up of multi-body correlations, or through simplified many-body calculations that allow significant entanglement to develop. In this work, we compare these two approaches in a simple neutrino-gas configuration, with particular emphasis on the role of non-forward scattering processes. These effects are incorporated either through a collision term in the kinetic description, or by considering the full neutrino-neutrino many-body Hamiltonian. We highlight differences between the two descriptions in both their characteristic timescales and asymptotic behavior. Motivated by the natural suitability of quantum computing for many-body calculations, we further investigate the non-classicality of neutrino evolution, discussing Trotter error scaling, along with the associated costs of constructing quantum circuits in terms of entangling gates and non-Clifford gates. We find that the resources needed for neutrino many-body evolution are on the low end of typical high-energy physics problems and on the mid to high end with respect to quantum chemistry problems. For the full Hamiltonian, resource requirements increase relative to the truncated version. We emphasize the importance of efficient fermion-to-qubit encodings, which are essential for reducing the substantial computational resources required for such simulations.