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arXiv:2412.15617

Simulating Three-Flavor Neutrino Oscillations on an NMR Quantum Processor

Gayatri Singh, Arvind, Kavita Dorai

Published Dec 20, 2024• 1 citation
arXivHTMLPDF

Abstract

Neutrino oscillations can be efficiently simulated on a quantum computer using the Pontecorvo-Maki-Nakagawa-Sakata (PMNS) theory in close analogy to the physical processes realized in experiments. We simulate three-flavor neutrino oscillations on a two-qubit NMR quantum information processor. The three-flavor neutrino states were encoded into the two-qubit system, leaving one redundant basis state (representing an unphysical sterile neutrino). We simulated the neutrino oscillations in different scenarios, including propagation in vacuum and through surrounding matter, and both with and without a CP violating phase $δ$ at a Deep Underground Neutrino Experiment (DUNE) baseline distance of L = 1285 km. The oscillation probabilities were obtained after unitarily time evolving the initial flavor state and and comparisons were performed between different scenarios. Further, we design and implement an optimized quantum circuit encoding all four parameters (three mixing angles-$θ_{12},θ_{23},θ_{13}$ and one complex phase $δ$) to implement the PMNS unitary matrix, which relates the flavor and mass eigenstates. The interaction with matter is considered as a perturbation to the vacuum Hamiltonian, and the same quantum circuit is employed with an approximation of two mixing angles ($θ_{12}$ and $θ_{13}$ ) and mass eigenvalues. Our experimental results match well with numerical simulations and highlight the potential of quantum computers for exploring the physics of neutrino oscillations.

DOI
10.48550/arxiv.2412.15617

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Neutrino oscillations can be efficiently simulated on a quantum computer using the Pontecorvo-Maki-Nakagawa-Sakata (PMNS) theory in close analogy to the physical processes realized in experiments. We simulate three-flavor neutrino oscillations on a two-qubit NMR quantum information processor. The three-flavor neutrino states were encoded into the two-qubit system, leaving one redundant basis state (representing an unphysical sterile neutrino). We simulated the neutrino oscillations in different scenarios, including propagation in vacuum and through surrounding matter, and both with and without a CP violating phase δδδ at a Deep Underground Neutrino Experiment (DUNE) baseline distance of L = 1285 km. The oscillation probabilities were obtained after unitarily time evolving the initial flavor state and and comparisons were performed between different scenarios. Further, we design and implement an optimized quantum circuit encoding all four parameters (three mixing angles-θ12,θ23,θ13θ_{12},θ_{23},θ_{13}θ12​,θ23​,θ13​ and one complex phase δδδ) to implement the PMNS unitary matrix, which relates the flavor and mass eigenstates. The interaction with matter is considered as a perturbation to the vacuum Hamiltonian, and the same quantum circuit is employed with an approximation of two mixing angles (θ12θ_{12}θ12​ and θ13θ_{13}θ13​ ) and mass eigenvalues. Our experimental results match well with numerical simulations and highlight the potential of quantum computers for exploring the physics of neutrino oscillations.
Abstract Neutrino oscillations can be efficiently simulated on a quantum computer using the Pontecorvo-Maki-Nakagawa-Sakata (PMNS) theory in close analogy to the physical processes realized in experiments. We simulate three-flavor neutrino oscillations on a two-qubit NMR quantum information processor. The three-flavor neutrino states were encoded into the two-qubit system, leaving one redundant basis state (representing an unphysical sterile neutrino). The neutrino oscillations were experimentally simulated in different scenarios, including propagation in vacuum and through surrounding matter, and both with and without a CP violating phase δ at a Deep Underground Neutrino Experiment (DUNE) baseline distance of L = 1285 km. The oscillation probabilities were obtained after unitarily time evolving the initial flavor state and comparisons were performed between different scenarios. The interaction with matter is considered as a perturbation to the vacuum Hamiltonian, and the same quantum circuit is employed with an approximation of two mixing angles (θ 12 and θ 13) and mass eigenvalues. Our experimental results match well with numerical simulations and highlight the potential of quantum computers for exploring the physics of neutrino oscillations.
Neutrino oscillations are genuine quantum phenomena in which coherent oscillations are maintained over a long distance. As a result, in principle, the phenomena can be studied efficiently using quantum simulations. In today's noisy quantum hardware, encoding neutrinos in a multiqubit system requires a redundant basis and tricky entangling gates. We encode a three-flavor neutrino in a superconducting qutrit and study its oscillations using Pontecorvo-Maki-Nakagawa-Sakata theory with time evolution expressed in terms of single qutrit gates. The qutrit is engineered from the multilevel structure of IBM transmon devices. High-fidelity gate control and readout are fine-tuned using programming microwave pulses using a high-level language. Our quantum simulations on real hardware match the analytical calculations well in three oscillation cases: vacuum, interaction with matter, and CPCPCP violation.
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.
Measurements of the Pontecorvo-Maki-Nakagawa-Sakata (PMNS) neutrino mixing parameters have entered a precision era, enabling increasingly stringent tests of neutrino oscillations. Within the framework of quantum estimation theory, we investigate whether flavor measurements, the only observables currently accessible experimentally, are optimal for extracting the oscillation parameters. We compute the Quantum Fisher Information (QFI) and the classical Fisher Information (FI) associated with ideal flavor projections for all oscillation parameters, considering accelerator muon (anti)neutrino and reactor electron antineutrino beams propagating in vacuum. Two main results emerge. First, flavor measurements saturate the QFI at the first oscillation maximum for θ13θ_{13}θ13​, θ23θ_{23}θ23​, and θ12θ_{12}θ12​, demonstrating their information-theoretic optimality for these parameters. In contrast, they are far from optimal for δCPδ_{CP}δCP​. In particular, only a small fraction of the available information on δCPδ_{CP}δCP​ is extracted at the first maximum; the sensitivity improves at the second maximum, in line with the strategy of ESSνννSB, a planned facility. Second, the QFI associated with δCPδ_{CP}δCP​ is approximately one order of magnitude smaller than that of the mixing angles, indicating that the neutrino state intrinsically encodes less information about CP violation. Nevertheless, this quantum bound lies well below current experimental uncertainties, implying that the present precision on δCPδ_{CP}δCP​ is not fundamentally limited. Our results provide a quantitative framework to disentangle fundamental from practical limitations and establish a benchmark for optimizing future neutrino facilities.
Oscillating neutrino beams exhibit quantum coherence over distances of thousands of kilometers. Their unambiguously quantum nature suggests an appealing test system for direct quantum simulation. Such techniques may enable presently analytically intractable calculations involving multineutrino entanglements, such as collective neutrino oscillations in supernovas, but only once oscillation phenomenology is properly reexpressed in the language of quantum circuits. Here we resolve outstanding conceptual issues regarding encoding of arbitrarily mixed neutrino flavor states in the Hilbert space of an n-qubit quantum computer. We introduce algorithms to encode mixing and oscillation of any number of flavor-mixed neutrinos, both with and without CPCPCP-violation, with an efficient number of prescriptive input parameters in terms of subrotations of the Pontecorvo-Maki-Nakagawa-Sakata matrix in standard form. Examples encoded for an IBM-Q quantum computer are shown to converge to analytic predictions both with and without CPCPCP-violation.
In this paper the authors demonstrate the emulation of neutrino oscillations on a quantum processor, directly encoding three-neutrino flavor evolution onto the two-qubit system of a publicly available quantum computer and time-evolving the system analogously to the physical neutrino. Excellent agreement with with the standard classical calculation is found, and extensions to more complex systems including beyond-standard-model physics involving sterile neutrinos, anomalous decoherence, and matter effects are explored.