Pathfinding Quantum Simulations of Neutrinoless Double-Beta Decay

TL;DR

This work demonstrates pathfinding quantum simulations of a rare nuclear process—neutrinoless double-beta decay ($0\nu\beta\beta$) in a simplified 1+1D lattice QCD model—on IonQ’s Forte trapped-ion hardware. By co-designing the Hamiltonian, state-preparation circuits, and error-mitigation strategies to exploit all-to-all connectivity and native $R_{ZZ}$ gates, the authors realize real-time lepton-number-violating dynamics and achieve a statistically significant signal (up to $10\sigma$) under realistic hardware limits. They systematically explore hardware boundaries, validating that full weak-interaction circuits are too deep for current devices and that valence-only approximations, coupled with advanced mitigation (including non-linear filtering and leakage flags), yield robust observables corroborated by noiseless simulations. The study lays a concrete roadmap toward larger, closer-to-physical simulations (e.g., 2+1D, larger volumes, varied neutrino masses) and highlights the interplay between quantum hardware advances and algorithmic co-design needed to extract physically relevant results from exotic weak decays. Overall, this work sets benchmarks for quantum simulations of complex nuclear processes and demonstrates a viable path to yocto-second insights into reaction pathways and strong-interaction dynamics with near-term quantum devices.

Abstract

We present results from co-designed quantum simulations of the neutrinoless double-beta decay of a simple nucleus in 1+1D quantum chromodynamics using IonQ's Forte-generation trapped-ion quantum computers. Electrons, neutrinos, and up and down quarks are distributed across two lattice sites and mapped to 32 qubits, with an additional 4 qubits used for flag-based error mitigation. A four-fermion interaction is used to implement weak interactions, and lepton-number violation is induced by a neutrino Majorana mass. Quantum circuits that prepare the initial nucleus and time evolve with the Hamiltonian containing the strong and weak interactions are executed on IonQ Forte Enterprise. Enabled by tuned model parameters, lepton-number violation is observed in real time, providing a clear signal of neutrinoless double-beta decay. This was made possible by co-designing the simulation to maximally utilize the all-to-all connectivity and native gate-set available on IonQ's quantum computers. Quantum circuit compilation techniques and co-designed error-mitigation methods, informed from executing benchmarking circuits with up to 2,356 two-qubit gates, enabled observables to be extracted with high precision. We discuss the potential of future quantum simulations to provide yocto-second resolution of the reaction pathways in these, and other, nuclear processes.

Figures (16)

• Figure 1: The structure of the quantum circuits used to simulate $0\nu\beta\beta$-decay. First, the initial $|\Delta^- \Delta^- \rangle$ state is prepared using SC-ADAPT-VQE Farrell:2023fgd. Next, weak decay dynamics are implemented using two steps of Trotterized time evolution with time step $\delta t=t/2$. The first Trotter step has been simplified because $|\Delta^- \Delta^- \rangle$ is a strong interaction eigenstate. Before the final measurement, leakage events are flagged by coupling the lepton qubits to a register of ancillas. All qubits are initialized in $|0\rangle$ and measured in the z-basis. Decompositions of each circuit block are provided in Supplementary Notes 10 and 5.
• Figure 1: The lepton number, $\hat{\mathcal{L}}$, the electric charge in the lepton sector, $\hat{Q}_e$, and the neutrino number, $\hat{N}_\nu$, computed throughout the time evolution starting from $\vert \psi_{\text{init}}\rangle = |\psi_{\text{vac}}^{(\text{lep})}\rangle|\Delta^- \Delta^-\rangle$ as a function of the number of Trotter steps. These quantities are computed for $L=2$ and for two Majorana masses, $m_M=\{0.0,1.7\}$. No approximations are made in the exact diagonalization results. An exact state-vector simulator is used to compute the time-evolution with $n_T$ Trotter steps, which have Trotter errors, as well as (small) errors coming from the SC-ADAPT-VQE preparation of $|\Delta^- \Delta^-\rangle$. The quantum simulations that we performed on IonQ's Forte-generation quantum processors employed $n_T=2$ and were limited to $t\le 2$.
• Figure 2: The time evolution of the difference of the lepton number (left), lepton electric charge (center) and neutrino number (right) during the decay of the $|\Delta^-\Delta^-\rangle$ two-baryon state in 1+1D QCD. Results are obtained from two steps of the first-order Trotterized circuit (2,356 native two-qubit gates) executed on IonQ Forte, and are derived from those given in Table \ref{['tab:2400_gate_data']}, displayed in green, as well as noiseless statevector simulator (Ideal Simulation), displayed in black. Both sea- and valence-weak interactions are included. The error bars are obtained from bootstrap resampling and represent one standard deviation. The gray dotted line is added for reference.
• Figure 2: The time-evolution of the lepton number, electric charge and neutrino number with varying levels of approximation, as explained in the text. The bar charts to the right give the number of the $CZ$ and CNOT gates required for each level of approximation. The number of two-qubit gates is the same for both the upper and lower panels, and the approximate time evolution is computed using $n_T=2$ steps of $1^{st}$ order Trotterization. The results from full $1^{st}$ order Trotterization and from the angle-truncated implementation essentially coincide.
• Figure 3: The time evolution of the lepton number (upper row), lepton electric charge (middle row) and neutrino number (lower row) during the decay of the $|\Delta^-\Delta^-\rangle$ two-baryon state in 1+1D QCD. Two steps of first-order Trotterized time evolution using the (approximate) valence-fermion weak interactions are implemented, requiring 470 two-qubit gates. The left panels show the results obtained with a Majorana mass of $m_M=1.7$, the center panels show results for $m_M=0$, and the right panels show the differences between the $m_M=1.7$ and $m_M=0$ results. The green points were obtained from IonQ Forte Enterprise, and the orange diamonds correspond to noiseless simulation. The error bars are obtained from bootstrap resampling and represent one standard deviation, and the gray dotted line is added for reference.