Preparations for Quantum Simulations of Quantum Chromodynamics in 1+1 Dimensions: (II) Single-Baryon $\beta$-Decay in Real Time

TL;DR

This paper develops a quantum simulation framework for real-time weak decays of hadrons and nuclei in 1+1 dimensions, demonstrating the simulation of baryon beta decay on a 20-qubit system and discussing potential error correction.

Contribution

It introduces a quantum simulation method for weak decays in a 2-flavor lattice theory, including QCD and weak interactions, with implementation on a trapped ion quantum computer.

Findings

Successfully simulated baryon beta decay with 20 qubits.

Developed quantum circuits for time evolution of lattice theory.

Discussed error correction properties and potential for simulating neutrinoless double beta decay.

Abstract

A framework for quantum simulations of real-time weak decays of hadrons and nuclei in a 2-flavor lattice theory in one spatial dimension is presented. A single generation of the Standard Model is found to require 16 qubits per spatial lattice site after mapping to spin operators via the Jordan-Wigner transformation. Both quantum chromodynamics and flavor-changing weak interactions are included in the dynamics, the latter through four-Fermi effective operators. Quantum circuits which implement time evolution in this lattice theory are developed and run on Quantinuum's H1-1 20-qubit trapped ion system to simulate the $\beta$-decay of a single baryon on one lattice site. These simulations include the initial state preparation and are performed for both one and two Trotter time steps. The potential intrinsic error-correction properties of this type of lattice theory are discussed and the leading lattice Hamiltonian required to simulate $0\nu\beta\beta$-decay of nuclei induced by a neutrino Majorana mass term is provided.