Preparations for quantum simulations of quantum chromodynamics in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mn>1</mml:mn><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:math> dimensions. II. Single-baryon <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>β</mml:mi></mml:math>-decay in real time
Roland C. Farrell, Ivan A. Chernyshev, Sarah J. M. Powell, Nikita A. Zemlevskiy, Marc Illa, Martin J. Savage
Abstract
A framework for quantum simulations of real-time weak decays of hadrons and nuclei in a two-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 that implement time evolution in this lattice theory are developed and run on Quantinuum's H1-1 20-qubit trapped ion system to simulate the $\ensuremath{\beta}$-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 $0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$-decay of nuclei induced by a neutrino Majorana mass term is provided.