C osmo L attice: A modern code for lattice simulations of scalar and gauge field dynamics in an expanding universe
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79 ASTRONOMY AND ASTROPHYSICS↗
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Present and future of $\mathcal{C}$osmo $\mathcal{L}$attice
We discuss the present state and planned updates of Cosmo Lattice, a cutting-edge code for lattice simulations of non-linear dynamics of scalar-gauge field theories in an expanding background. We first review the current capabilities of the code, including the simulation of interacting singlet scalars and of Abelian and non-Abelian scalar-gauge theories. We also comment on new features recently implemented, such as the simulation of gravitational waves from scalar and gauge fields. Secondly, we discuss new extensions of Cosmo Lattice that we plan to release publicly. We comment on new physics modules, which include axion-gauge interactions $\phi F\tilde{F}$, non-minimal gravitational couplings $\phi ^2R$, creation and evolution of cosmic-defect networks, and magnetohydrodynamics. Finally, we also discuss new technical features, including evolvers for non-canonical interactions, arbitrary initial conditions, simulations in 2+1 dimensions, and higher-accuracy spatial derivatives.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
General quantum algorithms for Hamiltonian simulation with applications to a non-Abelian lattice gauge theory
With a focus on universal quantum computing for quantum simulation, and through the example of lattice gauge theories, we introduce rather general quantum algorithms that can efficiently simulate certain classes of interactions consisting of correlated changes in multiple (bosonic and fermionic) quantum numbers with non-trivial functional coefficients. In particular, we analyze diagonalization of Hamiltonian terms using a singular-value decomposition technique, and discuss how the achieved diagonal unitaries in the digitized time-evolution operator can be implemented. The lattice gauge theory studied is the SU(2) gauge theory in 1+1 dimensions coupled to one flavor of staggered fermions, for which a complete quantum-resource analysis within different computational models is presented. The algorithms are shown to be applicable to higher-dimensional theories as well as to other Abelian and non-Abelian gauge theories. The example chosen further demonstrates the importance of adopting efficient theoretical formulations: it is shown that an explicitly gauge-invariant formulation using loop, string, and hadron degrees of freedom simplifies the algorithms and lowers the cost compared with the standard formulations based on angular-momentum as well as the Schwinger-boson degrees of freedom. The loop-string-hadron formulation further retains the non-Abelian gauge symmetry despite the inexactness of the digitized simulation, without the need for costly controlled operations. Such theoretical and algorithmic considerations are likely to be essential in quantumly simulating other complex theories of relevance to nature.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗