Renormalized Hamiltonians for Quantum Field Theories

To understand physics at the most fundamental level that we know of requires solving nonabelian gauge quantum field theories (QFTs). One of the most challenging examples is Quantum Chromodynamics (QCD) – a theory of quarks and gluons. Even though many high-energy observables can be approximated well using perturbative expansions, the same methods cannot be applied to compute low-energy properties of bound states of quarks and gluons. Energy spectra, magnetic moments, and structure functions of hadrons are examples of such low-energy properties. Fault-tolerant quantum computers will hopefully offer resources required to calculate all of these and much more. While particle physicists tend to prefer action-based aproaches to QFTs, in the context of quantum computing it is more natural to use Hamiltonian approaches. We present such an approach based on the front form of Hamiltonian dynamics first introduced by Dirac. Using canonical Hamiltonian of QCD as a starting point we derive an effective (renormalized) Hamiltonian up to second order in the coupling constant. Our Hamiltonian is free from utraviolet divergences and can be diagonalized without the need to adjust the parameters as a function of the basis size (accuracy of the calulation), as opposed to typical renormalization schemes. Therefore, it constitutes a well-defined input for calculations that use either classical or quantum computers. Moreover, one can separate the numerical uncertainties from the theoretical ones.