  Conformal truncation is a powerful numerical method for solving generic
strongly-coupled quantum field theories based on purely field-theoretic
technics without introducing lattice regularization. We discuss possible
speedups for performing those computations using quantum devices, with the help
of near-term and future quantum algorithms. We show that this construction is
very similar to quantum simulation problems appearing in quantum chemistry
(which are widely investigated in quantum information science), and the
renormalization group theory provides a field theory interpretation of
conformal truncation simulation. Taking two-dimensional Quantum Chromodynamics
(QCD) as an example, we give various explicit calculations of variational and
digital quantum simulations in the level of theories, classical trials, or
quantum simulators from IBM, including adiabatic state preparation, variational
quantum eigensolver, imaginary time evolution, and quantum Lanczos algorithm.
Our work shows that quantum computation could not only help us understand
fundamental physics in the lattice approximation, but also simulate quantum
field theory methods directly, which are widely used in particle and nuclear
physics, sharpening the statement of the quantum Church-Turing Thesis.
