Abstract
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.
Highlights
Quantum field theory is one of the most astonishing tools we have for the understanding of the universe
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, and the renormalization group theory provides a field theory interpretation of conformal truncation simulation
Our work shows that quantum computation could help us understand fundamental physics in the lattice approximation, and simulate quantum field theory methods directly, which are widely used in particle and nuclear physics, sharpening the statement of the quantum Church-Turing Thesis
Summary
Quantum field theory is one of the most astonishing tools we have for the understanding of the universe. Based on the above treatment, we reduce the simulation task of the corresponding quantum field theory as diagonalizing and evolving a possibly large matrix This method is called conformal truncation or Hamiltonian truncation in quantum field theory community (see some recent discussions, for instance, [61,62,63,64,65]).. Other than considering a quantum many-body problem with local interaction in a lattice, we formulate a quantum-mechanical problem with an explicit Hamiltonian, without any notion of locality It is not clear if this treatment is generically better than lattice regularization, we will hope that it will open up different possibilities for quantum field theory simulation at strong coupling. In terms of 2D QCD, the primary example that is considered in this work, the conformal truncation method is significantly different from light-front treatment by the following,. We look forward to furthering research on comparing those methods
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
