Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Discretizing quantum field theories for quantum simulation   To date, all proposed quantum algorithms for simulating quantum field theory
(QFT) simulate (continuous-time) Hamiltonian lattice QFT as a stepping stone.
Two overlooked issues are how large we can take the timestep in these
simulations while getting the right physics and whether we can go beyond the
standard recipe that relies on Hamiltonian lattice QFT. The first issue is
crucial in practice for, e.g., trapped-ion experiments which actually have a
lower bound on the possible ratio of timestep to lattice spacing. To this end,
we show that a timestep equal to or going to zero faster than the spatial
lattice spacing is necessary for quantum simulations of QFT, but far more
importantly a timestep equal to the lattice spacing is actually sufficient. To
do this, first for $\phi^4$ theory, we give a quantum circuit exactly
equivalent to the real-time path integral from the discrete-time Lagrangian
formulation of lattice QFT. Next we give another circuit with no lattice QFT
analogue, but, by using Feynman rules applied to the circuit, we see that it
also reproduces the correct continuum behaviour. Finally, we look at
non-abelian gauge fields, showing that the discrete-time lattice QFT
path-integral is exactly equivalent to a finite-depth local circuit. All of
these circuits have an analogue of a lightcone on the lattice and therefore are
examples of quantum cellular automata. Aside from the potential practical
benefit of these circuits, this all suggests that the path-integral approach to
lattice QFT need not be overlooked in quantum simulations of physics and has a
simple quantum information interpretation.

19
The categories of this paper are: eess
24
The categories of this paper are: dg-ga
2
The categories of this paper are: math
14
The categories of this paper are: math-ph
6
The categories of this paper are: astro-ph
18
The categories of this paper are: econ
10
The categories of this paper are: q-bio
1
The categories of this paper are: cs
35
The categories of this paper are: mtrl-th
15
The categories of this paper are: nucl-ex
29
The categories of this paper are: funct-an
16
The categories of this paper are: stat
31
The categories of this paper are: ao-sci
20
The categories of this paper are: acc-phys
9
The categories of this paper are: nlin
12
The categories of this paper are: nucl-th