# Quantum Computation and the Computational Complexity of Quantum Field Theory

Quantum field theory provides the framework for the Standard Model of

particle physics and plays a key role in physics. However, calculations

are generally computationally complex and limited to weak interaction

strengths. I'll describe polynomial-time quantum algorithms for computing

relativistic scattering amplitudes in both scalar and fermionic quantum

field theories. The algorithms achieve exponential speedup over known

classical methods. One of the motivations for this work comes from

computational complexity theory. Ultimately, one wishes to know what is

the computational power of our universe. Studying such quantum algorithms

probes whether a universal quantum computer is powerful enough to

represent quantum field theory; in other words, is quantum field theory in

BQP? Conversely, one can ask whether quantum field theory can represent a

universal quantum computer; is quantum field theory BQP-hard? We have

shown that massive phi^4 theory can implement universal quantum

computation and is thus BQP-complete.