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.
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