



@article {1949,
	title = {BQP-completeness of Scattering in Scalar Quantum Field Theory},
	journal = {Quantum},
	volume = {2},
	year = {2018},
	month = {2018/01/08},
	pages = {44},
	abstract = {<p><span style="font-family: \&quot;Lucida Grande\&quot;, helvetica, arial, verdana, sans-serif; font-size: 14.4px;">Recent work has shown that quantum computers can compute scattering probabilities in massive quantum field theories, with a run time that is polynomial in the number of particles, their energy, and the desired precision. Here we study a closely related quantum field-theoretical problem: estimating the vacuum-to-vacuum transition amplitude, in the presence of spacetime-dependent classical sources, for a massive scalar field theory in (1+1) dimensions. We show that this problem is BQP-hard; in other words, its solution enables one to solve any problem that is solvable in polynomial time by a quantum computer. Hence, the vacuum-to-vacuum amplitude cannot be accurately estimated by any efficient classical algorithm, even if the field theory is very weakly coupled, unless BQP=BPP. Furthermore, the corresponding decision problem can be solved by a quantum computer in a time scaling polynomially with the number of bits needed to specify the classical source fields, and this problem is therefore BQP-complete. Our construction can be regarded as an idealized architecture for a universal quantum computer in a laboratory system described by massive phi^4 theory coupled to classical spacetime-dependent sources.</span></p>},
	doi = {10.22331/q-2018-01-08-44},
	url = {https://quantum-journal.org/papers/q-2018-01-08-44/},
	author = {Stephen P. Jordan and Hari Krovi and Keith S. M. Lee and John Preskill}
}
