



@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}
}
@article {1403,
	title = {Quantum Algorithms for Fermionic Quantum Field Theories},
	year = {2014},
	month = {2014/04/28},
	abstract = {  Extending previous work on scalar field theories, we develop a quantum
algorithm to compute relativistic scattering amplitudes in fermionic field
theories, exemplified by the massive Gross-Neveu model, a theory in two
spacetime dimensions with quartic interactions. The algorithm introduces new
techniques to meet the additional challenges posed by the characteristics of
fermionic fields, and its run time is polynomial in the desired precision and
the energy. Thus, it constitutes further progress towards an efficient quantum
algorithm for simulating the Standard Model of particle physics.
},
	url = {http://arxiv.org/abs/1404.7115v1},
	author = {Stephen P. Jordan and Keith S. M. Lee and John Preskill}
}
@article {1395,
	title = {Quantum Computation of Scattering in Scalar Quantum Field Theories},
	journal = {Quantum Information and Computation},
	volume = {14},
	year = {2014},
	month = {2014/09/01},
	pages = {1014-1080},
	abstract = {  Quantum field theory provides the framework for the most fundamental physical
theories to be confirmed experimentally, and has enabled predictions of
unprecedented precision. However, calculations of physical observables often
require great computational complexity and can generally be performed only when
the interaction strength is weak. A full understanding of the foundations and
rich consequences of quantum field theory remains an outstanding challenge. We
develop a quantum algorithm to compute relativistic scattering amplitudes in
massive phi-fourth theory in spacetime of four and fewer dimensions. The
algorithm runs in a time that is polynomial in the number of particles, their
energy, and the desired precision, and applies at both weak and strong
coupling. Thus, it offers exponential speedup over existing classical methods
at high precision or strong coupling.
},
	url = {http://arxiv.org/abs/1112.4833v1},
	author = {Stephen P. Jordan and Keith S. M. Lee and John Preskill}
}
@article {1397,
	title = {Quantum Algorithms for Quantum Field Theories},
	journal = {Science},
	volume = {336},
	year = {2012},
	month = {2012/05/31},
	pages = {1130 - 1133},
	abstract = {  Quantum field theory reconciles quantum mechanics and special relativity, and
plays a central role in many areas of physics. We develop a quantum algorithm
to compute relativistic scattering probabilities in a massive quantum field
theory with quartic self-interactions (phi-fourth theory) in spacetime of four
and fewer dimensions. Its run time is polynomial in the number of particles,
their energy, and the desired precision, and applies at both weak and strong
coupling. In the strong-coupling and high-precision regimes, our quantum
algorithm achieves exponential speedup over the fastest known classical
algorithm.
},
	doi = {10.1126/science.1217069},
	url = {http://arxiv.org/abs/1111.3633v2},
	author = {Stephen P. Jordan and Keith S. M. Lee and John Preskill}
}
