



01856nas a2200169   4500008004100000245006600041210006500107260001500172300000700187490000600194520134900200100002401549700001601573700002201589700001901611856005601630       2018                        eng d00aBQP-completeness of Scattering in Scalar Quantum Field Theory0 aBQPcompleteness of Scattering in Scalar Quantum Field Theory  c2018/01/08  a440 v23 a<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>1 aJordan, Stephen, P.1 aKrovi, Hari1 aLee, Keith, S. M.1 aPreskill, John  uhttps://quantum-journal.org/papers/q-2018-01-08-44/01013nas a2200133   4500008004100000245006000041210006000101260001500161520060100176100002400777700002200801700001900823856003700842       2014                        eng d00aQuantum Algorithms for Fermionic Quantum Field Theories0 aQuantum Algorithms for Fermionic Quantum Field Theories  c2014/04/283 a  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.
1 aJordan, Stephen, P.1 aLee, Keith, S. M.1 aPreskill, John  uhttp://arxiv.org/abs/1404.7115v101375nas a2200157   4500008004100000245007100041210006900112260001500181300001400196490000700210520089800217100002401115700002201139700001901161856003701180       2014                        eng d00aQuantum Computation of Scattering in Scalar Quantum Field Theories0 aQuantum Computation of Scattering in Scalar Quantum Field Theori  c2014/09/01  a1014-10800 v143 a  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.
1 aJordan, Stephen, P.1 aLee, Keith, S. M.1 aPreskill, John  uhttp://arxiv.org/abs/1112.4833v101068nas a2200157   4500008004100000245005000041210005000091260001500141300001600156490000800172520062800180100002400808700002200832700001900854856003700873       2012                        eng d00aQuantum Algorithms for Quantum Field Theories0 aQuantum Algorithms for Quantum Field Theories  c2012/05/31  a1130 - 11330 v3363 a  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.
1 aJordan, Stephen, P.1 aLee, Keith, S. M.1 aPreskill, John  uhttp://arxiv.org/abs/1111.3633v2