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BQP-completeness of Scattering in Scalar Quantum Field Theory

Jordan, Stephen P. and Krovi, Hari and Lee, Keith S. M. and Preskill, John (2018) BQP-completeness of Scattering in Scalar Quantum Field Theory. Quantum, 2 . Art. No. 44. ISSN 2521-327X. doi:10.22331/q-2018-01-08-44.

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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.

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Additional Information:This paper is published in Quantum under the Creative Commons Attribution 4.0 International (CC BY 4.0) license. Copyright remains with the original copyright holders such as the authors or their institutions. We thank David Gosset, Mark Rudner, and Jacob Taylor for helpful discussions. JP gratefully acknowledges support from the Institute for Quantum Information and Matter (IQIM), an NSF Physics Frontiers Center with support from the Gordon and Betty Moore Foundation, from the Army Research Office, and from the Simons Foundation It from Qubit Collaboration. KL was supported in part by NSERC and the Centre for Quantum Information and Quantum Control (CQIQC). Parts of this manuscript are a contribution of NIST, an agency of the US government, and are not subject to US copyright.
Group:Institute for Quantum Information and Matter
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Gordon and Betty Moore FoundationUNSPECIFIED
Simons FoundationUNSPECIFIED
Army Research Office (ARO)UNSPECIFIED
Natural Sciences and Engineering Research Council of Canada (NSERC)UNSPECIFIED
Centre for Quantum Information and Quantum Control (CQIQC)UNSPECIFIED
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ID Code:79260
Deposited By: Joy Painter
Deposited On:21 Jul 2017 16:02
Last Modified:15 Nov 2021 17:46

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