Journal
QUANTUM
Volume 2, Issue -, Pages -Publisher
VEREIN FORDERUNG OPEN ACCESS PUBLIZIERENS QUANTENWISSENSCHAF
DOI: 10.22331/q-2018-01-08-44
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Funding
- Institute for Quantum Information and Matter (IQIM), an NSF Physics Frontiers Center
- Gordon and Betty Moore Foundation
- Army Research Office
- Simons Foundation
- NSERC
- Centre for Quantum Information and Quantum Control (CQIQC)
- Division Of Physics [1125565] Funding Source: National Science Foundation
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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) dimensions. We show that this problem is HQP-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 mm 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 14 a universal quantum computer in a laboratory system described by massive 04 theory coupled to classical spacetime-dependent sources.
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