Quantum mechanical Hamiltonian models of Turing machines

Benioff, Paul

doi:10.1007/bf01342185

Cited by 408Quantum Computing Algorithms and ArchitectureComputability, Logic, AI AlgorithmsDNA and Biological Computing

Quantum mechanical Hamiltonian models of Turing machines

Benioff, Paul·1982·Journal of Statistical Physics

DOI 10.1007/bf01342185

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As originally conceived, quantum computers act strictly in accordance with U, but at some point a measurement causes quantum state reduction R, so output is definite classical bits.
“As originally conceived, quantum computers would indeed act strictly in accordance with U, but at some point a measurement is made causing a quantum state reduction R (with some randomness normally introduced).Accordingly, the output is in the form of a definite state in terms of classical bits.”
From Consciousness in the universe (2014) · cites this paper as [137]
In the standard picture of quantum computers, information is represented not just as bits of 1 or 0, but during the U process also as quantum superposition of both 1 and 0 together (qubits), with large-scale entanglements among many qubits.
“In the standard picture of quantum computers [137][138][139], information is represented not just as bits of either 1 or 0, but during the U process, also as quantum superposition of both 1 and 0 together (quantum bits or 'qubits') where, moreover, large-scale entanglements among many qubits would also be involved.”
From Consciousness in the universe (2014) · cites this paper as [137]

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Authors: Benioff, P.
Affiliations: Argonne National Laboratory (US)
Corresponding author: Benioff, Paul
Venue: Journal of Statistical Physics
Publisher: Springer Science and Business Media LLC
Published: 1982-11
Volume: 29
Issue: 3
Pages: 515-546
ISSN: 0022-4715 (ISSN-L)
1572-9613
DOI: 10.1007/bf01342185
OpenAlex: W2026402424
Cited by: 402
References: 18
Citations by year: 2026: 3 · 2025: 17 · 2024: 18 · 2023: 44 · 2022: 11 · 2021: 14 · 2020: 16 · 2019: 9 · 2018: 9 · 2017: 13 · 2016: 12 · 2015: 8 · 2014: 11 · 2013: 14 · 2012: 8
FWCI: 4.16
Type: journal article
Language: en
Open access: closed
Licence: www.springer.com/tdm (tdm)
Locations: Journal of Statistical Physics (publishedVersion)
Topics: Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
Physical Sciences › Computer Science › Computational Theory and Mathematics › Computability, Logic, AI Algorithms
Life Sciences › Biochemistry, Genetics and Molecular Biology › Molecular Biology › DNA and Biological Computing
Keywords: Turing machines, quantum computing, time-energy uncertainty relation, time-independent Hamiltonian, time-dependent Hamiltonian, recording systems

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Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.

Statistics and arithmetic are recomputed, not judged.

Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.

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Quantum mechanical Hamiltonian models of Turing machines

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