Computational Capacity of the Universe
Open accessAbstract
All physical systems register and process information. The laws of physics determine the amount of information that a physical system can register (number of bits) and the number of elementary logic operations that a system can perform (number of ops). The Universe is a physical system. The amount of information that the Universe can register and the number of elementary operations that it can have performed over its history are calculated. The Universe can have performed ${10}^{120}\phantom{\rule{0ex}{0ex}}\mathrm{ops}$ on ${10}^{90}\phantom{\rule{0ex}{0ex}}\mathrm{bits}$ ( ${10}^{120}\phantom{\rule{0ex}{0ex}}\mathrm{bits}$ including gravitational degrees of freedom).
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We consider Hamiltonians that can be written as a polynomial number of terms, with respect to the system size.
“We consider Hamiltonians that can be written as a polynomial number of terms, with respect to the system size.”
From A variational eigenvalue solver on a photonic quantum processor (2014) · cites this paper as [20]
The Discussion (p. 14) says quantum computers can efficiently simulate systems with local interactions, but it does not specify Hamiltonians expressible as a polynomial number of terms in system size. Searches for polynomially many Hamiltonian terms found no passage addressing that condition. (LLM, conf=0.73)
Experimental — accuracy not yet measuredThis class of Hamiltonians encompasses a wide range of physical systems, including the electronic structure Hamiltonian of quantum chemistry, the quantum Ising Model, the Heisenberg Model, matrices that are well approximated as a sum of n-fold tensor products, and more generally any k-sparse Hamiltonian without evident tensor product structure.
“This class of Hamiltonians encompasses a wide range of physical systems, including the electronic structure Hamiltonian of quantum chemistry, the quantum Ising Model, the Heisenberg Model2021, matrices that are well approximated as a sum of n-fold tensor products2223, and more generally any k-sparse Hamiltonian without evident tensor product structure”
From A variational eigenvalue solver on a photonic quantum processor (2014) · cites this paper as [20]
The Discussion (p. 14) says quantum computers can efficiently simulate systems with local interactions, but it does not identify the claimed class of Hamiltonians or its examples. Searches for the Ising and Heisenberg models, electronic-structure Hamiltonians, tensor products, and k-sparse Hamiltonians found no passage addressing that classification. (LLM, conf=0.76)
Experimental — accuracy not yet measuredUhlmann's theorem states that the square root of the fidelity is given by the maximum over purifications.
“According to Uhlmann's theorem [18], the square root of the fidelity is given by”
From Geometric derivation of the quantum speed limit (2010) · cites this paper as [18]
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Complex Automata: Multi-scale Modeling with Coupled Cellular Automata
Hoekstra, A. G., Caiazzo, A., Lorenz, E., Falcone, J.-L., & Bastien Chopard, B. (2010) · Understanding complex systems · doi:10.1007/978-3-642-12203-3_3 · Cited by 31 · see citing works
Douglas, M. R. (2019) · Universe · doi:10.3390/universe5070176 · Cited by 30 · see citing works
Avoiding Unintended AI Behaviors
Hibbard, B. (2012) · Lecture notes in computer science · doi:10.1007/978-3-642-35506-6_12 · Cited by 30 · see citing works
Extensions of the Mandelstam–Tamm quantum speed limit to systems in mixed states
Hörnedal, N., Allan, D., & Sönnerborn, O. (2022) · New Journal of Physics · doi:10.1088/1367-2630/ac688a · Cited by 30 · see citing works
Kaveh, A., Kamalinejad, M., Hamedani, K. B., & Arzani, H. K. (2021) · Structures · doi:10.1016/j.istruc.2021.03.046 · Cited by 30 · see citing works
The Semantic Sphere 1: Computation, Cognition and Information Economy
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Elementary proof of the bound on the speed of quantum evolution
Kosiński, P., & Zych, M. (2006) · Physical Review A · doi:10.1103/physreva.73.024303 · Cited by 30 · see citing works
Open Question: Could a Causal Discontinuity Explain Fluctuations in the CMBR Radiation Spectrum?
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Fast optimization algorithms and the cosmological constant
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Complexity growth in minimal massive 3D gravity
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Emergent biological principles and the computational properties of the universePreprint
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Quantum speed limit for a relativistic electron in a uniform magnetic field
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Debates—Does Information Theory Provide a New Paradigm for Earth Science?
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The Physical Signature of Computation
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Entropy, Information and Complexity or Which Aims the Arrow of Time?
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- Authors
- Lloyd, S.
- Affiliations
- Massachusetts Institute of Technology (US)
- Corresponding author
- Lloyd, Seth
- ORCID
- Lloyd, Seth
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 2002-05-24
- Volume
- 88
- Issue
- 23
- Pages
- 237901-237901
- ISSN
- 0031-9007 (ISSN-L)
- 1079-7114
- OpenAlex
- W1993466133
- Cited by
- 571
- References
- 35
- Citations by year
- 2026: 39 · 2025: 32 · 2024: 39 · 2023: 36 · 2022: 17 · 2021: 27 · 2020: 23 · 2019: 40 · 2018: 27 · 2017: 24 · 2016: 29 · 2015: 27 · 2014: 13 · 2013: 30 · 2012: 16
- FWCI
- 8.07
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review Letters (publishedVersion)
- PubMed (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Cosmology and Gravitation Theories
- Physical Sciences › Computer Science › Computational Theory and Mathematics › Computability, Logic, AI Algorithms
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Black Holes and Theoretical Physics
- Keywords
- gravitational degrees of freedom
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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.
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