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- W3102290683 endingPage "P07006" @default.
- W3102290683 startingPage "P07006" @default.
- W3102290683 abstract "Computational complexity theory contains a corpus of theorems and conjectures regarding the time a Turing machine will need to solve certain types of problems as a function of the input size. Nature {em need not} be a Turing machine and, thus, these theorems do not apply directly to it. But {em classical simulations} of physical processes are programs running on Turing machines and, as such, are subject to them. In this work, computational complexity theory is applied to classical simulations of systems performing an adiabatic quantum computation (AQC), based on an annealed extension of the density matrix renormalization group (DMRG). We conjecture that the computational time required for those classical simulations is controlled solely by the {em maximal entanglement} found during the process. Thus, lower bounds on the growth of entanglement with the system size can be provided. In some cases, quantum phase transitions can be predicted to take place in certain inhomogeneous systems. Concretely, physical conclusions are drawn from the assumption that the complexity classes {bf P} and {bf NP} differ. As a by-product, an alternative measure of entanglement is proposed which, via Chebyshev's inequality, allows to establish strict bounds on the required computational time." @default.
- W3102290683 created "2020-11-23" @default.
- W3102290683 creator A5070109750 @default.
- W3102290683 creator A5084977467 @default.
- W3102290683 date "2014-07-02" @default.
- W3102290683 modified "2023-09-23" @default.
- W3102290683 title "Physical consequences of P≠NP and the density matrix renormalization group annealing conjecture" @default.
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- W3102290683 doi "https://doi.org/10.1088/1742-5468/2014/07/p07006" @default.
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