Exponential scaling of the wavefunction is the primary obstacle in solving the quantum many-body problem
The exponential scaling of exact methods presents a fundamental computational barrier in solving the quantum many-by problem across quantum chemistry and physics.
The claim states that exponential scaling of the wavefunction is the primary obstacle in solving the quantum many-body problem. Retrieved papers such as [0] and [3] directly confirm that the exponential increase in computational cost and exact methods' scaling is the long-standing primary barrier in quantum chemistry when solving the Schrödinger equation. There is no evidence refuting this standard computational limitation.
Rask AE, Huntington L, Kim S, Walker D, Wildman A, Wang R, Hazel N, Judi A, Pegg JT, Jha PK, Mayimfor Z, Dukatz C, Naseri H, Gleiser I, Hugues MR, Zimmerman PM, Zaribafiyan A, Plesch R, Yamazaki T. Breaking down per- and polyfluoroalkyl substances (PFAS): tackling multitudes of correlated electrons.. 2025. https://doi.org/10.1039/d5sc03019f
Paper 0 notes that the exponential scaling of exact methods has long impeded accurate computations of electronic structures in quantum chemistry.
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Graf D, Drontschenko V, Stan-Bernhardt A, Ochsenfeld C. Quantum chemistry - from the first steps to linear-scaling electronic structure methods.. 2025. https://doi.org/10.1515/pac-2025-0603
Paper 3 highlights that a key problem in quantum chemistry has been the exponential increase in computational cost with system size when approaching the exact solution of the Schrödinger equation.
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