Requirements for building effective Hamiltonians using quantum-enhanced density matrix downfolding

• URL: http://arxiv.org/abs/2403.01043v1
• Date: Sat, 2 Mar 2024 00:27:18 GMT
• Title: Requirements for building effective Hamiltonians using quantum-enhanced density matrix downfolding
• Authors: Shivesh Pathak, Antonio E. Russo, Stefan Seritan, Alicia B. Magann, Eric Bobrow, Andrew J. Landahl, Andrew D. Baczewski
• Abstract summary: Density matrix downfolding (DMD) is a technique for regressing low-energy effective Hamiltonians from quantum many-body Hamiltonians. One limiting factor in the accuracy of classical implementations of DMD is the presence of difficult-to-quantify systematic errors. We propose a hybrid quantum-classical protocol for circumventing this limitation.
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• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Density matrix downfolding (DMD) is a technique for regressing low-energy effective Hamiltonians from quantum many-body Hamiltonians. One limiting factor in the accuracy of classical implementations of DMD is the presence of difficult-to-quantify systematic errors attendant to sampling the observables of quantum many-body systems on an approximate low-energy subspace. We propose a hybrid quantum-classical protocol for circumventing this limitation, relying on the prospective ability of quantum computers to efficiently prepare and sample from states in well-defined low-energy subspaces with systematically improvable accuracy. We introduce three requirements for when this is possible, including a notion of compressibility that quantifies features of Hamiltonians and low-energy subspaces thereof for which quantum DMD might be efficient. Assuming that these requirements are met, we analyze design choices for our protocol and provide resource estimates for implementing quantum-enhanced DMD on both the doped 2-D Fermi-Hubbard model and an ab initio model of a cuprate superconductor.

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