Leveraging Small-Scale Quantum Computers with Unitarily Downfolded Hamiltonians

• Main Authors: Evangelista, F.A (Author), Huang, R. (Author), Li, C. (Author)
• Format: Article
• Language: English
• Published: American Physical Society 2023
• Subjects: Fault-tolerant; Isomerization; Many-body theory; Multi reference; Quanta computers; Quantum algorithms; Quantum device; Quantum optics; Qubits; Reduced-density matrix; Renormalization group; Scalings; Small scale; Statistical mechanics
• Online Access: View Fulltext in Publisher; View in Scopus
• ISBN: 26913399 (ISSN)
• DOI: 10.1103/PRXQuantum.4.020313

In this work, we propose a quantum unitary downfolding formalism based on the driven similarity renormalization group (QDSRG) that may be combined with quantum algorithms for both noisy and fault-tolerant hardware. The QDSRG is a classical polynomial-scaling downfolding method that avoids the evaluation of costly three- and higher-body reduced density matrices while retaining the accuracy of classical multireference many-body theories. We calibrate and test the QDSRG on several challenging chemical problems and propose a strategy for reducing the measurement cost. We report QDSRG computations of two chemical systems using the variational quantum eigensolver on IBM quantum devices: (i) the dissociation curve of H2 using a quintuple-ζ basis and (ii) the bicyclobutane isomerization reaction to trans-butadiene, demonstrating the reduction of problems that require several hundred qubits to a single qubit. Our work shows that the QDSRG is a viable approach to leverage near-term quantum devices for estimating molecular properties with chemical accuracy, using only up to the diagonal elements of the two-body reduced density matrix of the reference state. © 2023 authors. Published by the American Physical Society. Published by the American Physical Society under the terms of the "https://creativecommons.org/licenses/by/4.0/"Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.