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Abstract Molecular simulations generally require fermionic encoding in which fermion statistics are encoded into the qubit representation of the wave function. Recent calculations suggest that fermionic encoding of the wave function can be bypassed, leading to more efficient quantum computations. Here we show that the two-electron reduced density matrix (2-RDM) can be expressed as a unique functional of the unencodedN-qubit-particle wave function without approximation, and hence, the energy can be expressed as a functional of the 2-RDM without fermionic encoding of the wave function. In contrast to current hardware-efficient methods, the derived functional has a unique, one-to-one (and onto) mapping between the qubit-particle wave functions and 2-RDMs, which avoids the over-parametrization that can lead to optimization difficulties such as barren plateaus. An application to computing the ground-state energy and 2-RDM of H4is presented.
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This content will become publicly available on July 28, 2026
Spin adaptation of the cumulant expansions of reduced density matrices
We develop a systematic framework for the spin adaptation of the cumulants of p-particle reduced density matrices (RDMs), with explicit constructions for p = 1 to 3. These spin-adapted cumulants enable rigorous treatment of both Ŝz and Ŝ2 symmetries in quantum systems, providing a foundation for spin-resolved electronic structure methods. We show that complete spin adaptation—referred to as completeS-representability—can be enforced by constraining the variances of Ŝz and Ŝ2, which require the 2-RDM and 4-RDM, respectively. Importantly, the cumulants of RDMs scale linearly with system size—size-extensive—making them a natural object for incorporating spin symmetries in scalable electronic structure theories. The developed formalism is applicable to density-based methods, one-particle RDM functional theories, and two-particle RDM methods. We further extend the approach to spin–orbit-coupled systems via total angular momentum adaptation. Beyond spin, the framework enables the adaptation of RDM theories to additional symmetries through the construction of suitable irreducible tensor operators.
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- Award ID(s):
- 2155082
- PAR ID:
- 10618251
- Publisher / Repository:
- AIP
- Date Published:
- Journal Name:
- The Journal of Chemical Physics
- Volume:
- 163
- Issue:
- 4
- ISSN:
- 0021-9606
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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