Size-Consistent Quantum Chemistry on Quantum Computers

TL;DR

Size consistency is a fundamental requirement for scalable quantum chemistry, but noise in NISQ devices threatens this property. The authors employ a method-agnostic approach using optimally shallow unitary circuits to transform Hartree–Fock states into exact FCI ground states for growing numbers of non-interacting H2 molecules, and measure subsystem energies via Pauli-string tomography with simultaneous measurement of commuting operators. They report that additive separability and multiplicative separability of excitation populations are preserved within chemical accuracy for up to 118 H2 subsystems with single-qubit mappings and 71 H2 subsystems with two-qubit mappings, though four-qubit circuits display higher variance due to noise. This demonstrates that current quantum hardware can maintain size-consistent behavior across chemically relevant system sizes, supporting scalable simulations of strongly correlated molecules and informing the development of size-consistent quantum algorithms on near-term devices.

Abstract

Hybrid quantum-classical algorithms have begun to leverage quantum devices to efficiently represent many-electron wavefunctions, enabling early demonstrations of molecular simulations on real hardware. A key prerequisite for scalable quantum chemistry, however, is size consistency: the energy of non-interacting subsystems must scale linearly with system size. While many algorithms are theoretically size-consistent, noise on quantum devices may couple nominally independent subsystems and degrade this fundamental property. Here, we systematically evaluate size consistency on quantum hardware by simulating systems composed of increasing numbers of non-interacting H$_{2}$ molecules using optimally shallow unitary circuits. We find that molecular energies remain size-consistent within chemical accuracy for an estimated 118 and 71 H$_{2}$ subsystems for one- and two-qubit unitary designs, respectively, demonstrating that current quantum devices preserve size consistency over chemically relevant system sizes and supporting the feasibility of scalable, noise-resilient simulation of strongly correlated molecules and materials.

Figures (3)

• Figure 1: Energy per H2 as system size ($N$) increases. Energies are calculated with single-qubit (left) and two-qubit (right) representations per subsystem. The energies for the single-qubit representation are simulated using the selective sample procedure ($N$=2,4,8,16; $n$=8,4,2,1; $k$=3) with the exception of $N$=1, which is generated using the random sample procedure (s=50). The energies for the two-qubit representation are also modeled using the selective sample procedure ($N$=1,2,4,8; $n$=8,4,2,1; $k$=5). Sample procedures are discussed at the end of the Letter. The energies are reported as the energy per H2 subsystem, represented as single-qubit: $\times$ (orange) and two-qubit: $+$ (blue) with a weighted least squares (WLS) line: $--$ (gray)
• Figure 2: (a) Average double-excitation population per H2 subsystem as system size increases. (b) Average single-excitation population per H2 as system size increases. The CISD result overlaps exactly with the FCI line. The populations for both figures are represented as single-qubit: $\times$ (orange), two-qubit: $+$ (blue), four-qubit: $\circ$ (green), CISD: $-$ (purple), and FCI: $-$ (black).
• Figure 3: Average energy error per H2 subsystem as system size increases. The energy errors are represented as single-qubit: $\times$ (orange), two-qubit: $+$ (blue), Hartree-Fock: $\cdots$ (red), and FCI: $-$ (black).