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arXiv:2606.19457

Efficient classical representation and quantum state preparation of complete active space wavefunctions

Hamza Jnane

quant-phphysics.chem-phSubmitted Jun 17, 2026• Announced Jun 19, 2026• 0 citations• Revised Jun 21, 2026 (v2)
v1 · Jun 17, 2026v2 · Jun 21, 2026
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Abstract

Quantum computers promise to solve the electronic structure problem for a large class of molecules. However, the performance of relevant quantum algorithms hinges on preparing initial states with substantial overlap with the target eigenvector. For classically challenging molecules with strong electron correlation, starting from multi-reference states, such as complete active space (CAS) wavefunctions is necessary. Unfortunately, the most advanced state preparation protocols applied to such states result in a gate complexity that scales exponentially with the active space size $d$. In fact, even encoding a CAS state classically is traditionally believed to be intractable for chemically relevant systems. Here, we draw insights from the recently introduced Quantum Paldus Transform (QPT) to show that there exists an efficient classical representation of CAS states and to design a new state preparation routine outperforming previous ones. The QPT represents a transformation from the Fock basis to a friendlier symmetry-adapted basis. Our main contribution consists in showing that CAS states expanded in this basis can efficiently be represented as a matrix product state (MPS) with a bond dimension scaling as $O(d^2)$. One can then efficiently load the MPS on a quantum computer and use the inverse QPT to transform the state to the Fock basis. Moreover, our method can easily be extended to the efficient preparation of CAS states in first quantisation with similar complexity. Crucially, we demonstrate that the complexity of both state preparation protocols only grows polynomially as $O(d^3)$ , which constitutes to the best of our knowledge an exponential improvement over the state of the art.

Comments
In Theorem 1 the Schmidt rank is bounded by the number of nodes in the graph. But the node count controls only the support (which walks are allowed), not the amplitudes. The node label cannot distinguish the exponentially many walks passing through it. The argument thus holds only for the uniform superposition of CSFs and product-of-edge-weight states, not a generic CAS state

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