Abstract

Quantum computers promise to transform molecular simulation, but many existing algorithms overlook the powerful role of spin symmetry in chemistry. The Quantum Paldus Transform provides a new framework that makes spin adaptation a built-in feature of quantum computation.

At its core, the transform connects two representations of electronic states: the conventional occupation-number basis used in quantum chemistry, and a symmetry-adapted basis that organises states by total spin, particle number, and orbital symmetries. This shift, grounded in mathematical structure known as Paldus duality, allows quantum devices to work directly with spin-pure states – the natural language of chemistry.

The benefits are considerable. Spin-free Hamiltonians reduce to block-diagonal, sparser forms, enabling more efficient simulations. The transform itself admits polynomial-cost implementations and even highly compact circuit constructions. Beyond simulation, the framework facilitates efficient preparation of Configuration State Functions (CSFs) and naturally embeds quantum information in decoherence-free subsystems, offering potential protection against certain noise channels.

By extending the quantum Schur transform into the fermionic setting, the Quantum Paldus Transform establishes a principled and practical route for exploiting spin symmetry in quantum algorithms. This framework opens new directions for scalable, accurate, and symmetry-aware quantum chemistry algorithms on quantum computers