SQD-Enabled Circuit Compression for Resource-Efficient Quantum Chemistry

As quantum processors remain limited by noise and decoherence, researchers face a trade-off between circuit expressivity and hardware feasibility. This paper investigates whether the post-processing technique known as Subspace Quantum Diagonalization (SQD) can relax the requirements for variational quantum circuits. Specifically, the authors ask: how much can we prune excitation operators and simplify non-Clifford gates in a Variational Quantum Eigensolver (VQE) ansatz before the final SQD-refined energy accuracy degrades?

The authors propose a three-stage pipeline to improve resource efficiency in quantum chemistry simulations:

1. Qubit Reduction: The Hamiltonian is projected into a smaller 'contextual subspace' that captures the dominant low-energy physics, significantly reducing the required qubit count.
2. Compressed VQE: Within this reduced space, the authors apply two compression techniques: gradient-based operator pruning, which removes low-impact excitation operators, and Clifford rounding, which converts non-Clifford gates into Clifford gates (which are classically efficient to simulate).
3. SQD Recovery: The compressed circuit is used only as a sampler to generate bitstrings. These samples are then used to construct a configuration interaction matrix, which is solved classically to recover the ground-state energy.

The study demonstrates that SQD is remarkably robust to circuit imperfections. Across 21 molecules, the authors found that median SQD error remains within chemical accuracy even when 50% of the operators are pruned and 50% of the remaining parameters are rounded to Clifford angles. Simulation speedups reached up to 33x, and hardware validation on IBM quantum processors confirmed a 2.8x reduction in transpiled circuit depth with zero loss in final SQD accuracy.