Quantum resource trade-offs of mixed sparse single and double factorization for qubitization-based phase estimation

arXiv:2611.05603v1 Announce Type: new Abstract: We study a mixed block encoding of quantum-chemistry Hamiltonians for quantum phase estimation (QPE) on fault-tolerant quantum computers. Following a Cholesky decomposition of the electron repulsion integral tensor, we assign each Cholesky tensor to either a double-factorization (DF) branch or a sparse-single-factorization (SPSF) branch. This freedom permits a trade-off between reducing the block-encoding normalization factor $\lambda$ with DF and reducing the coefficient data loaded through quantum read-only memory (QROM) with SPSF. Resource estimates across molecular benchmarks show, however, that the mixed circuit does not generally reduce the Toffoli count relative to the less expensive pure circuit.