Resource-efficient Quantum Algorithms for Selected Hamiltonian Subspace Diagonalization

• URL: http://arxiv.org/abs/2603.13160v1
• Date: Fri, 13 Mar 2026 16:51:19 GMT
• Title: Resource-efficient Quantum Algorithms for Selected Hamiltonian Subspace Diagonalization
• Abstract summary: Quantum algorithms for selecting a subspace of Hamiltonians to diagonalize have emerged as a promising alternative to variational algorithms in the NISQ era.<n>We introduce the first QSCI developed in the CI-matrix framework, which is known to have optimal qubit scaling of exactly $lceil log rceil$ where $N$ is the size of the CIM.<n>We introduce an augmented version of QSCI called quantum selected heat-bath CI (QSHCI) to achieve comparable performance to classical heat-bath CI.
• Score: 0.06999740786886537
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Quantum algorithms for selecting a subspace of Hamiltonians to diagonalize have emerged as a promising alternative to variational algorithms in the NISQ era. So far, such algorithms, which include the quantum selected configuration interaction (QSCI) and sample-based quantum diagonalization (SQD), have been formulated in second-quantization in Fock space, which leads to inefficient usage of qubit resources. We introduce the first QSCI algorithm developed in the CI-matrix (CIM) framework, which is known to have optimal qubit scaling of exactly $\lceil \log_2 (N_{CSF}) \rceil$ where $N$ is the size of the CIM. In addition, we introduce a novel single-bit flip error mitigation which comes at the overhead of a single qubit and we combine this with a stochastic approximate Trotterization evolution adapted from qDRIFT. Simulating benchmark N$_2$ and naphthalene molecules on quantum hardware, our results achieved similar accuracy as SQD methods but with significantly less quantum resources. However, our CIM-QSCI algorithm and SQD methods could not match the performance of classical heat-bath CI (HCI) for the same task. Hence, we introduce an augmented version of QSCI called quantum selected heat-bath CI (QSHCI). This variant replaces classical heat-bath sampling with quantum sampling from QSCI to achieve performance comparable to HCI. We note that a current drawback of our approach is the preprocessing cost of $\mathcal{O}(N^2\log N)$ for constructing the CIM and performing the Pauli decomposition. This can be further improved by considering efficient CIM access models for the stochastic Trotter evolution.

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