Alleviating the Sparse Matrix Scaling Bottleneck in Adaptive VQE via High-Order Taylor State Evolution

• URL: http://arxiv.org/abs/2606.29692v1
• Date: Mon, 29 Jun 2026 01:40:26 GMT
• Title: Alleviating the Sparse Matrix Scaling Bottleneck in Adaptive VQE via High-Order Taylor State Evolution
• Abstract summary: Variational Quantum Eigensolver (VQE) is a leading algorithm for noisy intermediate-scale quantum devices.<n>Its adaptive variants (e.g., ADAPT-VQE) suffer from severe classical simulation bottlenecks during the ansatz growth phase.<n>We present a resource-efficient software-layer framework that completely bypasses dense matrix exponentiation.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The Variational Quantum Eigensolver (VQE) is a leading algorithm for noisy intermediate-scale quantum (NISQ) devices, but its adaptive variants (e.g., ADAPT-VQE) suffer from severe classical simulation bottlenecks during the ansatz growth phase. Representing and exponentiating pool operators for multi-qubit systems constructs massive sparse matrices that quickly scale to millions of elements, choking classical memory bandwidth and CPU/GPU cycle capacity. In this work, we present a resource-efficient software-layer framework that completely bypasses dense matrix exponentiation by evaluating state updates through a deterministic fifth-order (O(5)) Taylor series expansion. This approach reframes the costly unitary evolution into a chained sequence of five lightweight, successive sparse matrix-vector multiplications scaling strictly as O(Nz), where Nz is the number of non-zero elements. We validate our framework using equilibrium BeH2 (14 qubits), equilibrium H2O (12 qubits), and strongly correlated asymmetrically stretched H2O molecular profiles under both Jordan-Wigner (JW) and Bravyi-Kitaev (BK) transformations. The simulation results demonstrate that the O(5) truncation maintains exceptional numerical fidelity, retaining a state fidelity > 0.999999 and matching absolute ground state energies down to subchemical accuracy, while effortlessly navigating matrix spaces exceeding 268 million structural elements. This framework provides a scalable, high-performance pathway for executing deep variational simulations on hardware platforms with constrained computational budgets.

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