Efficient excited-state calculations for molecules based on contextual subspace method and symmetry optimizations

Abstract Quantum computing methods for excited-state calculations remain underexplored in noisy intermediate-scale quantum hardware, despite their critical role in photochemistry and material science. Herein, we propose a resource-efficient framework that integrates the contextual subspace method with the variational quantum deflation algorithm to enable systematic excited-state calculations for molecules while reducing qubit requirements. On the basis of the numerical results, we find that it is unproblematic to utilize this combination in calculating the excited state to reduce qubits. Furthermore, we demonstrate that the implementation of a spin-conserving hardware-efficient ansatz, namely the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mrow> <mml:mi class="MJX-tex-calligraphic">N</mml:mi> </mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:msub> <mml:mi>θ</mml:mi> <mml:mi>x</mml:mi> </mml:msub> <mml:mo>,</mml:mo> <mml:msub> <mml:mi>θ</mml:mi> <mml:mi>y</mml:mi> </mml:msub> <mml:mo>,</mml:mo> <mml:msub> <mml:mi>θ</mml:mi> <mml:mi>z</mml:mi> </mml:msub> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> </mml:math> block ansatz, allows exploitation of spin symmetry within the projected subspace, thereby achieving further reductions in computational resource demands. Compared to the commonly used <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>R</mml:mi> <mml:mrow> <mml:mi>Y</mml:mi> </mml:mrow> </mml:msub> <mml:msub> <mml:mi>R</mml:mi> <mml:mrow> <mml:mi>Z</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> ansatz, using the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mrow> <mml:mi class="MJX-tex-calligraphic">N</mml:mi> </mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:msub> <mml:mi>θ</mml:mi> <mml:mi>x</mml:mi> </mml:msub> <mml:mo>,</mml:mo> <mml:msub> <mml:mi>θ</mml:mi> <mml:mi>y</mml:mi> </mml:msub> <mml:mo>,</mml:mo> <mml:msub> <mml:mi>θ</mml:mi> <mml:mi>z</mml:mi> </mml:msub> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> </mml:math> ansatz can reduce the number of optimization iterations by up to three times at a similar circuit depth.