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H\"uckel molecular orbital (HMO) theory provides a semi-empirical treatmentof the electronic structure in conjugated {\pi}-electronic systems. A scalablesystem-agnostic execution of HMO theory on a quantum computer is reported herebased on a variational quantum deflation (VQD) algorithm for excited statequantum simulation. A compact encoding scheme is proposed here that provides anexponential advantage over direct mapping and allows quantum simulation of theHMO model for systems with up to 2^N conjugated centers in N qubits. Thetransformation of the H\"uckel Hamiltonian to qubit space is achieved by twodifferent strategies: a machine-learning-assisted transformation and theFrobenius-inner-product-based transformation. These methods are tested on aseries of linear, cyclic, and hetero-nuclear conjugated {\pi}-electronicsystems. The molecular orbital energy levels and wavefunctions from the quantumsimulation are in excellent agreement with the exact classical results. Thehigher excited states of large systems, however, are found to suffer from erroraccumulation in the VQD simulation. This is mitigated by formulating a variantof VQD that exploits the symmetry of the Hamiltonian. This strategy has beensuccessfully demonstrated for the quantum simulation of C_{60} fullerenecontaining 680 Pauli strings encoded on six qubits. The methods developed inthis work are system-agnostic and hence are easily adaptable to similarproblems of different complexity in other fields of research.

H\"uckel Molecular Orbital Theory on a Quantum Computer: A Scalable System-Agnostic Variational Implementation with Compact Encoding