  H\"uckel molecular orbital (HMO) theory provides a semi-empirical treatment
of the electronic structure in conjugated {\pi}-electronic systems. A scalable
system-agnostic execution of HMO theory on a quantum computer is reported here
based on a variational quantum deflation (VQD) algorithm for excited state
quantum simulation. A compact encoding scheme is proposed here that provides an
exponential advantage over direct mapping and allows quantum simulation of the
HMO model for systems with up to 2^N conjugated centers in N qubits. The
transformation of the H\"uckel Hamiltonian to qubit space is achieved by two
different strategies: a machine-learning-assisted transformation and the
Frobenius-inner-product-based transformation. These methods are tested on a
series of linear, cyclic, and hetero-nuclear conjugated {\pi}-electronic
systems. The molecular orbital energy levels and wavefunctions from the quantum
simulation are in excellent agreement with the exact classical results. The
higher excited states of large systems, however, are found to suffer from error
accumulation in the VQD simulation. This is mitigated by formulating a variant
of VQD that exploits the symmetry of the Hamiltonian. This strategy has been
successfully demonstrated for the quantum simulation of C_{60} fullerene
containing 680 Pauli strings encoded on six qubits. The methods developed in
this work are system-agnostic and hence are easily adaptable to similar
problems of different complexity in other fields of research.
