  Variational Quantum Algorithms (VQAs) represent a class of algorithms that
utilize a hybrid approach, combining classical and quantum computing
techniques. In this approach, classical computers serve as optimizers that
update circuit parameters to find approximate solutions to complex problems. In
this study, we apply a method known as Light Cone Cancellation (LCC) to
optimize variational circuits, effectively reducing the required number of
qubits and gates for circuit simulation. We then evaluate the performance of
LCC one of the VQAs -- the Variational Quantum Eigensolver (VQE) -- to address
the Max-Cut problem. Compared with the Quantum Approximate Optimization
Algorithm (QAOA), VQE offers greater degrees of freedom at lower circuit
depths. By applying LCC to VQE, we can shift the complexity of circuit
simulation from the number of qubits to the number of edges in the graph, i.e.,
from exponential time to polynomial time. This enables us to solve large
problems up to 50 vertices, without actually simulating the entire circuit.
From our simulation in a 7-qubit and a 27-qubit noisy devices, we show that LCC
yields higher approximation ratios than those cases without LCC, implying that
the effect of noise is reduced when LCC is applied.
