Light Cone Cancellation for Variational Quantum Eigensolver Ansatz

Abstract: 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 on 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 and brings better performance 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 with up to 100 vertices without actually simulating the entire circuit. From demonstration results on 7-qubit and 27-qubit fake backends, 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.