Light Cone Cancellation for Variational Quantum Eigensolver in Solving Noisy Max-Cut

Abstract

Variational Quantum Eigensolver (VQE) is a quantum-classical hybrid algorithm used to estimate the ground energy of a given Hamiltonian. It consists of a parameterized quantum circuit, which the parameters are optimized using a classical optimizer. With the increasing need in solving large-scale problems in real-world applications, solving those large problems with fewer qubits and fewer gates becomes essential, so that we reduce the simulation difficulty and mitigate the effect of noise in real quantum hardware. In this study, we applied the Light Cone Cancellation (LCC) method to reduce the number of qubits and gates required in a two-local ansatz. LCC removes redundant gates that are not required in the calculation of the expectation value for a local observable. This leads to two consequences: 1) the quantum circuit used to create the trial wavefunction of VQE can be broken down into multiple quantum subcircuits with fewer qubits, enabling large-scale problems to be solved without actually simulating the entire circuit; and 2) reduced number of quantum gates in the circuit leads to the noise mitigation in quantum hardware. The main purpose of this work is to demonstrate the effectiveness of this method (called the LCC-VQE) in mitigating the device noise when solving the Max-Cut problem up to 100 qubits, using simulations on small (7-qubit and 27-qubit) fake noisy backends. Employing a single-layer two-local ansatz circuit architecture, the reuslts show that LCC-VQE yields higher approximation ratios than those cases without LCC, implying that the effect of noise is mitigated when LCC is applied. An analysis of more than one layer of two-local ansatz is also performed, but empirical results show that the single-layer ansatz still performs the best among them. We also compare LCC-VQE under noiseless conditions with the Goemans-Williamson algorithm.