  Quantum critical point is one key concept for studying many-body physics but
its investigation may be resource-demanding even for a quantum computer due to
the intrinsic complexity. In this paper, we propose an approach based on
variational quantum eigensolver(VQE), dubbed as Delta-VQE, for locating the
quantum critical point using only shallow quantum circuits. With Delta-VQE, the
critical point can be identified as a most confusing point, quantified as zero
difference between two variational energies that use two representative
reference states of distinct phases of matter. Remarkably, the signature of a
critical point as a minimal point can be sharper while using shallower quantum
circuits. We test the algorithm for different quantum systems and demonstrate
the usefulness of Delta-VQE. The scheme suggests a new avenue for investigating
quantum phases of matter on near-term quantum devices with limited quantum
resources.
