  Variational quantum algorithms (VQAs) are promising methods to demonstrate
quantum advantage on near-term devices as the required resources are divided
between a quantum simulator and a classical optimizer. As such, designing a VQA
which is resource-efficient and robust against noise is a key factor to achieve
potential advantage with the existing noisy quantum simulators. It turns out
that a fixed VQA circuit design, such as the widely-used hardware efficient
ansatz, is not necessarily robust against imperfections. In this work, we
propose a genome-length-adjustable evolutionary algorithm to design a robust
VQA circuit that is optimized over variations of both circuit ansatz and gate
parameters, without any prior assumptions on circuit structure or depth.
Remarkably, our method not only generates a noise-effect-minimized circuit with
shallow depth, but also accelerates the classical optimization by substantially
reducing the number of parameters. In this regard, the optimized circuit is far
more resource-efficient with respect to both quantum and classical resources.
As applications, based on two typical error models in VQA, we apply our method
to calculate the ground energy of the hydrogen and the water molecules as well
as the Heisenberg model. Simulations suggest that compared with conventional
hardware efficient ansatz, our circuit-structure-tunable method can generate
circuits apparently more robust against both coherent and incoherent noise, and
hence is more likely to be implemented on near-term devices.
