I. Introduction
The current era of noisy-intermediate scale quantum computing (NISQ) [1] allows us to get in touch with a technology that, one day, might outperform classical digital computers on useful tasks. Quantum algorithms exist whose theoretical runtime guarantees supersede those of their classical coun-terparts [2]. However, the noise inherent to NISQ machines prevents the application of well-known quantum algorithms with proven speedups. Oppositely, variational quantum eigen-solvers (VQE) [3] are more robust and hence well suited to the available hardware. In VQE, one iteratively optimizes a set of parameters with respect to their performance on a given cost function. Applications include, among others, ground state approximation [4], [5], simulation of imaginary-time evolution [6] and quantum machine learning [7]. However, NISQ devices still suffer from limitations such as low circuit depth caused by large error probabilities and short decoherence times. Moreover, the recently exposed problem of barren plateaus [8] causes gradients of cost functions to become exceedingly small as the number of system qubits is increased. In turn, this diminishes some of VQE's potential for problems of a practically relevant size [9]. To bypass such issues, we consider evolutionary strategies for learning the parameters of circuits, which removes the need for gradient computations and further allows us to estimate the circuit structure jointly with the parameters.
Expected energy versus calls to a quantum computer for a gradient-descent method (gd) and our proposed evolutionary method (qneat). The expected energy of an 8-qubit transverse field ising hamiltonian has to be minimized. Qneat performs a (1 + 4) ea using the gates , starting with a circuit containing one random gate. Gd starts with a random pauli 2-design ansatz with 40 parameters and computes derivatives via parameter shifts [10] used for parameter updates with fixed learning rate . Five runs with random initial conditions yield mean and standard deviation. The variance stems from the random initial gates and the particular mutations for qneat, and from the random ansatz and parameter initialization for gd. The experiment was performed using a noise- free state vector simulation.