Quantum landscape tomography for efficient single-gate optimization on quantum computers

Several proposals aiming to demonstrate quantum advantage on near-term quantum computers rely on the optimization of variational circuits. These approaches include, for example, variational quantum eigensolvers and many-body quantum simulators and their realization with limited computational techniques critically depends on the development of efficient optimization techniques. In this paper, we introduce a new optimization strategy for dense quantum circuits, leveraging tensor network optimization principles. Our approach focuses on optimizing one gate at a time by fully characterizing the dependency of the cost function on the gate through environment tensor tomography, obtained via noisy measurements on a quantum device. We compute the minimal number of measurements needed to perform a full tensor tomography and relate this number to unitary 2-design. We then describe a general framework for landscape tomography based on linear regression and compare two different implementations based on shadow tomography and Clifford tableaux, respectively. Finally, we compare our strategy with both gradient-free optimization and gradient-based optimization based on the parameter-shift rule, highlighting potential benefits of our algorithm for the development of quantum algorithms in noisy devices.