Data for "Challenges of variational quantum optimization with measurement shot noise"

<p>In this repository, we save all the data used in the article <em>"Challenges of variational quantum optimization with measurement shot noise"</em> <a href="https://doi.org/10.1103/PhysRevA.109.032408" target="_blank" rel="noopener">Phys. Rev. A 109, 032408</a>.</p> <p>For reproducing the same figure as in the article, we provide an interactive notebook 'paper-figure.ipynb' and its HTML version.&nbsp;</p> <p><strong>Data</strong></p> <p>Unzip with</p> <pre><code>tar -xvf data.tar.gz</code></pre> <p>You will find ten&nbsp;data&nbsp;files:</p> <ul> <li>&nbsp;`dataferro.csv` Ferromagnetic model both for VQE and QAOA with random parameters initialization;</li> <li>`datanoise.csv`Ferromagnetic model for VQE with&nbsp;random parameters initialization and circuit noise;</li> <li>`data_spinglass.csv` Disordered model both for VQE and QAOA with random parameters initialization;</li> <li>`data_linopt.csv` Ferromagnetic model for QAOA with annealing-like parameters initialization;</li> <li>`data_lininit_rand.csv` Disordered model for QAOA with annealing-like parameters initialization;</li> <li>`data_spinglass_iter1.csv` Disordered model for QAOA, no optimization and random parameters initialization;</li> <li>`data_opt16shots.csv` Ferromagnetic model for QAOA, no optimization and annealing-like parameters initialization;</li> <li>`datagrad.csv` Ferromagnetic model for VQE with gradient-based optimization;</li> <li>`datagrad_eps05.csv` Ferromagnetic model for QAOA with gradient-based optimization;</li> <li>`grad_epsilon.npz` Ferromagnetic model for QAOA with gradient-based optimization, varying \(\varepsilon\)&nbsp;in the finite differences formula.</li> </ul> <p>Most of the data are CSV sheets, where you can find the aggregate results of the simulations described&nbsp;in our&nbsp;article.&nbsp;</p> <p><strong>Abstract</strong></p> <p>Quantum enhanced optimization of classical cost functions is a central theme of quantum computing due to its high potential value in science and technology.<br>The variational quantum eigensolver (VQE) and the quantum approximate optimization algorithm (QAOA) are popular variational approaches that are considered the most viable solutions in the noisy-intermediate scale quantum (NISQ) era.<br>Here, we study the scaling of the quantum resources, defined as the required number of circuit repetitions, to reach a fixed success probability as the problem size increases, focusing on the role played by measurement shot noise, which is unavoidable in realistic implementations.<br>Simple and reproducible problem instances are addressed, namely, the ferromagnetic and disordered Ising chains.&nbsp;<br>Our results show that:&nbsp;</p> <ol> <li>VQE with the standard heuristic ansatz scales comparably to direct brute-force search when energy-based optimizers are employed. The performance improves at most quadratically using a gradient-based optimizer;</li> <li>When the parameters are optimized from random guesses, also the scaling of QAOA implies problematically long absolute runtimes for large problem sizes;</li> <li>QAOA becomes practical when supplemented with a physically-inspired initialization of the parameters.</li> </ol> <p>Our results suggest that hybrid quantum-classical algorithms should possibly avoid a brute force classical outer loop, but focus on smart parameters initialization.</p>