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

In this repository, we save all the data used in the article "Challenges of variational quantum optimization with measurement shot noise" Phys. Rev. A 109, 032408.

For reproducing the same figure as in the article, we provide an interactive notebook 'paper-figure.ipynb' and its HTML version. 

Data

Unzip with

tar -xvf data.tar.gz

You will find ten data files:

•  `dataferro.csv` Ferromagnetic model both for VQE and QAOA with random parameters initialization;
• `datanoise.csv`Ferromagnetic model for VQE with random parameters initialization and circuit noise;
• `data_spinglass.csv` Disordered model both for VQE and QAOA with random parameters initialization;
• `data_linopt.csv` Ferromagnetic model for QAOA with annealing-like parameters initialization;
• `data_lininit_rand.csv` Disordered model for QAOA with annealing-like parameters initialization;
• `data_spinglass_iter1.csv` Disordered model for QAOA, no optimization and random parameters initialization;
• `data_opt16shots.csv` Ferromagnetic model for QAOA, no optimization and annealing-like parameters initialization;
• `datagrad.csv` Ferromagnetic model for VQE with gradient-based optimization;
• `datagrad_eps05.csv` Ferromagnetic model for QAOA with gradient-based optimization;
• `grad_epsilon.npz` Ferromagnetic model for QAOA with gradient-based optimization, varying \(\varepsilon\) in the finite differences formula.

Most of the data are CSV sheets, where you can find the aggregate results of the simulations described in our article. 

Abstract

Quantum enhanced optimization of classical cost functions is a central theme of quantum computing due to its high potential value in science and technology.
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.
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.
Simple and reproducible problem instances are addressed, namely, the ferromagnetic and disordered Ising chains. 
Our results show that: 

1. 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;
2. When the parameters are optimized from random guesses, also the scaling of QAOA implies problematically long absolute runtimes for large problem sizes;
3. QAOA becomes practical when supplemented with a physically-inspired initialization of the parameters.

Our results suggest that hybrid quantum-classical algorithms should possibly avoid a brute force classical outer loop, but focus on smart parameters initialization.