QEM-aware Quantum Advantage Benchmarking

Benchmarking toolkit for quantifying the likeliness of quantum advantage for quantum optimization problems in the presence of quantum error mitigation.

Corresponding article

This is the code used in relation to the article Error-mitigation aware benchmarking strategy for quantum optimization problems by Marine Demarty, Bo Yang, Kenza Hammam and Pauline Besserve.

Case considered

As a work example we have implemented the following problem instance, error mitigation strategy and quantum circuit, however, generalization to other problems, noise models and quantum error mitigation techniques is possible.

• Problem: 2D Fermi-Hubbard model with periodic boundary conditions with $L$ sites.
• Quantum circuit: $n$-qubit circuit with $D$ layers of quantum gates.
• Noise model on quantum hardware: layerwise global depolarizing noise with probability $P$.
• Quantum error mitigation method: probabilistic error mitigation (PEC).

Example code output

Phase diagram function of the noise level $P$ and allowed shot count $N_\text{shots}$ for the target quantum hardware platform indicating in which regime quantum advantage is possible whether or not in the presence of quantum error mitigation, and when the noise level and shot count do not allow quantum advantage. Here for a Hubbard model with $L=64$ sites, and parameters $(U, t, mu) = (8, 1, 3.75)$, a quantum circuit with depth $D=L=64$ and $n=2L=128$ qubits, and a quantum advantage threshold of $0.95$.

How to use this code

Setup

qemqadv.yml contains all necessary dependencies for running this code.

Workflow for obtaining the plots from our paper

• get_hubbard_properties.py is used to compute properties of the target Fermi-Hubbard problem instance, in particular the trace of the Hamiltonian and its Pauli-norm. Those are stored in a json file in the Hubbard folder.
• get_success_proba.py loads the previous json file, then implements the computes the success probability of quantum advantage in the presence and absence of PEC. This is stored in a json file in the PEC/data folder.
• plot_success_proba.py loads the previous json file, then plots the figures shown in our article and saves them to the PEC/plots folder.
• jupyter notebook compute_error_tails_with_true_E0.ipynb is used to obtain the plot presented as Fig.6, in Appendix C.