Early fault-tolerant quantum algorithms in practice

This is the code for the paper arXiv:2405.03754.

Initial state

The first step is to compute the initial state. This can be done with DMRG in the file dmrg.py using tenpy. Otherwise, a random initial state will be provided.

Dynamics

The second part of the algorithm is to compute the Fourier moments of the target Hamiltonian $\langle \psi| e^{-iH\tau j}|\psi\rangle$. This can be done with dynamics_pl.py and dyncamics_qsim.py scripts, which rely on pennylane and qsimcirq, respectively. In these scripts we consider the fully connected Heisenberg model and the evolution is performed with Trotterization via a swap network. The latter also supports GPU execution.

Lin and Tong algorithm

The bulk of the algorithm can be run using the main.py, which computes the Fourier decomposition (present in the algorithms/Fk.py), samples from the Fourier moments, and builds the estimator. The CDF for 26 spins fully connected Hamiltonian using low-bond dimension initial is displayed below.

Step detection

The steps are automatically detected within the main script through the algorithms/trendfliter.py. The step detection is better illustrated in the notebook resources_comparison.ipynb, which estimates the number of samples required to detect a step of a given size.

How to cite

If you use this work for your research, please cite us!

@misc{EFTQC_practice, title = "Early Fault-Tolerant Quantum Algorithms in Practice: Application to Ground-State Energy Estimation", author = {Oriel Kiss and Utkarsh Azad and Borja Requena and Alessandro Roggero and David Wakeham and Juan Miguel Arrazola }, year={2024}, month = {5}, eprint={2405.03754}, archivePrefix={arXiv}, primaryClass={quant-ph} }