This repository contains an implementation of simulated annealing (SA) and simulated quantum annealing (SQA) with path integral monte carlo (PIQMC). The interface to the code is written in Python 3 and the Monte Carlo sampling is written in Cython. This code was used to produce some of the results of this paper https://arxiv.org/abs/2101.10154.
Here, we have an implementation that supports the 2D Edwards-Anderson model, the Sherrington-Kirkpatrick model and the Wishart Planted Ensemble.
We note that this code is an adaptation from Hadayat Seddiqi's Cython code. We fixed some bugs, added global moves to the quantum annealing monte carlo dynamics and stripped the code of things that were not needed for our purposes.
In order to call the Cython code, we need to install the package. First, install the packages in environment.yml and then run
python setup.py installto install the piqmc module. The installation takes less than one minute with a typical CPU if the the packages in environment.yml are already available.
To test multiple experimental setups use the command line interface
python run_<EXPERIMENT>.py --<ARG1>=<VALUE1> --<ARG2>=<VALUE2> ...See the respective files to see which arguments can be passed.
We can save the residual energies, the MC times tested and the experiement parameters in the ./results/ folder.
This implementation consists of 4 parts:
- High performance SA and PIQMC QA Cython code. (
src/qmc.pyxandsrc/sa.pyx) - A python interface to call this code (
python_interface.py) that contains aQuantumPIAnnealclass for PIQMC andClassicalAnnealclass for SA. - A file with different spin models. Our implementation supports the 2D Edwards-Anderson model, and fully-connected models such as the Sherrington-Kirkpatrick model and the Wishart Planted Ensemble (
models.py). - Scripts to run different annealing experiments for either SA with (
run_SA_....py) or for PIQMC with (run_PIQMC_....py). Here, each run file corresponds to a different model.
We will list the availabe arguments below. The default settings are similar to Santoro (2002).
tau_schedule: The spacing of the quantum annealing schedule. Default is [1, 10, 100, 1000,10000,100000].
mcsteps: The number of MC sweeps to perform at each point in the schedule. The total number of MC steps is then equal to tau * mcsteps. Default value is 1.0.
gamma_0: The initial value of the transverse field gamma. Default value is 1.0.
gamma_T: The final value of the transverse field gamma. Default is 1e-8.
P: The number of Trotter slices. Default is 20.
PT: According to Santoro, the value of P*T is essential for the dynamics of the annealing. Here, T is the temperature, which is calculated from the value of PT. Default is 1.0.
q_scheds: This is a list of numpy arrays corresponding to the annealing schedules. Per default, these arrays are linearly spaced, beginning at gamma_0 and ending with gamma_T in tau_schedule[i] steps. One can in principle submit any list of schedules here, as long as they're arrays of length tau_schedule[i]
In order to make sure the system is sufficiently thermalized, we perform short thermal annealing scheme from T_0 to T (T defined above).
preannealing_temperature: Starting temperature for the pre-annealing schedule. Default is 3.0.
preannealing_schedule_steps: Number of steps in the pre-annealing schedule. Default is 60.
preannealing_mcsteps: Number of MC steps per point in the annealing schedule. Default is 100.
preannealing_sched: Linearly spaced annealing schedule starting at preannealing_temperature and ending at PT / P
tau_schedule: The spacing of the classical annealing schedule. Default is [1, 10, 100, 1000,10000,100000].
mcsteps: The number of MC sweeps to perform at each point in the schedule. The total number of MC steps is then equal to tau * mcsteps. Default value is 1.0.
T_0: The initial value of temperature. Default value is 1.0.
T_f: The final value of the temperature. Default is 1e-8.
num_warmup: The number of warmup steps to thermalize SA at T_0.
T_scheds: This is a list of numpy arrays corresponding to the annealing schedules. Per default, these arrays are linearly spaced, beginning at T_0 and ending with T_f in tau_schedule[i] steps. One can in principle submit any list of schedules here, as long as they are arrays of length tau_schedule[i]
numruns: Number of SA/PIQMC annealing runs. Each run corresponds to a specific random seed to control the initialization and MCMC random number generator.
seed: Random seed to identify the random instance of couplings to be imported from the data folder.
Using an Intel(R) Xeon(R) CPU E5-2683 v4 @ 2.10GHz, the typical number of monte carlo steps for PIQMC with 20 trotter slices on the 2D Edwards-Anderson model with 40x40 spins is ~50 per second. For SA, ~2000 monte carlo steps per second are performed on the same model. Similarly for the Sherrington-Kirkpatrick model with 100 spins, we have ~50 iterations per second for PIQMC with 100 trotter slices, while ~9000 iteractions per second for SA.
This code is licensed under the Do No Harm license and is intended for academic research that will be beneficial to humanity.
@misc{VNA2021,
title={Variational Neural Annealing},
author={Mohamed Hibat-Allah and Estelle M. Inack and Roeland Wiersema and Roger G. Melko and Juan Carrasquilla},
year={2021},
eprint={2101.10154},
archivePrefix={arXiv},
primaryClass={cond-mat.dis-nn}
}