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author description ms.author ms.date ms.service ms.subservice ms.topic title uid
sanjgupt
This document provides a basic guide about how to use the Quantum Monte Carlo solver.
sanjgupt
02/01/2021
azure-quantum
optimization
how-to
Quantum Monte Carlo
microsoft.quantum.optimization.quantum-monte-carlo

Quantum Monte Carlo

Quantum Monte Carlo is a Metropolis annealing algorithm, similar in concept to simulated annealing that starts at a low temperature and improves the solution by searching across barriers with some probability as an external perturbation is applied to the system. As this external field is varied over every Monte Carlo step, the configuration may be able to tunnel through energy barriers and evolve towards a desired ground state (without possessing the thermal energy needed to climb the barriers, as would be required in simulated annealing).

In Azure Quantum the core of algorithmic approach to our QMC implementation is based on the Wolff algorithm for annealing and we extended this approach with various improvement in our computational efficiency.

Features of Quantum Monte Carlo on Azure Quantum

  • Parameterized mode (with parameters)
  • Ising and PUBO input formats
  • CPU only

When to use Quantum Monte Carlo

This algorithm should perform best in the following two scenarios:

  • When there are tall, narrow barriers in the energy landscape (cost function)
  • If the solution is already at a feasible configuration at a low temperature and the user wishes to improve the solution

Note

For further information on determining which solver to use, refer to Which optimization solver should I use?.

Parameterized Quantum Monte Carlo (CPU)

Quantum Monte Carlo supports the following parameters:

Parameter Name Description
sweeps Number of sets of iterations to run over the variables of a problem. More sweeps will usually always improve the solution (unless it is already at the global min).
trotter_number The number of copies of every variable to generate for running the simulation.
restarts The number of repeats of the annealing schedule to run. Each restart will start with a random configuration unless an initial configuration is supplied in the problem file. The restarts will be executed in parallel and split amongst the threads of the virtual machine. Recommended to set this value to at least 72.
beta_start Represents the temperature at which the annealing schedule is executed. This should be a value low enough to produce a feasible configuration.
transverse_field_start & transverse_field_stop Represents the starting and stopping values of the external field applied to the annealing schedule. A suitable value for these parameters will depend entirely on the problem and the magnitude of its changing moves. In general a non-zero and declining acceptance probability is sufficient.
seed (optional) Seed value - used for reproducing results.

To create a parameterized Quantum Monte Carlo solver using the SDK:

from azure.quantum.optimization import QuantumMonteCarlo
# Requires a workspace to be already created
solver = QuantumMonteCarlo(workspace, sweeps = 2, trotter_number = 10, restarts = 72, beta_start = 0.1, transverse_field_start = 10, transverse_field_stop = 0.1, seed = 22)