State Parameters

Our QCML model will build a representation of the data as quantum states. The method for solving for these states is a parameter that can be chosen and usually results in a tradeoff between cost and accuracy.

The recommendation from the Qognitive team is that the state_method = 'LOBPCG_FAST' should be used for the majority of cases.

The state parameterization has to be passed for both training (as the model will build quantum states of the data as it trains, refining the state representation as it goes) and for inference (the model will build a state from the provided data and generate inference from that state).

This documentation is broken up by each state_method parameter, each having their own parameters.

LOBPCG_FAST

The recommended method for most cases. This method uses the Locally Optimal Block Preconditioned Conjugate Gradient method to find the optimal state. We call this FAST because it reduces redundant numerical calculations when operating on a batch of data to speed up the computation versus a generic implementation of LOBPCG.

iterations: int The maximum number of iterations to run the LOBPCG algorithm for. You should think of this as a maximum number of internal iterations that are made to attempt the states to converge to within the tolerance. Both parameters work together, so if your tolerance is very large then you will need few iterations, so even if you set iteration count to 100 if it only takes 5 to converge to your tolerance only 5 iterations will be done. If your tolerance is very low but the iteration count is low then the algorithm will stop after the iteration count is reached, regardless of the tolerance. A good recommended range is 5-20, noting that the more iterations you do the more accurate the state will be, but the more computationally expensive it will be. tol: float, default=0.2. The tolerance for the LOBPCG algorithm. This is a relative tolerance and not an absolute one, so the units are arbitrary. Generally 0.2 which is the default is a very loose tolerance. If you want to have the output from this method close to one of the more exact solvers then try 1e-4 -> 1e-8 for the tolerance. As per the above discussion you should also increase your iterations if you are decreasing your tolerance. The tolerance and iterations are more important for inference as the model will only pass over that data once.

POWER_ITER

Here we use the power iteration method to find the optimal state. This method also exploits internal symmetries of the problem to speed up the computation versus more generic implementations of such as subspace solvers.

iterations: int The maximum number of iterations to run the POWER_ITER algorithm for. You should think of this as a maximum number of internal iterations that are made to attempt the states to converge to within the tolerance. Both parameters work together, so if your tolerance is very large then you will need few iterations, so even if you set iteration count to 100 if it only takes 5 to converge to your tolerance only 5 iterations will be done. If your tolerance is very low but the iteration count is low then the algorithm will stop after the iteration count is reached, regardless of the tolerance. A good recommended range is 5-20, noting that the more iterations you do the more accurate the state will be, but the more computationally expensive it will be. tol: float, default=0.2. The tolerance for the POWER_ITER algorithm. This is a relative tolerance and not an absolute one, so the units are arbitrary. Generally 0.2 which is the default is a very loose tolerance. If you want to have the output from this method close to one of the more exact solvers then try 1e-4 -> 1e-8 for the tolerance. As per the above discussion you should also increase your iterations if you are decreasing your tolerance. The tolerance and iterations are more important for inference as the model will only pass over that data once. max_eig_iter: int, default=5 The number of iterations to execute to find the largest eigenvalue, which is used as a parameter in a spectral shift to find the smallest eigenvalue. 5 is generally a good default.

EIGS

This uses the scipy EIGS solver.

tol: float, default=0.2. The tolerance for the EIGS algorithm. This is a relative tolerance and not an absolute one, so the units are arbitrary. Generally 0.2 which is the default is a very loose tolerance. If you want to have the output from this method close to one of the more exact solvers then try 1e-4 -> 1e-8 for the tolerance. You can see more details about this method here. Only tol is supported as a parameter for this method.

EIGH

This uses the scipy EIGH solver. EIGH takes no parameters. You can see more details about this method here.

NP_EIGH

This uses the numpy EIGH solver. EIGH takes no parameters. You can see more details about this method here.

LOBPCG

This uses the scipy LOBPCG solver. You can see more details about this method here.

iterations: int You should think of this as a maximum number of internal iterations that are made to attempt the states to converge to within the tolerance. Both parameters work together, so if your tolerance is very large then you will need few iterations, so even if you set iteration count to 100 if it only takes 5 to converge to your tolerance only 5 iterations will be done. If your tolerance is very low but the iteration count is low then the algorithm will stop after the iteration count is reached, regardless of the tolerance. A good recommended range is 5-20, noting that the more iterations you do the more accurate the state will be, but the more computationally expensive it will be. tol: float, default=0.2. This is a relative tolerance and not an absolute one, so the units are arbitrary. Generally 0.2 which is the default is a very loose tolerance. If you want to have the output from this method close to one of the more exact solvers then try 1e-4 -> 1e-8 for the tolerance. As per the above discussion you should also increase your iterations if you are decreasing your tolerance. The tolerance and iterations are more important for inference as the model will only pass over that data once.

GRAD

Using a gradient descent procedure with fixed learning rate we find our way to the optimal state.

iterations: int This is how many gradient descent steps will be made before considering the state to have converged. Having more iterations and a lower learning rate corresponds to a better path through the energy landscape. So if you were to take 10 steps at 1e-3 learning rate that is more accurate, as we recompute our gradient 10 times, than a single step of 1e-2 learning rate. The recommended range is 3-10. learning_rate: float The learning rate for the gradient descent algorithm. This is fixed and does not decay during optimization. Recommended values are around 1e-3.