Introduce groundstate
#412
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| function groundstate( | ||
| A::QuantumObject{OpType}; | ||
| safe::Bool = true, | ||
| tol::Real = 1e-8, | ||
| kwargs..., | ||
| ) where {OpType<:Union{OperatorQuantumObject,SuperOperatorQuantumObject}} | ||
| # TODO: support for sparse eigsolve | ||
| #if !sparse | ||
| result = eigen(A; kwargs...) | ||
| #else | ||
| # eigvals = safe ? 2 : 1 # number of eigenvalues to calculate | ||
| # result = eigsolve(A; eigvals = eigvals, tol = tol, kwargs...) | ||
| #end | ||
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| # the tolarence should be less strick than the `tol` for the eigensolver | ||
| # so it's numerical errors are not seen as degenerate states. | ||
| evals = result.values | ||
| safe && (abs(evals[2] - evals[1]) < (10 * tol)) && @warn "Ground state may be degenerate." | ||
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| return evals[1], QuantumObject(result.vectors[:, 1], _eigenvector_type(OpType), result.dimensions) |
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I would suggest to use eigenstates instead of eigen. In this way we can use all the internal kwargs, including also the sparse one.
In the case of sparse, it automatically finds the largest eigenvalue by the nature of the Arnoldi algorithm. However, this can be fixed by defining a sigma argument, which performs the shift-inverse procedure.
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That is why I didn't use the eigenstates
Because this function is only for calculating ground state. We should assign some of the keyword arguments, make it not adjustable from the users.
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What value should I set for sigma in eigsolve to make it search for the lowest eigenvalue first?
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Because this function is only for calculating ground state. We should assign some of the keyword arguments, make it not adjustable from the users.
What do you mean exactly? If we use eigenstates(A; kwargs...) we can forward all the kwargs to that, even the sparse = ... (which by default is false, so that we fall in this case). If the user specify sparse=true, then he/she is supposed to be more advanced, and should know that the shift-inverse method applies here. By doing so, they should also specify a sigma shift value. We can even write a note on that.
What value should I set for
sigmaineigsolveto make it search for the lowest eigenvalue first?
sigma should be a value smaller than the supposed ground state energy. Let say that you expect the ground state energy to me close to 0, then sigma=-0.1 is fine.
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So, in general, I should set sigma = -Inf ?
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No this won't work. This is problem dependent.
The user using sparse=true is supposed to be advanced to be able to set this value.
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Hmm
Ok
I would probably close this PR.
Seems like we cannot make it.
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Description
This PR introduce a new function:
groundstateto calculate the ground state eigenvalue and corresponding eigenvector.This function currently doesn't support
sparseeigsolve. Because it seems thatsparseeigsolve doesn't find the smallest eigenvalue first.