MPS emulator for LUCJ circuits #334
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bartandrews
changed the title
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Note that by default, i.e. after running I think that this issue transcends tenpy and becomes a more general question of whether or not to link numpy/scipy against MKL, which is a matter of personal preference. Therefore, I suggest that we leave this as is. |
Thank you for reviewing this! 😃 I will implement these changes asap |
| abs(mpo_expectation.imag), | ||
| rtol=1e-05, | ||
| atol=1e-08, | ||
| ) |
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Shouldn't the expectation values be the same? Why do you only compare the absolute values of the real and imaginary parts?
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Yes, I also think that the expectation values should be the same. The diagonal matrix elements are exactly the same. For the off-diagonal matrix elements, sometimes there is a minus sign for either the real or imaginary part. I tried tinkering with the Hamiltonian to fix this, however I really don't understand why this is... 😕 If you have any ideas, please do let me know. I was planning to get back to it this week.
| # copyright notice, and modified files need to carry a notice indicating | ||
| # that they have been altered from the originals. | ||
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| """Tests for the TeNPy basic gates.""" |
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I see that in the gate tests, you do the following:
- Apply the gate to a product state as a state vector
- Apply the gate to a product state as an MPS
- Check that the expectation value on a molecular Hamiltonian matches in both cases.
Is it possible to retrieve the state vector amplitudes from the MPS? If so, then we don't need to introduce a Hamiltonian. We can just directly check that amplitudes stored by the MPS match the exact ones.
Another question is whether we can apply the evolution not to a product state, but to a random state instead. The basic gates often have trivial action on a product state. For example, applying a Givens rotation between two occupied orbitals doesn't do anything.
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It is possible to convert an MPS to statevector using the mps_to_full function. Yes, I agree that we should remove the MolecularHamiltonian from these gate tests, and keep the tests for the molecular Hamiltonian separate.
Generating a completely random MPS is non-trivial, since a generic random state from Hilbert space will have volume law entanglement, whereas MPS are good at representing states with area law entanglement. I presume that you mean a completely random state, and not just a random product state? One solution is to start with a random product state and then perform a TEBD RandomUnitaryEvolution to introduce some short-range entanglement. This will not result in a completely random state but it will be entangled to as much as the computational cost / bond dimension will allow.
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A uniformly random state would be ideal, but perhaps unnecessary. We should be able to represent such a state for small test sizes though, right? You can generate a uniformly random state vector using ffsim.random.random_state_vector. Is it possible to convert such a state vector into an MPS using Tenpy? Otherwise, I think your idea of generating a random evolution should be fine.
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Yes, for small system sizes you may be able to convert a completely random statevector into an MPS using the full_to_mps function. However, the bond dimension will blow up quite quickly. I will try this in the first instance and if it's not tractable, I will try the random unitary evolution approach.
The aims for this pull request: