Answering a question if photonic circuits with time delays (PRL 116, 093601, 2016) could be implemented within openMPS. Here one possible scheme:
Dear Dr. *****,
from the initial reading of this system I would say the simulations include system plus environment, which is a pure state. Pure states are suitable for the openMPS library and our focus has been on long-range interactions for statics and dynamics. I am not aware that anyone was or is trying to simulate such a system with our library, and I am most concerned about the time delays. The bins with different values of +/- p have to be coupled at different times. The long-range terms that we have implemented, would turn couplings on or off for all p. Other approaches using our long-range features get inefficient for many bins p. They key in their implementation are the swap gates; I assume they implement the gate directly and not as unitary evolution, which is not supported in openMPS. I assume they tailored their code for this purpose based on a good initial library.
The approach I can see is to implement the system with our library are multiple time-dependent evolutions, i.e., executing alternating the unitary evolution under the Hamiltonian and the SWAP gates as unitary time evolution. That is the way I would go with our openMPS package. If Fig. 2 in the supplemental material depicts everything, one time step would add up to
Add SWAP (k-2, k-l)
Add SWAP (k-1, k-l)
Add Evolution under H for three sites for time step dt
Add SWAP (k, S) and SWAP (k-l, k-1)
Add SWAP (k-l, k-2)
This series of time evolution you would then add n-times for a total time t = n * dt. I hope this descriptions provides you with a good first overview. If you have more questions, please let me know and I will try to answer them; especially in case you try to implement it.
Kind regards,
Daniel Jaschke
Last edit: Daniel Jaschke 2017-08-14
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Answering a question if photonic circuits with time delays (PRL 116, 093601, 2016) could be implemented within openMPS. Here one possible scheme:
Dear Dr. *****,
from the initial reading of this system I would say the simulations include system plus environment, which is a pure state. Pure states are suitable for the openMPS library and our focus has been on long-range interactions for statics and dynamics. I am not aware that anyone was or is trying to simulate such a system with our library, and I am most concerned about the time delays. The bins with different values of +/- p have to be coupled at different times. The long-range terms that we have implemented, would turn couplings on or off for all p. Other approaches using our long-range features get inefficient for many bins p. They key in their implementation are the swap gates; I assume they implement the gate directly and not as unitary evolution, which is not supported in openMPS. I assume they tailored their code for this purpose based on a good initial library.
The approach I can see is to implement the system with our library are multiple time-dependent evolutions, i.e., executing alternating the unitary evolution under the Hamiltonian and the SWAP gates as unitary time evolution. That is the way I would go with our openMPS package. If Fig. 2 in the supplemental material depicts everything, one time step would add up to
Add SWAP (k-2, k-l)
Add SWAP (k-1, k-l)
Add Evolution under H for three sites for time step dt
Add SWAP (k, S) and SWAP (k-l, k-1)
Add SWAP (k-l, k-2)
This series of time evolution you would then add n-times for a total time t = n * dt. I hope this descriptions provides you with a good first overview. If you have more questions, please let me know and I will try to answer them; especially in case you try to implement it.
Kind regards,
Daniel Jaschke
Last edit: Daniel Jaschke 2017-08-14