Spin lattice demo with Aquila #808
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| coordinates = [(i * 6, 0) for i in range(9)] | ||
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| H_interaction = qml.pulse.rydberg_interaction(coordinates, wires=rydberg_simulator.wires, **settings) |
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Traceback (most recent call last):
File "/home/qottmann/Qottmann/Xanadu/qml/demonstrations/rydberg_simulation_spin_lattice.py", line 118, in <module>
H_interaction = qml.pulse.rydberg_interaction(coordinates, wires=rydberg_simulator.wires, **settings)
^^^^^^^^
NameError: name 'settings' is not defined
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Really cool stuff @lillian542 !
I think some of the intro is missing because the demo was split in two, would be good to link that but also repeat the essentials like the rydberg Hamiltonian. I didnt go into detail here for the review and focussed on the physics parts for now 🙂
| specifically, the transition from ferromagnetic to anti-ferromagnetic order in a 1D Ising chain. An | ||
| Ising chain has the Hamiltonian: | ||
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| .. math:: - \sum_{ij} J_{ij} \sigma_i \sigma_j - \mu \sum_j h_j \sigma_j |
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| .. math:: - \sum_{ij} J_{ij} \sigma_i \sigma_j - \mu \sum_j h_j \sigma_j | |
| .. math:: H_\text{Ising} = - \sum_{ij} J_{ij} \sigma_i \sigma_j - \mu \sum_j h_j \sigma_j |
Missing x, y, z superscripts, or is this a classical Hamiltonian?
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| - use an atom to represent a single spin in the chain, with spin-up and spin-down encoded as the | ||
| Rydberg and ground states respectively | ||
| - the van der Waals interaction term between the atoms, :math:`\sum_j \sum_k V_{jk} n_j n_k`, |
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Should first introduce those terms somewhere 🙃 (and link to your previous demo 🙂 !)
| this analogy, this corresponds to applying an external magnetic moment that encourages the spins | ||
| to align | ||
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| Adiabatic phase change etc. |
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So the algorithm here is supposed to be something like adiabatic quantum computing, starting in a well controlled ground state of a known Hamiltonian and then adiabatically changing the parameters to slowly drive it to a different phase? Sounds cool! Would be good to explicitly show the original Ising Hamiltonian and rydberg Hamiltonian quenches :)
| # We’ll upload and run the full duration (:math:`4 \mu s`) program to the Aquila hardware. As | ||
| # discussed above, to run on hardware we will need to slightly modify our amplitude function, to | ||
| # ensure it is 0 at the beginning and end of the pulse program, and that we respect the maximum |
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I think it would actually be easier to read by not mentioning the point of the amplitude having to be 0 at start and end above but start making that point here
| # Let’s define a piecewise constant function that sets the values of an array based on the maximum | ||
| # value and maximum rate of change, assuming a 4 microsecond pulse program. This will be sampled and converted | ||
| # to a piecewise linear function that approximates it for hardware upload, but in this case a | ||
| # piecewise constant function is an easy way to define our pulse. Since we can’t go to maximum | ||
| # amplitude faster than 60ns, and we have a bin size of 50ns (so it will match the function sampling | ||
| # rate when converting from PennyLane to hardware instructions), let’s increase amplitude over two bins: |
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Could be nice to show how to access the maximum rate of change in amplitude here (and use that value?)
| # :target: javascript:void(0); | ||
| # | ||
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| # hardware set-points after conversion and discretization |
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What is this here? Is this a relic or intentional? (the part of a constant detuning)
| expect to observe blockade. | ||
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| """ | ||
| import pennylane as qml |
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missing some imports (numpy, matplotlib)
| ax1.plot(input_times, input_detuning) | ||
| ax1.set_xlabel('Time [$\mu s$]') | ||
| ax1.set_ylabel('MHz') | ||
| ax1.set_title('detuning_fn') |
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Co-authored-by: Korbinian Kottmann <[email protected]>
…o spin_lattice_aquila
…o spin_lattice_aquila
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