diff --git a/demonstrations/rydberg_simulation_spin_lattice.py b/demonstrations/rydberg_simulation_spin_lattice.py
new file mode 100644
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+++ b/demonstrations/rydberg_simulation_spin_lattice.py
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+# ToDo: flesh out Z2 phase background text
+# ToDo: review references and incorporate any relevant information better
+# ToDo: flesh out conclusion
+
+r"""Analog Hamiltonian simulation of anti-ferromagnetism
+========================================================
+
+.. meta::
+ :property="og:description": Analog Hamiltonian simulation of anti-ferromagnetism on neutral atom hardware
+ :property="og:image": https://pennylane.ai/qml/_images/thumbnail_tutorial_pulse_on_hardware.png
+
+.. related::
+ ahs_aquila Pulse programming on Rydberg atom hardware
+ tutorial_neutral_atoms Neutral-atom quantum computers
+ tutorial_pasqal Quantum computation with neutral atoms
+ tutorial_pulse_programming101 Differentiable pulse programming with qubits in PennyLane
+
+*Author: Lillian M.A. Frederiksen — Posted: 15 October 2023.*
+
+
+Analog Hamiltonian simulation (AHS) is a paradigm of quantum computation that uses an engineered
+and controlled system to simulate and investigate the behaviours of other, analogous systems.
+This is an alternative to the typical gate-based paradigm of quantum computation. AHS can be
+implemented and produce meaningful results with relatively few, relatively noisy physical qubits.
+
+In this demo, we will implement AHS to simulate anti-ferromagnetic order on QuEra’s 256 qubit neutral
+atom hardware, Aquila. We will use the pulse-level control available in PennyLane's :mod:`~pennylane.pulse`
+module in combination with the `pennylane-braket plugin
+<https://amazon-braket-pennylane-plugin-python.readthedocs.io/en/latest/>`_ to access the hardware.
+
+If you are curious to learn more about the hardware before diving into an application for AHS, take a
+look at some previous demos covering the `physics behind netural atom devices
+<https://pennylane.ai/qml/demos/tutorial_neutral_atoms>`_ and the basics of `accessing the Aquila
+device <https://pennylane.ai/qml/demos/ahs_aquila>`_! You can also learn more about general implementation of
+pulse programming in Pennylane in the `differentiable pulse programming demo
+<https://pennylane.ai/qml/demos/tutorial_pulse_programming101>`_.
+
+
+
+Analog Hamiltonian Simulation
+-----------------------------
+
+With analog Hamiltonian simulation, rather than implementing gates that represent a logical
+abstraction, we aim to compute the behaviour of physical systems by using a programmable
+device that simulates the target system’s behaviour. Studying the effects in an engineered system
+allows us to investigate the behaviour of the system of interest in a controlled manner.
+
+This approach is in the spirit of Feynman’s original proposal for quantum computation:
+
+ “Nature isn’t classical […] and if you want to make a simulation of Nature, you’d better make it
+ quantum mechanical, and by golly it’s a wonderful problem because it doesn't look so easy. […] I
+ want to talk about the possibility that there is to be an exact simulation, that the computer will
+ do *exactly* the same as nature.” (emphasis in original)
+
+ – Richard P. Feynman, International Journal of Theoretical Physics, Vol 21, Nos. 6/7, 1982
+
+The ability to implement low-level modification of the Hamiltonian through application of a control pulses
+makes pulse programming an ideal tool for implementing an AHS program, if an appropriately engineered system
+is selected. Neutral atom hardware allows us to adjust the interaction term of the Hamiltonian via placement
+of the atoms.
+
+Applications of AHS
+~~~~~~~~~~~~~~~~~~~
+Researchers are already using AHS devices to study quantum mechanical phenomena and fundamental
+physics models that are difficult to study directly or simulate on classical computers, using
+realizations of the technology based on a number of physical platforms, including trapped ions,
+superconducting qubits, and Rydberg atom devices (like Aquila!).
+
+Rydberg devices are useful for a variety of tasks in simulation of complex physical systems that may
+be difficult to measure directly, and have been proposed or demonstrated to have applications in
+fields ranging from `condensed matter physics <https://arxiv.org/abs/1708.01044>`__,
+`high-energy physics <https://arxiv.org/abs/2007.07258>`__,
+and `quantum dynamics <https://journals.aps.org/prx/abstract/10.1103/PhysRevX.8.021070>`__, to
+`quantum gravity <https://arxiv.org/abs/1911.06314>`__.
+
+For example, recent results demonstrated using a Rydberg system to run an AHS program implementing
+controlled experimental exploration of topological quantum matter by simulating the behaviour of
+`quantum spin liquids <https://arxiv.org/abs/2104.04119>`__!
+
+
+
+
+
+
+Rybderg Atom Hamiltonian
+------------------------
+
+Basic rundown of the Hamiltonian we will be manipulating
+
+For more in-depth background on the physics of Rydberg atoms and Rydberg blockade, see `physics behind netural atom devices
+<https://pennylane.ai/qml/demos/tutorial_neutral_atoms>`_
+
+You can also see a simple implementation of Rydberg blockade on the QuEra hardware in our `intro demo for using Aquila
+ <https://pennylane.ai/qml/demos/ahs_aquila>`_!
+
+
+
+
+
+Simulating a phase transition
+-----------------------------
+
+
+Now let us use the physical properties of the device to perform a simple analog Hamiltonian
+simulation task. Here we will be simulating a phase transition in condensed quantum matter -
+specifically, the transition from ferromagnetic to anti-ferromagnetic order in a 1D Ising chain. An
+Ising chain has the Hamiltonian:
+
+.. math:: - \sum_{ij} J_{ij} \sigma_i \sigma_j - \mu \sum_j h_j \sigma_j
+
+- 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`,
+ corresponds to the spin interaction term of the Ising chain Hamiltonian,
+ :math:`-\sum_{ij} J_{ij} \sigma_i \sigma_j`, where the sign for :math:`J_{ij}` can only be
+ negative or 0 (corresponding to antiferromagnetic or non-interacting systems), and the magnitude
+ of :math:`J_{ij}` is adjusted by modifying the distance between atoms and thus their interaction
+ strength
+- The amplitude term of the driving field couples the down and up states (but does not
+ energetically favour one over the other)
+- The detuning term controls the energy reward (or penalty) for being in the excited state - in
+ this analogy, this corresponds to applying an external magnetic moment that encourages the spins
+ to align
+
+Adiabatic phase change etc.
+
+|
+
+.. figure:: ../demonstrations/rydberg_simulation_spin_lattice/rydberg_atom_chain.png
+ :align: center
+ :scale: 20%
+ :alt: Four Rubidium atoms trapped in optical tweezers, in alternating ground and excited states
+ :target: javascript:void(0);
+
+|
+
+A 1D chain on a local simulator
+~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+To begin, let’s initialize the devices, now with more wires, and create a 1D chain of 9 spins.
+While the radius for Rydberg blockade is dependent on drive strength, for a typical drive amplitude
+(on the order of 1 MHz), placing them at a distance of :math:`6 \mu m` should ensure that the energy
+contribution from van der Waals interactions is much larger than the scale of the drive, and we
+expect to observe blockade.
+
+"""
+import pennylane as qml
+
+rydberg_simulator = qml.device("braket.local.ahs",
+ wires=9)
+
+coordinates = [(i * 6, 0) for i in range(9)]
+
+H_interaction = qml.pulse.rydberg_interaction(coordinates, wires=rydberg_simulator.wires, **settings)
+
+######################################################################
+# In this case, we aim to apply a constant amplitude, while slowly varying detuning. A constraint of
+# the hardware is that amplitude must be 0 and the beginning and end of the pulse, and must respect
+# the maximum rate of change for the control hardware. Once we’ve simulated the function and settled on an
+# amplitude, we’ll calculate how much time we need to provide to ramp up, and modify our amplitude
+# function accordingly. For now, we will ignore the restriction and set the amplitude to a fixed value
+# for the entire duration of the pulse program.
+#
+# First let’s look at the behaviour of the system in the absence of phase or detuning, for a
+# :math:`4 \mu s` pulse program.
+#
+
+global_drive = qml.pulse.rydberg_drive(amplitude=qml.pulse.constant, phase=0, detuning=0, wires=rydberg_simulator.wires)
+
+amplitude = 2.4
+
+params = [amplitude]
+
+ts = jnp.array([0, 4])
+
+
+@qml.qnode(rydberg_simulator)
+def circuit(params, t):
+ qml.evolve(H_interaction + global_drive)(params, t)
+ return qml.sample()
+
+
+results = circuit(params, ts)
+
+average_density = np.mean(results, axis=0)
+plt.bar(range(len(average_density)), average_density)
+plt.xlabel("Indices of atoms")
+plt.ylabel("Average Rydberg density")
+plt.ylim(0, 1)
+
+##############################################################################
+#
+# .. figure:: ../demonstrations/rydberg_simulation_spin_lattice/atom_chain_no_detuning_simulator.png
+# :align: center
+# :scale: 50%
+# :alt: The Rydberg state density at each atom index for chain of 9 atoms without detuning (0.2-0.4 at each index)
+# :target: javascript:void(0);
+#
+#
+# The effect of the Rydberg blockade is discernible in the system; even-indexed atoms are more likely
+# to be in the excited state than odd-indexed atoms. However, overall, the system is in a fairly
+# disordered state, which each atom having 60-80% chance of being in the ground state.
+#
+#
+# Now let’s add a slowly varying detuning, starting in the regime where detuning is negative (ground
+# state strongly favoured for all atoms), and shifting to a positive detuning (where the excited state
+# is strongly favored for each individual atom, but discouraged for adjacent atoms by the interaction
+# term).
+#
+
+# the final timestamp in our pulse will be 4us, the maximum duration of a pulse program
+max_time = 4
+
+
+def detuning_fn(params, t):
+ if t < 0.25:
+ return params[0]
+
+ if t > max_time - 0.25:
+ return params[1]
+
+ else:
+ slope = (params[1] - params[0]) / (max_time - 0.5)
+ offset = params[0] - slope * 0.25
+ return slope * t + offset
+
+
+detuning_range = [-8, 8]
+
+times = np.linspace(0, max_time, 500)
+detuning = [detuning_fn(detuning_range, t) for t in times]
+
+plt.plot(times, detuning)
+plt.xlabel("Time ($\mu$s)")
+plt.ylabel("Detuning ($2\pi$ MHz)")
+plt.show()
+
+##############################################################################
+#
+# .. figure:: ../demonstrations/rydberg_simulation_spin_lattice/detuning_fn.png
+# :align: center
+# :scale: 50%
+# :alt: The function describing detuning for the pulse sequence, starting at -8 and increasing linearly to +8
+# :target: javascript:void(0);
+#
+
+amp_fn = qml.pulse.rect(qml.pulse.constant, windows=[0.001, 3.999])
+global_drive = qml.pulse.rydberg_drive(amplitude=amp_fn, phase=0, detuning=detuning_fn, wires=rydberg_simulator.wires)
+
+params = [amplitude, detuning_range]
+
+ts = jnp.array([0, 4])
+
+
+@qml.qnode(rydberg_simulator)
+def circuit(params, t):
+ qml.evolve(H_interaction + global_drive)(params, t)
+ return qml.sample()
+
+
+results = circuit(params, ts)
+
+average_density = np.mean(results, axis=0)
+plt.bar(range(len(average_density)), average_density)
+plt.xlabel("Indices of atoms")
+plt.ylabel("Average Rydberg density")
+plt.ylim(0, 1)
+
+##############################################################################
+#
+# .. figure:: ../demonstrations/rydberg_simulation_spin_lattice/atom_chain_with_detuning_simulator.png
+# :align: center
+# :scale: 50%
+# :alt: The Rydberg state density at each atom index with the detuning (alternates roughly between 0.1 and 0.9)
+# :target: javascript:void(0);
+#
+
+times = np.linspace(0.5, 4, 8)
+results = []
+
+for time in times:
+ res = circuit(params, time)
+ average_density = np.mean(res, axis=0)
+ results.append(average_density)
+
+time_vs_results = np.array(results).transpose()
+
+fig, ax1 = plt.subplots()
+
+data = ax1.imshow(time_vs_results, cmap='Blues', vmin=0, vmax=1)
+ax1.set_xticks(np.arange(len(times)), labels=times)
+plt.colorbar(data)
+plt.xlabel('Pulse duration [$\mu s$]')
+plt.ylabel('Indices of atoms')
+
+##############################################################################
+#
+# .. figure:: ../demonstrations/rydberg_simulation_spin_lattice/atom_chain_heatmap.png
+# :align: center
+# :scale: 50%
+# :alt: The Rydberg density for each atom, taken at different points in the pulse sequence, showing the emergence of antiferromagnetic order
+# :target: javascript:void(0);
+#
+#
+# At strongly negative detuning (:math:`0.5 \mu s`), the drive is not sufficient to excite the atoms
+# because of the large energy penalty for being in the excited state in the detuning term of the
+# Hamiltonian.
+#
+# Around :math:`2.5 \mu s` into the program, as we approach :math:`\Delta = 0`, we see something
+# similar to the results above (taken with detuning=0), where the drive has some effect, and the
+# probability of being in the excited state is roughly 20-40%. At this point we begin to see the
+# antiferromagnetic behaviour, but the system is still fairly disordered.
+#
+# Shifting further to positive detuning, we reach a regime where the Rydberg state is strongly favored
+# energetically - but the scale of the Rydberg blockade is still high enough to ensure we reach
+# antiferromagnetic, rather than ferromagnetic order. Here we see a
+#
+#
+#
+# A 1D chain on the Aquila hardware
+# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+#
+# 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
+# rate of change for the control hardware, 39788735 MHz/s. We are going to a maximum amplitude of
+# 2.4 MHz, so the duration needed to respect the maximum rate of change is just over 60 nanoseconds:
+#
+
+max_amp = 2.4 # MHz
+max_rate = 39788735 # MHz/s
+
+max_amp / max_rate # s
+
+##############################################################################
+# .. rst-class:: sphx-glr-script-out
+#
+# Out:
+#
+# .. code-block:: none
+#
+# 6.031858012073014e-08
+#
+#
+# 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:
+#
+
+max_time = 4 # in microseconds
+bin_size = 50e-3 # in microseconds
+num_bins = int(max_time // bin_size + 1)
+
+
+# define set-points for the function that have the desired shape
+def get_amp_array(max_amp):
+ ramp_up = [0, max_amp / 2] # ramp up over two bins
+ constant_output = [max_amp for _ in range(num_bins - 4)]
+ ramp_down = [max_amp / 2, 0] # ramp down over two bins
+ return jnp.array(ramp_up + constant_output + ramp_down)
+
+
+# create a pwc function based on the setpoints
+def amp_fn(max_amp, t):
+ output_array = get_amp_array(max_amp)
+ return qml.pulse.pwc(max_time)(output_array, t)
+
+
+times = np.linspace(0, 4, 8001)
+amp = [amp_fn(2.4, t) for t in times]
+
+plt.plot(times, amp)
+plt.xlabel("Time ($\mu$s)")
+plt.ylabel("Amplitude ($2\pi$ MHz)")
+plt.show()
+
+##############################################################################
+#
+# .. figure:: ../demonstrations/rydberg_simulation_spin_lattice/square_amplitude_pulse.png
+# :align: center
+# :scale: 50%
+# :alt: The square pulse function used to define the amplitude envelope
+# :target: javascript:void(0);
+#
+#
+# Our drive then becomes:
+#
+
+global_drive = qml.pulse.rydberg_drive(amplitude=amp_fn, phase=0, detuning=detuning_fn, wires=rydberg_simulator.wires)
+
+max_amp = 2.4 # MHz
+detuning_range = [-8, 8] # MHz
+
+params = [max_amp, detuning_range]
+
+######################################################################
+# Let’s look at our upload data:
+#
+
+op = qml.evolve(H_interaction + global_drive)(params, [0.0, 4])
+ahs_program = aquila.create_ahs_program(op)
+
+ahs_x_coordinates = ahs_program.register.coordinate_list(0)
+ahs_y_coordinates = ahs_program.register.coordinate_list(1)
+
+op_register = op.H.settings.register
+
+op_x_coordinates = [x * 1e-6 for x, _ in op_register]
+op_y_coordinates = [y * 1e-6 for _, y in op_register]
+
+plt.scatter(ahs_x_coordinates, ahs_y_coordinates, label='AHS program')
+plt.scatter(op_x_coordinates, op_y_coordinates, marker='x', label='Input register')
+plt.xlabel("μm")
+plt.ylabel("μm")
+plt.legend()
+
+##############################################################################
+#
+# .. figure:: ../demonstrations/rydberg_simulation_spin_lattice/atom_chain_discretization.png
+# :align: center
+# :scale: 50%
+# :alt: The initial and uploaded atom positions still match after discretization
+# :target: javascript:void(0);
+#
+
+# hardware set-points after conversion and discretization
+amplitude_setpoints = ahs_program.hamiltonian.amplitude.time_series
+
+# values for plotting the function defined in PennyLane for amplitude
+input_times = np.linspace(*ts, 1000)
+input_amplitude = [amp_fn(params[0], _t) for _t in np.linspace(*ts, 1000)]
+
+# plot PL input and hardware set-points for comparison
+fig, (ax1, ax2) = plt.subplots(1, 2)
+ax1.plot(input_times, input_amplitude)
+ax1.set_xlabel('Time [$\mu s$]')
+ax1.set_ylabel('MHz')
+ax1.set_title('detuning_fn')
+
+ax2.plot(amplitude_setpoints.times(), amplitude_setpoints.values())
+ax2.set_xlabel('Time [s]')
+ax2.set_ylabel('rad/s')
+ax2.set_title('upload data')
+
+plt.tight_layout()
+plt.show()
+
+##############################################################################
+#
+# .. figure:: ../demonstrations/rydberg_simulation_spin_lattice/square_amplitude_fn_vs_upload.png
+# :align: center
+# :scale: 50%
+# :alt: The square envelope defining the amplitude matches the corresponding amplitude output created for hardware
+# :target: javascript:void(0);
+#
+
+# consider plotting maximum ramp rate on here to compare
+
+# hardware set-points after conversion and discretization
+detuning_setpoints = ahs_program.hamiltonian.detuning.time_series
+
+# values for plotting the function defined in PennyLane for amplitude
+input_times = np.linspace(*ts, 1000)
+input_detuning = [detuning_fn(params[1], _t) for _t in np.linspace(*ts, 1000)]
+
+# plot PL input and hardware set-points for comparison
+fig, (ax1, ax2) = plt.subplots(1, 2)
+ax1.plot(input_times, input_detuning)
+ax1.set_xlabel('Time [$\mu s$]')
+ax1.set_ylabel('MHz')
+ax1.set_title('detuning_fn')
+
+ax2.plot(detuning_setpoints.times(), detuning_setpoints.values())
+ax2.set_xlabel('Time [s]')
+ax2.set_ylabel('rad/s')
+ax2.set_title('upload data')
+
+plt.tight_layout()
+plt.show()
+
+
+##############################################################################
+#
+# .. figure:: ../demonstrations/rydberg_simulation_spin_lattice/detuning_vs_upload.png
+# :align: center
+# :scale: 50%
+# :alt: The function defining the detuning matches the corresponding detuning output created for hardware
+# :target: javascript:void(0);
+#
+#
+# Everything looks as expected, so let’s do a final sanity check on simulator and then upload our
+# program:
+#
+
+# sanity check on simulator
+@qml.qnode(rydberg_simulator)
+def circuit_simulator(params):
+ qml.evolve(H_interaction + global_drive)(params, [0.0, 4])
+ return qml.sample()
+
+
+results = circuit_simulator(params)
+
+average_density = np.mean(results, axis=0)
+plt.bar(range(len(average_density)), average_density)
+plt.xlabel("Indices of atoms")
+plt.ylabel("Average Rydberg density")
+plt.ylim(0, 1)
+
+##############################################################################
+#
+# .. figure:: ../demonstrations/rydberg_simulation_spin_lattice/sanity_check_on_simulator.png
+# :align: center
+# :scale: 50%
+# :alt: The alternating excited-ground-excited pattern is demonstrated on simulator as expected
+# :target: javascript:void(0);
+#
+
+# reinitialize aquila with the correct number of wires
+s3 = ("my-bucket", "my-prefix")
+aquila = qml.device("braket.aws.ahs",
+ device_arn="arn:aws:braket:us-east-1::device/qpu/quera/Aquila",
+ s3_destination_folder=s3,
+ wires=9)
+
+
+@qml.qnode(aquila)
+def circuit_hardware(params):
+ qml.evolve(H_interaction + global_drive)(params, [0.0, 4])
+ return qml.sample()
+
+
+results = circuit_hardware(params)
+
+# we need to use np.nanmean here instead of np.mean, because
+# occasionally a shot returns nan instead of 0 or 1, and np.nanmean
+# handles as having one fewer input instead of returning NaN
+average_density = np.nanmean(results, axis=0)
+plt.bar(range(len(average_density)), average_density, color='C3')
+plt.xlabel("Indices of atoms")
+plt.ylabel("Average Rydberg density")
+plt.ylim(0, 1)
+
+##############################################################################
+#
+# .. figure:: ../demonstrations/rydberg_simulation_spin_lattice/simple_chain_hardware_results.png
+# :align: center
+# :scale: 50%
+# :alt: The alternating excited-ground-excited state for the atoms measured on hardware
+# :target: javascript:void(0);
+#
+#
+# Anti-ferromagnetic order in a 2D grid
+# -------------------------------------
+#
+# We can create the same kind of order in a 2D lattice as well. Here we will create two separate Hamiltonians,
+# with different numbers of atoms. The local simulator can handle up to 15 atoms, but is faster below 10; here
+# we've elected to use a 3x3 grid for local simulation. Execution time for hardware doesn't scale with the number
+# of qubits, so we will create a 5x10 grid for the hardware device.
+
+# reinitialize aquila with the correct number of wires
+s3 = ("my-bucket", "my-prefix")
+aquila = qml.device("braket.aws.ahs",
+ device_arn="arn:aws:braket:us-east-1::device/qpu/quera/Aquila",
+ s3_destination_folder=s3,
+ wires=50) # 5x10 = 50 atoms for hardware
+
+rydberg_simulator = qml.device("braket.local.ahs", wires=9) # 3x3 = 9 atoms for local simulation
+
+##############################################################################
+#
+# Similarly, we'll create two different sets of coordinates. We'll use a spacing of $6 \mu m$ so that
+# we observe Rydberg blockade between nearest neighbors. We also need to create two drive terms, as they
+# differ with regard to the wires the drive is applied to.
+
+a = 6
+
+coordinates_aquila = []
+coordinates_local_simulator = []
+
+# 10x5 sets of coordinates for hardware
+for i in range(10):
+ for j in range(5):
+ coordinates_aquila.append((i * a, j * a))
+
+# 3x3 sets of coordinates for local simulation
+for i in range(3):
+ for j in range(3):
+ coordinates_local_simulator.append((i * a, j * a))
+
+H_int_aquila = qml.pulse.rydberg_interaction(coordinates_aquila,
+ wires=aquila.wires,
+ **aquila.settings)
+global_drive_aquila = qml.pulse.rydberg_drive(amplitude=amp_fn,
+ phase=0,
+ detuning=detuning_fn,
+ wires=aquila.wires)
+
+H_int_simulator = qml.pulse.rydberg_interaction(coordinates_local_simulator,
+ wires=rydberg_simulator.wires,
+ **rydberg_simulator.settings)
+global_drive_simulator = qml.pulse.rydberg_drive(amplitude=amp_fn,
+ phase=0,
+ detuning=detuning_fn,
+ wires=rydberg_simulator.wires)
+
+
+##############################################################################
+#
+# text text
+#
+#
+
+@qml.qnode(rydberg_simulator)
+def circuit_simulator(params):
+ qml.evolve(H_int_simulator + global_drive_simulator)(params, [0.0, 4])
+ return qml.sample()
+
+
+@qml.qnode(aquila)
+def circuit_hardware(params):
+ qml.evolve(H_int_aquila + global_drive_aquila)(params, [0.0, 4])
+ return qml.sample()
+
+
+##############################################################################
+#
+# text text
+#
+#
+
+results = circuit_simulator(params)
+
+average_density_2d = np.mean(results, axis=0)
+density_data_2d = average_density_2d.reshape(3, 3)
+
+fig, ax1 = plt.subplots()
+
+data = ax1.imshow(density_data_2d, cmap='Blues', vmin=0, vmax=1)
+plt.colorbar(data, label='Rydberg density')
+plt.xlabel('Atom horizontal index')
+plt.ylabel('Atom vertical index')
+
+plt.tight_layout
+
+##############################################################################
+#
+# .. figure:: ../demonstrations/rydberg_simulation_spin_lattice/3_by_3_grid_simulator_result.png
+# :align: center
+# :scale: 50%
+# :alt: The alternating excited-ground-excited state for the atoms simulated locally
+# :target: javascript:void(0);
+#
+# comment on results - now we run on hardware
+
+results = circuit_hardware(params)
+
+# we need to use np.nanmean here instead of np.mean, because occasionally a shot returns
+# nan instead of 0 or 1, and np.nanmean handles as having one fewer input instead of
+# returning NaN
+average_density_2d = np.nanmean(results, axis=0)
+density_data_2d = average_density_2d.reshape(10, 5)
+
+fig, ax1 = plt.subplots()
+
+data = ax1.imshow(density_data_2d, cmap='Reds', vmin=0, vmax=1)
+plt.colorbar(data, label='Rydberg density')
+plt.xlabel('Atom horizontal index')
+plt.ylabel('Atom vertical index')
+
+##############################################################################
+#
+# .. figure:: ../demonstrations/rydberg_simulation_spin_lattice/5_by_10_grid_hardware_result.png
+# :align: center
+# :scale: 50%
+# :alt: The Rydberg density for a 5x10 grid of atoms, showing antiferromagnetic order due to the pulse sequence
+# :target: javascript:void(0);
+#
+# comment on results
+#
+#
+# Conclusion
+# ----------
+#
+# - AHS is an interesting and active area of research in a different kind of quantum computation
+# - “Already today, researchers are using such devices to study quantum phenomena that otherwise
+# would be hard to simulate on classical computers.”
+# - lots of applications
+# - we made a phase transition - yay! More complex phase trasitions have been simulated... spin liquid...
+#
+#
+# References
+# ----------
+#
+# .. [#Cubitt]
+#
+# Toby S. Cubitt, Ashley Montanaro, Stephen Piddock
+# "Universal quantum Hamiltonians"
+# `arxiv.1701.05182 <https://arxiv.org/abs/1701.05182>`__, 2018
+#
+# .. [#Semeghini]
+#
+# G. Semeghini, H. Levine, A. Keesling, S. Ebadi, T.T. Wang, D. Bluvstein, R. Verresen, H. Pichler,
+# M. Kalinowski, R. Samajdar, A. Omran, S. Sachdev, A. Vishwanath, M. Greiner, V. Vuletic, M.D. Lukin
+# "Probing topological spin liquids on a programmable quantum simulator"
+# `arxiv.2104.04119 <https://arxiv.org/abs/2104.04119>`__, 2021.
+#
+# .. [#BraketDevGuide]
+#
+# Amazon Web Services: Amazon Braket
+# "Hello AHS: Run your first Analog Hamiltonian Simulation"
+# `AWS Developer Guide <https://docs.aws.amazon.com/braket/latest/developerguide/braket-get-started-hello-ahs.html>`__
+#
+# .. [#Asthana2022]
+#
+# Alexander Keesling, Eric Kessler, and Peter Komar
+# "AWS Quantum Technologies Blog: Realizing quantum spin liquid phase on an analog Hamiltonian Rydberg simulator"
+# `arXiv:2203.06818 <https://aws.amazon.com/blogs/quantum-computing/realizing-quantum-spin-liquid-phase-on-an-analog-hamiltonian-rydberg-simulator/>`__, 2021.
\ No newline at end of file
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diff --git a/demos_quantum-computing.rst b/demos_quantum-computing.rst
index c87cb185f8..35317c7ced 100644
--- a/demos_quantum-computing.rst
+++ b/demos_quantum-computing.rst
@@ -138,6 +138,12 @@ such as benchmarking and characterizing quantum processors.
:description: :doc:`demos/tutorial_qutrits_bernstein_vazirani`
:tags: qutrits algorithm
+.. gallery-item::
+ :tooltip: Create and run a pulse program on neutral atom hardware
+ :figure: demonstrations/rydberg_simulation_spin_lattice/rydberg_atom_chain.png
+ :description: :doc:`demos/rydberg_simulation_spin_lattice`
+ :tags: pulses pulse programming neutral atom hardware ising analog hamiltonian simulation
+
.. gallery-item::
:tooltip: Master the basics of the quantum singular value transformation
:figure: demonstrations/intro_qsvt/thumbnail_intro_qsvt.png
@@ -174,6 +180,7 @@ such as benchmarking and characterizing quantum processors.
:description: :doc:`demos/tutorial_apply_qsvt`
:tags: quantumcomputing qsvt optimization
+
:html:`</div></div><div style='clear:both'>`
.. toctree::
@@ -201,9 +208,8 @@ such as benchmarking and characterizing quantum processors.
demos/tutorial_neutral_atoms
demos/ahs_aquila
demos/tutorial_qutrits_bernstein_vazirani
+ demos/rydberg_simulation_spin_lattice
demos/tutorial_circuit_compilation
demos/tutorial_intro_qsvt
demos/tutorial_grovers_algorithm
demos/tutorial_apply_qsvt
-
-