Add tutorial #1075

minhtriet · 2024-04-17T23:02:05Z

Title: Find the first excitation energy of hydrogen molecule with VQD

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GOALS — Finding first excitation energy is necessary to model reaction
AUDIENCE — Chemistry researchers, beginners in quantum computing.
KEYWORDS — Quantum Chemistry
Which of the following types of documentation is most similar to your file?
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Tutorial
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[sc-64060]

minhtriet · 2024-04-18T20:25:13Z

Hi can I get a thumbnail please :) Right now "/_static/large_demo_thumbnails/thumbnail_large_vqe_vqd.png is copied from another one

github-actions · 2024-04-18T21:34:07Z

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Pull Request ID: 1075
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KetpuntoG

Hey @minhtriet Thanks for working on the demo and good job 😄
Here I leave you some first comments to make the demo shine more brightly 💪

demonstrations/tutorial_vqe_vqd.metadata.json

demonstrations/tutorial_vqe_vqd.py

Co-authored-by: Guillermo Alonso-Linaje <[email protected]>

KetpuntoG

At the moment it is going well but what do you think if we do a little restructuring? 😄
Here are a few comments. Don't worry about the final code part. Let's work in this first part

demonstrations/tutorial_vqe_vqd.py

KetpuntoG · 2024-06-03T18:29:00Z

demonstrations/tutorial_vqe_vqd.py

+import jax
+import optax
+import pennylane as qml
+from pennylane import numpy as np
+
+jax.config.update("jax_platform_name", "cpu")
+jax.config.update("jax_enable_x64", True)


To follow our usual formatting, could you the libraries in the first cell where they are used.

demonstrations/tutorial_vqe_vqd.py

KetpuntoG · 2024-06-03T19:06:53Z

demonstrations/tutorial_vqe_vqd.py

+
+h2_dataset = qml.data.load("qchem", molname="H2", bondlength=0.742, basis="STO-3G")
+h2 = h2_dataset[0]
+H, qubits = h2.hamiltonian, len(h2.hamiltonian.wires)
+print("Number of qubits = ", qubits)
+print("The Hamiltonian is ", H)
+
+######################################################################
+# The `hf_state` is our starting point to find the ground state energy. Let’s see what it is.
+#
+h2.hf_state


I would recommend replacing the current code with this one. On the other hand, there is no need to explain neither what Hartree Fock is nor what Double Excitation is. Here you can point to the demo instead of the introduction.

import pennylane as qml from pennylane import numpy as np h2 = qml.data.load("qchem", molname="H2", bondlength=0.742, basis="STO-3G")[0] H, qubits = h2.hamiltonian, len(h2.hamiltonian.wires) def generate_ground_state(wires): qml.BasisState(h2.hf_state, wires=wires) for op in h2.vqe_gates: # use the gates data the datasets package provided op = qml.map_wires(op, {op.wires[i]: wires[i] for i in range(len(wires))}) qml.apply(op) dev = qml.device("default.qubit") @qml.qnode(dev) def circuit(): generate_ground_state(range(qubits)) return qml.expval(H) print("The ground energy of H2 is: ", circuit())

KetpuntoG · 2024-06-03T19:07:43Z

demonstrations/tutorial_vqe_vqd.py

+######################################################################
+# In the Hartree Fock representation, a qubit with state :math:`1`/:math:`0` means that there is/isn’t an
+# electron occupying the respective spinning molecular orbital. Here we are starting from the config where the two electrons occupy the lowest two energy levels.
+#
+# Let’s also see the gates used to evolve the hf state.
+#
+print(h2.vqe_gates)
+
+######################################################################
+# This is a single Double excitement gate with the rotation angle of ~ 0.2732 radians.
+#
+excitation_angle = 0.27324054462951564
+


Let's not focus on this

KetpuntoG · 2024-06-03T19:13:08Z

demonstrations/tutorial_vqe_vqd.py

+# Setting expectation
+# -------------------------------------------
+#
+# Before any training takes place, let’s first look at some of the experimental value.
+# The energy of an atom at :math:`n` th excitement level is denoted as :math:`E_n`. Physicists starts the value
+# of :math:`n` from :math:`1`. It is to avoid dividing by zero in the equation :math:`E_n=\frac{E_I}{n^2}`, where :math:`E_I` is the ionization energy.
+#
+# - Ground state energy:
+# - :math:`H_2` molecule: -1.1357 Hartree ! Help I cannot find the source for this
+#
+# - 1st level excitation energy! Help I cannot find the source for this
+#
+# All the measures are in :math:`eV` (electron volt). However, later when running the optimization circuit, we would meet another unit called :math:`Ha` (Hartree energy). They both measure energy, just like Joule or calorie
+# but in the scale for basic particles. Let's define a unit conversion function.
+#
+
+
+def hartree_energy_to_ev(hartree: float):
+ return hartree * 27.2107


From my point of view, there is no need to look for these values, we will use the demo to deduce them (In the previous block with the code, you already have the energy value -1.13). I would suggest eliminating this part

KetpuntoG · 2024-06-03T19:17:58Z

demonstrations/tutorial_vqe_vqd.py

+
+
+######################################################################
+# Ansatz and the ground state


Reading this section, I get the feeling that you start with the code very quickly, how about making a theoretical section explaining VQD: "The VQD Algorithm".

After this, once we have worked through this part, we could see how to implement the code section: "VQD in PennyLane" for example.

Although I told you to delete the VQE formula, it may make sense to include it in this context.
Something like, although the usual way to find the ground state is through this formula [...] this is not enough in this case since we are not looking for the minimum. Therefore, we must create a penalty that results in this formula [...]. By taking a sufficiently large beta we can guarantee that [...]. In addition, iteratively, we could calculate other excited states [...].

Co-authored-by: Guillermo Alonso-Linaje <[email protected]>

minhtriet

Thank you @KetpuntoG for the restructure. There are several things I love about this

New structure makes it easy to read
Test if the excited energy found is correct

Just have a couple of points I don't understand yet. Perhaps people who read the tutorial may have the same question :)

demonstrations/tutorial_vqe_vqd.py

minhtriet · 2024-05-31T06:21:44Z

demonstrations/tutorial_vqe_vqd.py

@@ -0,0 +1,251 @@
+r"""Ground State and Excited State of H2 Molecule using VQE and VQD


Yes I made it more VQD focused :) Thank you

minhtriet · 2024-06-03T21:24:41Z

demonstrations/tutorial_vqe_vqd.py

+# Setting expectation
+# -------------------------------------------
+#
+# Before any training takes place, let’s first look at some of the experimental value.
+# The energy of an atom at :math:`n` th excitement level is denoted as :math:`E_n`. Physicists starts the value
+# of :math:`n` from :math:`1`. It is to avoid dividing by zero in the equation :math:`E_n=\frac{E_I}{n^2}`, where :math:`E_I` is the ionization energy.
+#
+# - Ground state energy:
+# - :math:`H_2` molecule: -1.1357 Hartree ! Help I cannot find the source for this
+#
+# - 1st level excitation energy! Help I cannot find the source for this
+#
+# All the measures are in :math:`eV` (electron volt). However, later when running the optimization circuit, we would meet another unit called :math:`Ha` (Hartree energy). They both measure energy, just like Joule or calorie
+# but in the scale for basic particles. Let's define a unit conversion function.
+#
+
+
+def hartree_energy_to_ev(hartree: float):
+ return hartree * 27.2107


minhtriet · 2024-06-03T22:21:27Z

demonstrations/tutorial_vqe_vqd.py

+
+
+######################################################################
+# Ansatz and the ground state


minhtriet · 2024-06-07T17:28:41Z

demonstrations/tutorial_vqe_vqd.py

+ for i in range(n_qubits):
+ qml.CSWAP(wires=[0, 1 + i + n_qubits, 1 + i])
+ qml.Hadamard(wires=0)
+ return qml.expval(qml.Z(0))


According to Wikipedia shouldn't we take the qml(prob) and see the 0th value? I am trying to understand expval(Z) here

Suppose we have x=α|0>+β|1> then expval(Z)=<x|Z|x>=α^2-β^2? But we expected α^2 only here?

The expected value is over Z is equivalent to P(0) - P(1). I invite you to do the maths and check the solution 😄 I'll look for a reference to add, so the reader can go there

Ah yes of course α^2-β^2 is P(0) - P(1)

demonstrations/tutorial_vqe_vqd.py

Co-authored-by: cmt <[email protected]>

_static/authors/minh_chau.txt

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Add tutorial #1075

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		######################################################################
		# Ansatz and the ground state

		@@ -0,0 +1,251 @@
		r"""Ground State and Excited State of H2 Molecule using VQE and VQD

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minhtriet commented Apr 17, 2024 • edited by ikurecic

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minhtriet commented Apr 17, 2024 •

edited by ikurecic

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