Cp/tfqa add

[christopherporter1]

Starting to add content for the Tools for Quantum Advantage course.

[review-notebook-app]

Check out this pull request on 

See visual diffs & provide feedback on Jupyter Notebooks.

---

Powered by ReviewNB

[abbycross]

Suggested change

	"(a) Qubit 3 could be affected, as well as obviously qubit 2 itself. No others! If you listed qubits 0 and 1, note that qubit 2 is the target of the ECR entangling it with qubit 1. No change is made to qubit 1 in that gate. (b) qubits 0-3 could be affected. The bit flip or X-type error does not commute with the ZZ coupling in the ECR gate and thus can propagate from the target to the control.\n",
	"(a) Qubit 3 could be affected, as well as obviously qubit 2 itself. No others! If you listed qubits 0 and 1, note that qubit 2 is the target of the ECR entangling it with qubit 1. No change is made to qubit 1 in that gate. (b) Qubits 0-3 could be affected. The bit flip or X-type error does not commute with the ZZ coupling in the ECR gate and thus can propagate from the target to the control.\n",

[abbycross]

Suggested change

	"For an error $E$ that occurs before some part of the logical payload of a circuit $U$, error propagation means finding the equivalent operator $E'$' that reproduces the same faulty outcome when applied after $U$ instead of before it.\n",
	"For an error $E$ that occurs before some part of the logical payload of a circuit $U$, error propagation means finding the equivalent operator $E'$ that reproduces the same faulty outcome when applied after $U$ instead of before it.\n",

[abbycross]

Suggested change

	"Let control be qubit 0 and target be qubit 1. And consider X and Z errors on the control and target qubits ($X_c$, $Z_c$, $X_t$, and $Z_t$, respectively). Moving these errors past a $\\text{CNOT}_{0\\to1}$ causes the errors to become:\n",
	"Let control be qubit 0 and target be qubit 1. Consider X and Z errors on the control and target qubits ($X_c$, $Z_c$, $X_t$, and $Z_t$, respectively). Moving these errors past a $\\text{CNOT}_{0\\to1}$ causes the errors to become:\n",

[abbycross]

Suggested change

"We state the above without proof. But if you are like the author of this lesson, and prefer the Schr\\\"odinger picture, you can also write down arbitrary control and target states, apply the error, then the CNOT, and examine the final state. Comparing that final state to an error free case allows you to see what error combination applied after the CNOT would yield the erroneous state, and in particular, you can see if the error operation has spread from one qubit to the other.\n",

"We state the above without proof. But if you are like the author of this lesson, and prefer the Schr\\\"odinger picture, you can also write down arbitrary control and target states, apply the error, then the CNOT, and examine the final state. If you compare that final state to an error-free case, you can see what error combination applied after the CNOT would yield the erroneous state, and in particular, you can see if the error operation has spread from one qubit to the other.\n",

[abbycross]

Suggested change

"There is a Qiskit addon called [Shaded Lightcones](https://qiskit.github.io/qiskit-addon-slc/). The shaded lightcones (SLC) addon analyzes error propagation in quantum circuits using Pauli propagation to identify which parts of a circuit can actually influence a target observable. It is designed primarily to make error mitigation more efficient, especially for probabilistic error cancellation (PEC) workflows. We will only briefly explore this tool here, and make wider use of it in the context of error mitigation techniques in future lessons. It uses Pauli operator propagation to map out propagation of errors of different types, producing a light cone for X, Y, and Z type errors.\n",

"There is a Qiskit addon called [Shaded Lightcones](https://qiskit.github.io/qiskit-addon-slc/). The shaded lightcones (SLC) addon analyzes error propagation in quantum circuits by using Pauli propagation to identify which parts of a circuit can actually influence a target observable. It is designed primarily to make error mitigation more efficient, especially for probabilistic error cancellation (PEC) workflows. We will only briefly explore this tool here, and make wider use of it in the context of error mitigation techniques in future lessons. It uses Pauli operator propagation to map out propagation of errors of different types, producing a light cone for X, Y, and Z type errors.\n",

[abbycross]

Suggested change

	"Separates it into \"boxes\" useful for learning noise behavior:\n",
	"The workflow separates the circuit into \"boxes\" useful for learning noise behavior:\n",

[abbycross]

Suggested change

	"And finally uses operator propagation and noise learning to produce a shaded map of error susceptibility throughout the circuit:\n",
	"Finally, it uses operator propagation and noise learning to produce a shaded map of error susceptibility throughout the circuit:\n",

[abbycross]

Suggested change

	"It must be done after transpilation. In order for these different maps to be useful we must make sure that the adjacent qubits in our circuit corresponded to adjacent qubits on our quantum chip. Otherwise, entangling gates shown as acting on the adjacent qubits in the circuit diagram would end up requiring SWAP gates and more complicated circuit structure.\n",
	"It must be done after transpilation. In order for these different maps to be useful we must make sure that the adjacent qubits in our circuit corresponded to adjacent qubits on our quantum chip. Otherwise, entangling gates shown as acting on the adjacent qubits in the circuit diagram would end up requiring SWAP gates and more a complicated circuit structure.\n",

[abbycross]

Suggested change

"Recall from our discussion of thermal noise that at any non-zero temperature, there is some probability of a quantum system undergoing a transition between energy eigenstates. The relaxation ($|1\\rangle> \\rightarrow |0\\rangle$) dominates because it's driven by spontaneous emission (independent of temperature), while low temperature suppresses the competing excitation process. The longer a qubit sits idle, the more time it has to undergo such a transition. The probability that a qubit prepared in the state $|1\\rangle$ remains in $|1\\rangle$ after a time $t$ is given by\n",

"Recall from our discussion of thermal noise that at any non-zero temperature, there is some probability of a quantum system undergoing a transition between energy eigenstates. The relaxation ($|1\\rangle \\rightarrow |0\\rangle$) dominates because it's driven by spontaneous emission (independent of temperature), while low temperature suppresses the competing excitation process. The longer a qubit sits idle, the more time it has to undergo such a transition. The probability that a qubit prepared in the state $|1\\rangle$ remains in $|1\\rangle$ after a time $t$ is given by\n",

[christopherporter1]

Perfect! Thank you!