Each homework assignment consists of several problems, some of which are quite ambitious. The homework problems are assigned individually, and the solution is available along with the problem. You can choose to work the problem and then consult the solution to see how well you did, or you can work through the problem with the solution at hand. You should view the homework problems as study tools and use whatever strategy helps you best to learn.
You do not turn in the homework problems for grading, and there are no exams. Your grade is determined by your attendance at and active participation in the lectures.
| Homework | Class session | Lectures | Nielsen and Chuang |
|
HW #1
1.1 Solution 1.2 Solution 1.3 Solution 1.4 Solution 1.5 Solution 1.6 Solution |
T, 1-17 |
L1: Probabilities and laws of large numbers
Probabilities as betting odds and the Dutch book Simple Dutch-book derivation of the probability rules, taken from a seminar talk Coin tossing: analysis and experiments | |
| Th, 1-19 |
L2: Classical information and Shannon entropy. I
L2-3 Axiomatic derivation of Shannon information, taken from Chris Fuchs's 1996 UNM PhD dissertation |
11.1-11.2
12.2.1 |
|
| T, 1-24 | L3: Classical information and Shannon entropy. II | ||
|
HW #2
2.1 Solution 2.2 Solution 2.3 Solution 2.4 Solution 2.5 Solution 2.6 Solution |
Th, 1-26
|
L4: Linear algebra and axioms of quantum mechanics. I
L4-5 |
2.1-2.3 |
| T, 1-31 | L5: Linear algebra and axioms of quantum mechanics. II | ||
| Th, 2-2 |
L6: Qubits. I
L6-7 |
1.2-1.3 | |
| T, 2-7 | L7: Qubits. II | ||
|
HW #3
3.1 Solution 3.2 Solution 3.3 Solution 3.4 Solution 3.5 Solution 3.6 Solution 3.7 Solution 3.8 Solution |
Th, 2-9 | L8: Quantum states. I. Mixed states | 2.2-2.6 |
| T, 2-14 |
L9: Quantum states. II. Multiple systems and entanglement
L9-12 Multiple systems, the tensor-product space, and the partial trace Polar decomposition, singular-value decomposition, and Autonne-Takagi factorization An example of how the polar decomposition is used An example of the Kochen-Specker theorem |
||
| Th, 2-16 | L10: Quantum states. III. Multiple systems and entanglement | ||
| T, 2-21 | L11: Quantum states. IV. Multiple systems and entanglement | ||
| Th, 2-23 | No lecture | ||
| T, 2-28 | L12: Quantum states. V. Multiple systems and entanglement | ||
|
HW #4
4.1 Solution 4.2 Solution 4.3 Solution 4.4 Solution |
Th, 3-2 |
L13: Quantum dynamics. I. Generalized measurements
L13-14 |
2.2 |
| T, 3-7 | L14: Quantum dynamics. II. Generalized measurements | ||
| Th, 3-9 |
L15: Quantum dynamics. III. Superoperators and completely positive maps
L15-17 |
8 | |
| T, 3-14 | Spring Break | ||
| Th, 3-16 | Spring Break | ||
| T, 3-21 | L16: Quantum dynamics. IV. Superoperators and completely positive maps | ||
| Th, 3-23 | L17: Quantum dynamics. V. Superoperators and completely positive maps | ||
|
HW #5
5.1 Solution 5.2 Solution 5.3 Solution |
T, 3-28 |
L18: Quantum circuit model. I
L18-20 |
1.2-1.3
4.1-4.4 |
| Th, 3-30 | No lecture | ||
| T, 4-4 | No lecture | ||
| Th, 4-6 | No lecture | ||
| T, 4-11 | No lecture | ||
| Th, 4-13 | L19: Quantum circuit model. II | ||
| T, 4-18 | No lecture | ||
| Th, 4-20 | No lecture | ||
| T, 4-25 | L20: Quantum circuit model. III | ||
|
HW #6
6.1 Solution |
Th, 4-27 |
L21-22: Qubit operations. I-II
L21-22 |
8.3 |
|
HW #7
7.1 Solution 7.2 Solution 7.3 Solution 7.4 Solution |
T, 5-2 |
L23: Cloning and distinguishability. I
L23-24 |
9 |
| Th, 5-4 | L24: Cloning and distinguishability. II | ||
|
HW #8
8.1 Solution |
L25-27: Quantum entropy
We do not have time for these lectures, which is unfortunate, because they circle back to the beginning lectures on classical information by providing the justification for thinking of qubits as the unit of quantum information and von Neumann entropy as measuring the number of qubits. All the material is here should you want to consult it. |
11.1-11.4
12.1-12.2 |