程序代写案例-CMSC 657 FALL
时间:2020-12-19
CMSC 657 FALL 2020 HOMEWORK 12
DUE: 5PM ET FRIDAY, NOVEMBER 20TH. SUBMIT ON GRADESCOPE.
GORJAN ALAGIC
Instructions. Please carefully read through the homework rules and the grading policy on the
syllabus before starting the homework. Note that late homeworks are not accepted; no exceptions.
This week’s reading:
(1) KLM: Sections 10.5.4 and 10.6
(2) NC (optional): Sections 10.4.2, 10.5, 10.6
(3) Daniel Gottesman’s Intro to QEC and FT (optional): https://arxiv.org/abs/0904.2557
(4) Dave Bacon’s notes (optional):
• https://courses.cs.washington.edu/courses/cse599d/06wi/lecturenotes18.pdf
• https://courses.cs.washington.edu/courses/cse599d/06wi/lecturenotes19.pdf
Video lectures. Watch lecture 12A (QEC II) and 12B (QEC III) on ELMS.
Problems.
(1) Analyze the code whose stabilizer is generated by the below.
X Z Z X I
I X Z Z X
X I X Z Z
Z X I X Z
Z Z X I X
(a) Use the stabilizer formalism to compute n, k, and d, and prove that this is a [[n, k, d]]
code for the values you found.
(b) How many arbitrary single-qubit errors can this code detect? How many can it correct?
Justify your answers.
(2) Analyze the code whose stabilizer is generated by the below.
X X I I
I I X X
Z Z Z Z
1
2 GORJAN ALAGIC
(a) Write down explicitly the codewords for logical |0〉 and logical |1〉. Verify that they are
stabilized by the stabilizer defined above.
(b) Use the stabilizer formalism to compute n, k, and d, and prove that this is a [[n, k, d]]
code for the values you found.
(c) How many arbitrary single-qubit errors can this code detect? How many can it correct?
Justify your answers.
(3) Give a fault-tolerant circuit for implementing logical X and logical Z gates in the 9-qubit
Shor code. Show that your circuits satisfy the definition of fault tolerance (Definition 10.6.1)
as stated in the KLM textbook.






































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