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33658, 758 Quantum Computation and Information Spring Semester, 2012
Assignment No. 1. Due Tuesday, January 24
In the future all assignments will be posted at the COURSE WEB SITE:
http://www.andrew.cmu.edu/course/33658 = http://quantum.phys.cmu.edu/QCQI/
READING:
QCQI = Nielsen and Chuang, Quantum Computation and Quantum Information
CQT = GriFths, Consistent Quantum Theory
HSQM = “Hilbert Space Quantum Mechanics” Course web site
History: QCQI Sec. 1.1
Linear algebra: Review using your favorite book. What you need to know is in:
CQT Secs. 3.1 to 3.7;
QCQI Sec. 2.1
Introduction to quantum mechanics:
CQT Ch. 2 and Secs. 4.1 and 4.2;
QCQI Secs. 1.2, 2.2;
HSQM Secs. 1,2,3
Composite systems:
CQT Ch. 6;
QCQI Secs. 1.2.1, 2.1.7;
HSQM Sec. 4
READING AHEAD:
Unitary dynamics and quantum circuits:
CQT Ch. 7; QCQI Secs. 1.3.1, 1.3.2, 1.3.4, 1.3.6; 2.2.2; 4.2, 4.3
EXERCISES:
1. Turn in at most one page, and not less than half a page, indicating what you have read, examples
or exercises (apart from those assigned below) that you worked out, diFculties you encountered, questions
that came to mind, etc. You may include complaints about the course. You will ±nd a sample at the end of
the problem set.
2. Let

χ
±
=

0
±
i

1
±
,

ω
±
=
(1 +
i
)
√
2

0
±
+

1
±
a) ²ind the matrix of the operator

χ
±²
ω

in the standard basis.
b) Check that Tr(

χ
±²
ω

)=
²
ω

χ
±
.
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