Chapter 5: Architecture - Computer and Information Science - CUNY
Chapter 5: Architecture - Computer and Information Science - CUNY Chapter 5: Architecture - Computer and Information Science - CUNY
12 CHAPTER 5. ARCHITECTURE Let us be formal with the number of inputs and the number of outputs. If A is an operation with m input bits and n output bits, then we shall draw this as / m A / n (5.40) The matrix A will be of size 2 n by 2 m . Say B takes the n outputs of A as input and outputs p bits, i.e., / m A / n B / p (5.41) Then B is represented by 2 p by 2 n matrix B, and performing one operation sequentially followed by another operations corresponds to B ⋆ A which is a (2 p by 2 n ) ⋆ (2 n by 2 m ) = (2 p by 2 m ) matrix. Besides sequential operations, there are parallel operations:
5.2. CLASSICAL GATES 13 A (5.42) B Here we are doing A to some bits and B to other bits. This will be represented by A ⊗ B (see section 2.7). Let us be exact with the number of inputs and the number of outputs. / m A / n / m′ B / n′ (5.43) A will be of size 2 n by 2 m . B will be of size 2 n′ by 2 m′ . Following equation [CITE EQUATION] in section 2.7, A ⊗ B is of size 2 n 2 n′ = 2 n+n′ by 2 m 2 m′ = 2 m+m′ . Exercise 5.2.4 In Exercise CITE EXERCISE we proved that A ⊗ B ∼ = B ⊗ A. What does this fact correspond to in terms of doing parallel operations to different bits?
- Page 1 and 2: Chapter 5 Architecture Noson S. Yan
- Page 3 and 4: 5.1. BITS AND QUBITS 3 A bit is eit
- Page 5 and 6: 5.1. BITS AND QUBITS 5 It is import
- Page 7 and 8: 5.1. BITS AND QUBITS 7 In the class
- Page 9 and 10: 5.2. CLASSICAL GATES 9 This matrix
- Page 11: 5.2. CLASSICAL GATES 11 A B (5.3
- Page 15 and 16: 5.2. CLASSICAL GATES 15 A is a 2 m
- Page 17 and 18: 5.3. REVERSIBLE GATES 17 Exercise 5
- Page 19 and 20: 5.3. REVERSIBLE GATES 19 Figure 5.5
- Page 21 and 22: 5.3. REVERSIBLE GATES 21 |x〉 |x
- Page 23 and 24: 5.3. REVERSIBLE GATES 23 output wil
- Page 25 and 26: 5.4. QUANTUM GATES 25 |x〉 • |x
- Page 27 and 28: 5.4. QUANTUM GATES 27 In other word
- Page 29 and 30: 5.4. QUANTUM GATES 29 Let us spend
- Page 31 and 32: 5.4. QUANTUM GATES 31 will work. R
- Page 33 and 34: 5.4. QUANTUM GATES 33 Throughout th
- Page 35 and 36: 5.4. QUANTUM GATES 35 Multiplying t
- Page 37: Bibliography [1] Charles H. Bennett
12 CHAPTER 5. ARCHITECTURE<br />
Let us be formal with the number of inputs <strong>and</strong> the number of outputs. If<br />
A is an operation with m input bits <strong>and</strong> n output bits, then we shall draw this<br />
as<br />
/ m A / n (5.40)<br />
The matrix A will be of size 2 n by 2 m . Say B takes the n outputs of A as<br />
input <strong>and</strong> outputs p bits, i.e.,<br />
/ m A / n B / p (5.41)<br />
Then B is represented by 2 p by 2 n matrix B, <strong>and</strong> performing one operation<br />
sequentially followed by another operations corresponds to B ⋆ A which is a<br />
(2 p by 2 n ) ⋆ (2 n by 2 m ) = (2 p by 2 m ) matrix.<br />
Besides sequential operations, there are parallel operations:
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