Errata list for Dancing with Qubits by Robert S. Sutor

Errata list for “Dancing with Qubits” by Robert S. Sutor

Chapter 4

Page 112: $\left(\frac{5}{2},-1\right); \longrightarrow ;\left(-\frac{5}{2},-1\right)$

Page 127: $\frac{\pi}{2} \ge \frac{\pi}{2}; \longrightarrow; -\frac{\pi}{2} \ge \frac{\pi}{2}$ (inside of the upper box)

Chapter 5

Page 139: $v = \left( v1,v_2 \right); \longrightarrow; v = \left( v_1,v_2 \right)$

Page 164:

$$ \begin{align} \begin{bmatrix} 1 \\ 0 \end{bmatrix} \begin{bmatrix} t \end{bmatrix} &= \begin{bmatrix} t & 0 \end{bmatrix} \;\;\; \longrightarrow \;\;\; \begin{bmatrix} 1 \\ 0 \end{bmatrix} \begin{bmatrix} t \end{bmatrix} = \begin{bmatrix} t \\ 0 \end{bmatrix} \\ \begin{bmatrix} 0 \\ 1 \end{bmatrix} \begin{bmatrix} t \end{bmatrix} &= \begin{bmatrix} 0 & t \end{bmatrix} \;\;\; \longrightarrow \;\;\; \begin{bmatrix} 0 \\ 1 \end{bmatrix} \begin{bmatrix} t \end{bmatrix} = \begin{bmatrix} 0 \\ t \end{bmatrix} \end{align} $$

\
Page 165: all $\frac{\pi}{4}$ should be $\frac{\pi}{2}$

Chapter 6

Page 208:

  1. oatmeal + oatmeal $\longrightarrow$ oatmeal + coconut (row 3, column 4)
  2. $P($ oatmeal and sugar $);= \frac{2}{16} + \frac{1}{8} = 0.125$ $\longrightarrow$ $P($ oatmeal and sugar $);= \frac{2}{16} = \frac{1}{8} = 0.125$

Page 217: \
Question 6.7.1 “at the beginning of this section” should be “at the beginning of section 6.6”

Chapter 7

Page 230:

$$ \begin{equation} \left| v \right\rangle \left\langle w \right| = \begin{bmatrix} v_1\overline{w_1} & v_1\overline{w_2} & \cdots & v_1\overline{w_m} \\ v_2\overline{w_1} & v_2\overline{w_2} & \cdots & v_2\overline{w_m} \\ \vdots & \vdots & \ddots & \vdots \\ v_n\overline{w_1} & v_n\overline{w_2} & \cdots & v_n\overline{w_m} \end{bmatrix} \end{equation}\;\;\;\mathrm{(first\; box,\; last\; line)} $$

\
Page 233: Question 7.2.2

$$ \begin{equation} P(i)P(j) = \begin{cases} \left| e_i \right\rangle \left\langle e_i \right| & (\mathrm{if}\;i=j) \\[5pt] 0 & \mathrm{otherwise} \end{cases} \end{equation} $$

\
Page 245:\
When $\left| a \right| \ge 1$ then $y_0 \ge0$. Similarly, $\left| a \right| < 1$ implies $y_0 < 0$.\
$\longrightarrow$ When $\left| a \right| \ge 2$ then $y_0 \ge0$. Similarly, $\left| a \right| < 2$ implies $y_0 < 0$.

\
Page 246:

$$ \begin{align} g:\; &\left( 0 \le \theta < \frac{\pi}{4} \right)\;\mathrm{or}\; \left( \frac{\pi}{4} < \theta < 2\pi \right)\;\rightarrow \mathbb{R} \\ \longrightarrow\; g:\; & \left( 0 \le \theta < \frac{\pi}{2} \right)\;\mathrm{or}\; \left( \frac{\pi}{2} < \theta < 2\pi \right)\;\rightarrow \mathbb{R} \end{align} $$

\
Page 260: $\vartheta$ should be $\varphi$ (last line).

\
Page 261:

$$ \begin{align} &\boldsymbol{R_{\varphi}^z} = \cos\left( \frac{\varphi}{2} \right)I_2 - \cos \left( \frac{\varphi}{2} \right)i\sigma_z \\ \longrightarrow\; &\boldsymbol{R_{\varphi}^z} = \cos\left( \frac{\varphi}{2} \right)I_2 - \sin \left( \frac{\varphi}{2} \right)i\sigma_z \end{align} $$

\
Page 264:

$$ \begin{align} &\boldsymbol{R_{\varphi}^x} = \cos\left( \frac{\varphi}{2} \right)I_2 - \cos \left( \frac{\varphi}{2} \right)i\sigma_x \\ \longrightarrow\; &\boldsymbol{R_{\varphi}^x} = \cos\left( \frac{\varphi}{2} \right)I_2 - \sin \left( \frac{\varphi}{2} \right)i\sigma_x, \\ &\boldsymbol{R_{\varphi}^y} = \cos\left( \frac{\varphi}{2} \right)I_2 - \cos \left( \frac{\varphi}{2} \right)i\sigma_y \\ \longrightarrow\; &\boldsymbol{R_{\varphi}^y} = \cos\left( \frac{\varphi}{2} \right)I_2 - \sin \left( \frac{\varphi}{2} \right)i\sigma_y, \end{align} $$

\
Page 266:

$$ \begin{align} c_{\sigma_x},\;c_{\sigma_y}, \;\mathrm{and}\; c_{\sigma_z}\; \mathrm{are\; Pauli\; matrices }\\ \sigma_x,\;\sigma_y, \;\mathrm{and}\; \sigma_z\; \mathrm{are\; Pauli\; matrices } \end{align} $$

Chapter 8

\
Page 287: all upper bounds of sums should be $2^n-1$ instead n-1 except first box.

\
Page 290: $\left|\psi\right\rangle_1\otimes 2\left|\psi\right\rangle_2 \longrightarrow \left|\psi\right\rangle_1\otimes\left|\psi\right\rangle_2$ (first line)

Chapter 9

\
Page 319:\

  1. Table: Step 3, Qubit8 $\left| 1 \right\rangle \longrightarrow \left| 0 \right\rangle$ \
  2. Second paragragh: $3(n+1)+1 \longrightarrow 3n+1$

\
Page 320: partial sums $\longrightarrow$ partial products

\
Page 336: $\left| 00 \right\rangle$ and $\left| 01 \right\rangle$ are untouched $\left| 00 \right\rangle$ and $\left| 10 \right\rangle$ are untouched

\
Page 340:\

  1. $\left| 00 \right\rangle,; \left| 01 \right\rangle,; \left| 10 \right\rangle,;$ and $\left| 00 \right\rangle ; \longrightarrow ; \left| 00 \right\rangle,; \left| 01 \right\rangle,; \left| 10 \right\rangle,;$ and $\left| 11 \right\rangle$

$$ \begin{align} \left( H\otimes H \right)\left| u \right\rangle = &\left( \frac{\sqrt{2}}{2} \sum_{v_1\; in\; \left\{ 0,1 \right\}} \left( -1 \right)^{u_1 v_1}\left| v_1 \right\rangle \right) \otimes \left( \frac{\sqrt{2}}{2} \sum_{v_2\; in \; \left\{ 0,1 \right\}} \left( -1 \right)^{u_2 y_2} \left| v_2 \right\rangle \right)\\ \longrightarrow &\left( \frac{\sqrt{2}}{2} \sum_{v_1\; in\; \left\{ 0,1 \right\}} \left( -1 \right)^{u_1 v_1}\left| v_1 \right\rangle \right) \otimes \left( \frac{\sqrt{2}}{2} \sum_{v_2\; in \; \left\{ 0,1 \right\}} \left( -1 \right)^{u_2 v_2} \left| v_2 \right\rangle \right) \end{align} $$
$$ \begin{align} &\left( H \otimes H \right) \left| u \right\rangle = \frac{1}{2} \sum_{v\; in \; \left\{ 0,1 \right\}^n} \left( -1 \right)^{u\cdot v} \left| v \right\rangle \\ \longrightarrow & \left( H\otimes H \right) \left| u \right\rangle = \frac{1}{2}\sum_{v\; in \; \left\{ 0,1 \right\}^2} \left( -1 \right)^{u\cdot v} \left| v \right\rangle \end{align} $$

\
Page 343:

$$ \begin{align} &\left( -1 \right)^{f(x)}\left( \left| 0 \right\rangle - \left| 1 \right\rangle \right) \\ \longrightarrow &\frac{\sqrt{2}}{2} \left( -1 \right)^{f(x)} \left( \left| 0 \right\rangle - \left| 1 \right\rangle \right) \end{align} $$