Errata

$\def\i{\mathbf {i}}\def\ket#1{|{#1}\rangle}\def\bra#1{\langle{#1}|}\def\braket#1#2{\langle{#1}|{#2}\rangle}$

p. 14, 3rd bullet in inner product definition: $(a\bra{v_2} + b\bra{v_3})\ket{v_1} = a\braket{v_2}{v_1} + b\braket{v_3}{v_1}$ —> $\bra{v_1}(a\ket{v_2} + b\ket{v_3}) = a\braket{v_1}{v_2} + b\braket{v_1}{v_3})$

p. 22, 3 lines from bottom there is an extra 's': normalizations factor —> normalization factor

p. 23, 3 lines from bottom: $C$ —> $R^3$

p. 24, Figure 2.6. The zero at the bottom of the picture should be $\ket{0}$.

p. 25, Section 2.5.3, paragraph 2, line 1: equation is linear —> equation is linear and homogeneous

p. 25, Section 2.5.3, paragraph 2, line 10: nothing more … complex vector spaces —> nothing more … complex vector spaces equipped with inner product

p. 168, Figure 8.1 caption. Replace 211 with 11 to obtain $X = \{x | 11^x \mod 21 = 8\}$.

p. 281, first full paragraph, sentence containing equation 11.9. Switch "express" and "to." In the line following eq. 11.9 delete one occurrence of "defined"

p. 312, "Lamont" —> "Lomont"

p. 360, "Lamont" —> "Lomont"

The errors above appear to have been fixed in the First MIT Press paperback edition, 2014. The following still appear in that edition:

p. 24, Figure 2.6. If the arrow on the $z$ axis is to indicate the positive direction, the $\ket{0}$ state should be at the top and $\ket{1}$ (0, 0, -1) at the bottom.

p. 27, Exercise 2.3 d: an unnecessary closing parenthesis at the end

p. 30, Exercise 2.14: "Block" —> "Bloch"

p. 36: The formulae in the Bell basis definition are missing the closing parenthesis.

p. 47, The formula following "so relations such as the following hold": $\bra{b} \ket{c}$ —> $\langle b | c \rangle$

p. 50, The definition of $P_s$, the sum should be $\sum_{i=0}^{s-1} \dots$

p.52, Example 4.2.5: "Let $c_1 = \bra{\psi}P_1\ket{\psi} = \sqrt{|a_{00}|^2 + |a_{11}|^2}$" —> "Let $c_1 = \sqrt{\bra{\psi}P_1\ket{\psi}} = \sqrt{|a_{00}|^2 + |a_{11}|^2}$". Ditto for $c_2$.

p. 53, The proof that eigenvalues of a Hermitian operator are real: $\bra{x_\lambda} (O \ket{x_\lambda})$ —> $\bra{x} (O \ket{x})$

p. 114, The qubit labeling on the circuit diagram for $Sum$ at the top of the page does not match the definition of $Sum$ on the previous page. From top to bottom, the qubits should be labeled c, a, b instead of a, b, c.

p. 116 The indices in the and program are incorrect. The program should read

$AndTemp\;\ket{a_{m-1}\dots a_k}\, \ket{t_0}\, \ket{a_{j-1}\dots a_0}$
$AndTemp\;(\ket{t}\ket{a_{k-1}\dots a_0})\, \ket{b_0}\,\ket{a_{m-2}\dots a_{m-k}}$
$AndTemp\;\ket{a_{m-1}\dots a_k}\, \ket{t_0}\, \ket{a_{j-1}\dots a_0}$

p. 120, The definition of $ExpMod$ should read as follows:

p. 133, third qubit —> second qubit

p. 154, The definition of $F_{ij}^{(n)}$ should be $F_{ij}^{(n)} = \frac{1}{\sqrt{2^n}} \omega_{(n)}^{ij}$ to be consistent with the definition of $F$ on the previous page, and to make the factor of $\frac{1}{\sqrt2}$ appear in the decomposition of $F^{(k)}$.

p. 154, The second line of the definition of $R_{ij}^{(k)}$ should read: "if $2(i-2^{k-1}) + 1 = j$". This is to be consistent with the text above, which says that vector entries at index $2i+1$ get mapped to position $i + 2^{k-1}$.

p. 166, Section 8.2.2: In the bottom paragraph the condition $\left| \frac{v}{2^n} - \frac{p}{q}\right| < \frac{1}{M^2}$ should be $\left| \frac{v}{2^n} - \frac{p}{q}\right| < \frac{1}{2M^2}$.

p. 172, Section 8.6.1: $b$ being relatively prime to $p-1$ is not a sufficient condition for $b$ to be a generator in the cyclic group mod $p$. For example with $p=11$, 3 is relatively prime to $p-1$, but 3 has order 5 mod $p$.
But generators are abundant, there are $\varphi(p-1)$ of them since, if $g$ is a generator and $k$ is relatively prime to $(p-1)$, then there is an $m$ such that $mk = 1 \pmod{p-1}$, so $g^k$ is also a generator because it will produce $g$ again as $g^{mk}$.
This may be how the small slip came about.

p. 195, Section 9.4.2. Middle of page: The expression for $Q(\phi, \tau)\ket{v}$ corresponds to the original definition $Q(\phi, \tau) = -US_0^{\phi}U^{-1}S_G^{\tau}$ by Brassard, HÃ¸yer and Tapp. But the sign difference is just a global phase and has no consequences on the subsequent condition $b(\phi, \tau)=0$.
Line 8 from bottom: $Q(\phi, \tau)\ket{\psi}$ should more precisely be $Q(\phi, \tau)\ket{\psi_s}$.

p. 199, line 4: $t = \sqrt{\sin \theta}$ should be $t = \sin^2\theta$.

p. 210, Box 10.2: $\sum_j \bra{a_j'}\bra{b_1}O_{AB}\ket{b_2}\ket{a} \ket{a_j'}$ —> $\sum_j \bra{a_j'}\bra{b_1}O_{AB}\ket{a}\ket{b_2} \ket{a_j'}$.

p. 219, line 15: $\operatorname{\bf tr}_A \rho = \operatorname{\bf tr}_B \rho$ —> $S(\operatorname{\bf tr}_A \rho) = S(\operatorname{\bf tr}_B \rho)$.

p. 228, Example 10.2.8: The normalization constant on the last line should be $\frac{1}{\sqrt2}$.

p. 231, line 9: $\ket{x}$ is just the sum of its projections, $\ket{x} = \sum_{j=0}^{K-1}P_j\ket{x} = \sum_{i=0}^{N-1}x_i\ket{\alpha_i}$.

p. 241, Exercise 10.3: The Bell states are mislabeled. They should read: $\ket{\Phi^-} = \frac{1}{\sqrt2}( \ket{00} - \ket{11} )$ and $\ket{\Psi^+} = \frac{1}{\sqrt2}( \ket{01} + \ket{10} )$.

p. 241, Exercise 10.8: $m_{ij}$ should be $a_{ij}$.

p. 242, Exercise 10.8: Inside the summation, $\ket{\beta_j}$ should be $\ket{\beta_i}$.

p. 242, Exercise 10.9 c: $\ket{x_i}$ should be $\ket{u_i}$.

page revision: 40, last edited: 01 May 2024 15:03