Historical errata for Quantum Computing

“easy verify” should read “easy to verify”

“Kunth’s book is a great resource…” should read “Knuth’s book is a great resource…”

“k means that Jimmy Kimmel does Bellagio…” here the underscore is not placed under the k.

para 4, line 2
“… computing a solution differently then classical …”
“then” -> “than”

Link results in 404 error, file seems to have been moved or removed:

people.eecs.berkeley.edu/~christos/classics/Feynman.pdf

I can’t figure out which volume of The Art of Computer Programming that describes the scheduling problem. Could you add the volume number to [Knu11]? Thanks.

The measuring of the q registers to the classical registers in the table do not match those in the Bellagio circuit on PDF page 109. Here q[6] -> c[0] which is different from the table, q[6] -> c[3]. This confused me a little.

“Thus, both back-to-back Z gates…” should be “Thus, both back-to-back H gates…”

Bullet points refer to “Maher” as one of the hotels.

E.g., “at Bellagio on Day 1 and at Maher on Day 2”

In the answer to “Try your Hand”, #10, The proof of the OR GATE Circut , Applying DeMogan’s Law on the first line makes the 2nd line:
|1⟩ ⊕ ⌐ ( ⌐|a⟩ ∨ ⌐|b⟩ )

That makes the 3rd line (using the carats as ‘AND’ instead of dots)
|1⟩ ∧ ( ⌐|a⟩ ∨ ⌐|b⟩ ) ∨ |0⟩ ∧ ⌐( ⌐|a⟩ ∨ ⌐|b⟩ )

The fourth line
⌐ |a⟩ ∨ ⌐|b⟩ ∨ |0⟩

simplifies to
⌐ |a⟩ ∨ ⌐|b⟩

But since we flipped those bits at the beginning, that means:
|a⟩ ∨ |b⟩

Alternatively, we could begin the proof showing the values of |a⟩ ∧|b⟩ before the OR Circut:

|1⟩ ⊕( ⌐|a⟩ ∧⌐|b⟩ )
|1⟩ ⊕ ⌐ ( |a⟩ ∨ |b⟩ )
|1⟩ ∧ ( |a⟩ ∨ |b⟩ ) ∨ |0⟩ ∧ ⌐( |a⟩ ∨ |b⟩ )
|a⟩ ∨ |b⟩ ∨ |0⟩
|a⟩ ∧ |b⟩

Anyway that’s my understanding. This book is fantastic so far, I’ve been watching for errata and haven’t seen any, but this was puzzling to me. Thanks!

Is it worth discussing unpredictability of some IBM machines compared to others, perhaps due to overheating? Running identical circuits, I’ve noticed consistently higher error rates on busy machines, such as IBM Melbourne. I first noticed this when running the Bellagio_Constraints_k_1_m_0.qasm on the Melbourne machine. The error rates propagate each time a qubit is flipped.

Bullet 3 refers to the “0-biased quantum register array”. The author probably meant “0-based quantum register array”.

Problem 6c asks to write down the values in the classical registers, but the problem as stated in 6a and 6b never specified to measure any of the qubits.

When looking at the “epub” version of the book on the Apple “books” app, the sub-numbering of the problem sets doesn’t go like 1a>i. Instead it’s just using regular numerals for each level: 11>1. I don’t know if this is a problem with epub or the Apple app, but hopefully it can be fixed.

The language of 6a is ambiguous and doesn’t necessarily lead to the answer in the key. Once one reads to the end of 6b, it is clear at that stage, that the target qubit is to be initially set to |1>. That is not at all clear in 6a when one is drawing the diagram initially, though.

The table answering 8a looks all correct to me, except I think it should be |d> = |0> on the last row corresponding to |xy> = |11>.

The paragraph at the bottom of the (correctly, I think) refers to a classical result string c[2]c[1]c[0], but the supporting table just above says on the last row that the measurement q[6]↦c[3] was made. I believe this should state q[6]↦c[2] in order to match convention, and the paragraph.

Answer 15a:
The H gates are placed on qubits q[0] and q[1] representing |k and |n⟩
should read “qubits q[0] and q[2] ” to match the image.

In doing exercises 11-13 of chapter 3, there’s a lot of flipping back and forth to pages 5-7. If the problem statement could be restated here (perhaps in a summarized form) it could make doing the exercises easier (present relevant information close to context of use).

Exercise 6 solution: It wasn’t clear to me that “inversion of a qubelet” was one of my “quantum operation” choices. I ended up using a chain of H and X operations to transform |1> to -|0>. Maybe make clear in the text that we can consider qubelet inversion to be a member of our quantum operation vocabulary, or explain in the framing of the exercise.

There is an inconsistency between the solution to 14c, and a notation convention declared on page 54. The solution is expressed in terms of a string built from the multi-bit classical register: c[0]c[1], but in the explanatory section about that register on page 54, a convention for the book is declared that such strings will be expressed as c[n-1]c[n-2]…c[1]c[0].

Try your Hand:
2. Draw the qubit represented by the following quantum state:
−0.35 |0⟩ + 0.28 |1⟩

Is that a valid Quantum state? Squaring the given amplitudes suggests no.

In describing using the U3 Gate to replicate the H Gate, it’s printed twice, the second time wrong:
H Gate: = U3 (π/2,π, 0)
H Gate: = U3 (π/2,0, π)

The Errata I reported on this is wrong, the second H Gate is correct, but the first is backwards.

Then the following U gate is backwards, and so is the U2 Gate, it should be
U2 (0,π)
to mimic H gate, as works in the exercise below it.

The equation here uses across to get an angle from amplitude, I don’t thin it’s mentioned anywhere else.

… maybe explain this operation before the questions, or in the appendix somewhere?

In “From 2D to 3D Qubelets Try Your Hand” section, “4. Consider a qubit with the 2 pentagon…” should be “4. Consider a qubit with the single pentagon…”, otherwise it doesn’t match with the answer.

The “vertical bar” at the start of the definition below “Substituting for…” is not required.

The equation below “…, the angle (phi) is:” should be “(phi) = - pi/r radians”.

Since the angle (phi) = - pi/6 radians, shouldn’t we calculate e to the power of i (-pi/6) instead of i (pi/6) in the equation following “Thus, 30 degrees clockwise… Thus,”?

In epub version on iPad, the “Probability of Collapsing to” equation lines are missing the exponents. The PDF has the correct formulas.

ω₁² is shown to calculate as 0.1551, but I calculate 0.1552, which also, added to 0.8448, is a more satisfying 1.0000 instead of 0.9999.

Exercise 1a: replace “following qubit” with “qubit above”

Typesetting issue in PDF in solution to 6e, where the denominator of a fraction overlaps the numerator on the next line.

This text is confusing, when actually referring back to page 156: “Recall from Normalizing Qubelets, on page 156, the normalized value of the pentagon |0⟩ qubelets is cos θ/2.” The wording implies that θ is discussed back on page 156. Instead, the form a|0⟩+b|1⟩ is discussed. I might say instead, “The normalized value of the pentagon |0⟩ qubelets is cos θ/2. Relating this to the amplitude formulae in Normalizing Qubelets, on page 156, for the state expressed as a|0⟩+b|1⟩, yields the following equation:”

Misspelling of unchanged (“unchainged”)

Figure and rest of discussion refer to the angle between r|1⟩ and the Z-axis as β, but the first sentience on this page calls it χ.

Subject-verb disagreement, should be: “Thus, a qubit’s quantum state depicted using pentagon |0⟩ and triangle |1⟩ qubelets maps to points on the Bloch Sphere.”

Inline comments would enhance the adaptability of code

ex :
OPENQASM 2.0;
include “qelib1.inc”;
// init register
qreg q[7];
creg c[7];

// q[0] - Kimmel k
// q[1] - Kimmel complement (-k)
// q[2] - Meher m
// q[3] - Meher complement (-m)

// initial values of k,m
x q[0];

//fanout k
cx q[0], q[1];
x q[1];

//fanout m
cx q[2], q[3];
x q[3];

// OR gate on m, k
x q[0];
x q[2];
x q[5];
ccx q[0], q[2], q[5];
x q[0];
x q[2];

// OR gate on -m, -k
x q[1];
x q[3];
x q[4];
ccx q[1], q[3], q[4];
x q[1];
x q[3];

// AND gate output from above OR gate
ccx q[4], q[5], q[6];

// measure
measure q[6] -> c[0];
measure q[0] -> c[1];
measure q[2] -> c[2];

‘i. … as a vector of this “blended”.’ should be ‘i. … as a vector of this “blended”qubit.’

Shouldn’t the conjugate transpose of the bra equation have daggers instead of asterisks?

Shouldn’t the last sentence in “Writing the Conjugate Transpose of a Matrix” be “A dagger” instead of “A asterisk”?

I think the answer to e. i. and ii. should work with A U matrix instead of the A dagger U matrix.

The equation “Probability of qubit collapsing to |1>” shouldn’t have square(1/squareroot(2)). Also do we need the “-” in square(-i * 1/squareroot(2)), because amplitude of |1> was defined as i * 1/squareroot(2) upstream.

Would be great to have a description of why “lambda = 0”.

In c., I think you’re giving away the answer to a. by providing the U3 parameter values in the quantum circuit. :)

Remove “<” from “Like the Rx < (theta) gate…” in the first sentence of Ry Gate section.

Shouldn’t the RHS |0> rotate clockwise instead of anticlockwise in the diagram in the Y Gate section?

Shouldn’t the definition of the H gate in e. be “- 1/squareroot(2)” [with minus] in the right bottom corner instead of “1/squareroot(2)”?

The second line of the tensor product equation should be “= ac |0>|0> + ad|0>|1> + bc|1>|0> + bd|1>\\1>” instead of “= ac |0>|0> + ad|0>|0> + bc|1>|0> + bd|1>\\1>”.

“A Entangler” equation is missing a “1/squareroot(2)” in the third line.

Could you talk about the complementary of |keep> here at the second paragraph of “Design Loader Block”? It was difficult for me to figure out what “… two ways, |keep> or |keep>” meant. Especially when the bar looked like an underscore for the “joint” word.

In 4., the quantum state should be 2/5|00> + 4i/5|01> - i/5|10> + 2/5|11>. If not the probabilities do not add up to 1

In 4.c., shouldn’t the new state be “4i/squareroot(20)|01> + 2/squareroot(20)|11>”?

In the first sentence, the classical register for the sixth qubit should c[5] instead of c[6].

In the paragraph starting with “Compare the two quantum states:”, shouldn’t “a negative sign when they act on |10>” be “… when they act on |01>” instead?

You talk about the IBM Experience not having a CZ gate in the paragraph starting “Since, the CZ gate is not…”, but version 1.14.0 of the IBM Quantum Experience has CZ gate in the palette.

If you search for ‘cz’ in the ‘Quantum logic gate glossary’, you should be able to find a description of the cz gate.

In section b, I think you’re missing a ’’. |00> - |01> |10> |11> should be |00> - |01> + |10> + |11>

On the MOBI version of the book, viewed on an Oasis Kindle, the code for the ‘Logic Expressions to Quantum Circuit’ section from chapter 2 is rendered as (using the FAN OUT gate for k and khat as an example):
…
c
x
q
[
0
]
,
q
[
1
]
…
And the same case for the rest of the circuit gates.

Sorry but my kindle does not give me precise page only location, which I think is dependent of the kindle model and text size

The picture in question 2 doesn’t match question / answer. The question asks about rotating the |0> qublet clockwise, but the answer on print page 514 talks about leaving the |0> qublet alone, and then an S-dagger gate rotating the |1> qublet clockwise.

The image for the Y gate’s effect, after switching the qublets, shows both qublets turned counterclockwise, but the |0> queblet, the green pentagon on the right, should be turned clockwise.

The sentence “To “twist” certain qubelets so that they either don’t cancel out. " feels incomplete. Should it be “To “twist” certain qubelets so that they either do or don’t cancel out." ? The next sentence would also need to change to keep the flow. BTW - Really enjoying this book!

qiskit code for u3 gate omits the qubit:
circuit.u3(0,math.pi,0,3)
should be:
circuit.u3(0,math.pi,0,q[3])

The answer to Q. 3. a. omits the minus signs in both Hadamard matrices in the bottom right corner.

Under “Alternatively, you can also use the gate matrices” , the
answer seems to have dropped the 1/sqrt(2) from the previous line .

“To see how this circuit creates a mega-qubit where the quantum state |ψ0⟩ is tied with both |keep⟩ and |keep⟩”

Should that say " both|keep⟩ and |send⟩ " ?

Question 4.c.ii “In other words, the probability of detecting an
interceptor is 0.25.”

Isn’t that the probability that and interceptor goes undetected, or collapses qubits to their expected value? I think that should be 0.75 , and in section 4.c.iii 0.125 should say 0.875

Later in 4.ciii it says “Thus, with increasing number of matching qubits, the probability to detect an interceptor increases. ” but the examples above show the probabilites decreasing.

Looks like the wrong image pasted in from the IBM Circuit composer. Should be one with an H gate on each qubit then a CZ gate.

I think the second line of the two H gates equation should be:
= 1/2 (|0> (|0> - |1>) + |1> (|0> - |1>))

The second line of the equation is missing “-”

= 1/squareroot(2) (|0> - |1>)/squareroot(2) |0> - 1/squareroot(2) (|0> - |1>)/squareroot(2) |1>

The code line 5 should be:

circuit.measure(0, 0)

instead of passing the array elements, since you talk about index below.

When I tried getting the result using a new notebook, I get the following error:

%matplotlib inline

1. Importing standard Qiskit libraries and configuring account
   from qiskit import QuantumCircuit, execute, Aer, IBMQ
   from qiskit.compiler import transpile, assemble
   from qiskit.tools.jupyter import *
   from qiskit.visualization import *
   from qiskit.visualization import plot_histogram

1. Loading your IBM Q account(s)
   provider = IBMQ.load_account()

job = backend.retrieve_job(‘abc123…’)

hist = job.result().get_counts()
plot_histogram(hist)

Credentials are already in use. The existing account in the session will be replaced.
—————————————————————————————————————-
NameError Traceback (most recent call last)
in
10 provider = IBMQ.load_account()
11
—-> 12 job = backend.retrieve_job(‘5e9ce4396ad41d00184b537f’)
13
14 hist = job.result().get_counts()

NameError: name ‘backend’ is not defined

I understand that I need to define backend, but perhaps that should be noted in the text.

I think “The system will return an array of name-values…” should be “The system will return a dictionary of name-values…”

I think “… 2 independent sets of qubits:(q[0],q[1]) and (q[3]).” should be “… 2 independent sets of qubits:(q[0],q[1]) and (q2).”

In section c. last sentence, I think “F (|x>, |y>)” should be “UF (|x>, |y>)”.

Since we’re not using CNOT, I think Line 2 of the cirq code should be

from cirq.ops import H, X

Two interesting developments you may have already heard. 1) The company Qutech has launched a quantum computer in Europe with a web UI called Quantum Inspire. www.quantum-inspire.com/projects . 2) There’s a great resource from Cornell University of Quantum Algorithms for Beginners complete with Qiskit code: arxiv.org/abs/1804.03719

An error at the scheme q[6] is displayed twice.