Ciro Santilli @cirosantilli 37

Ciro Santilli 37 Updated 2025-07-16

On Qiskit qiskit==0.44.1:

qc.qasm()

E.g. with our qiskit/hello.py, we obtain the Bell state circuit:

OPENQASM 2.0;
include "qelib1.inc";
qreg q[2];
creg c[2];
h q[0];
cx q[0],q[1];
measure q[0] -> c[0];
measure q[1] -> c[1];

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Regular expression by

Ciro Santilli 37 Updated 2025-07-16

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PyZX by

Ciro Santilli 37 Updated 2025-07-16

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github.com/Quantomatic/pyzx

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Bell circuit by

Ciro Santilli 37 Updated 2025-07-16

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A quantum circuit which when fed with input

∣ 00 ⟩

produces the Bell state.

In Qiskit at: qiskit/hello.py.

Figure 1.
Quantum circuit that generates the Bell state
. Source.
The fundamental intuition for this circuit is as follows.
First the Hadamard gate makes the first qubit be in a 50/50 state.
Then, the CNOT gate gets controlled by that 50/50 value, and the controlled qubit also gets 50/50 chance as a result.
However, both qubits are now entangled: the result of the second qubit depends on the result of the first one. Because:
if the first qubit is 0, cnot is not active, and so the second qubit remains 0 as its input
if the first qubit is 1, cnot is active, and so the second qubit is flipped to 1

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Turing machine regex tape notation by

Ciro Santilli 37 Updated 2025-07-16

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Turing machine regex tape notation is Ciro Santilli's made up name for the notation used e.g. at:

Most of it is just regular regular expression notation, with a few differences:

$0^{i n f}$ denotes the right or left edge of the (zero initialized) tape. It is often omitted as we always just assume it is always present on both sides of every regex
A, B, C, D and E denotes the current machine state. This is especially common notation in the context of the BB(5) problem
< and > next to the state indicate if the head is on top of the left or right element. E.g.:
```
11 (01)^n <A 00 (0011)^{n+2}
```
indicates that the head A is on top of the last 1 of the last sequence of n 01s to the left of the head.

This notation is very useful, as it helps compress long repeated sequences of Turing machine tape and extract higher level patterns from them, which is how you go about understanding a Turing machine in order to apply Turing machine acceleration.

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Binet Gaussienne by

Ciro Santilli 37 Updated 2025-07-16

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This is likely a joke binet, but the idea is epic: its members would in principle take the hardest courses and purposefully get bad grades on them to improve the grades of others, as grades are always normalized to a normal distribution.

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SageMath by

Ciro Santilli 37 Updated 2025-07-16

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A Python wrapper over a bunch of numeric and computer algebra system packages to try and fully replace MATLAB et. al.

For example, their

Quickstart tutorial at: www.sagemath.org/tour-quickstart.html From this we see that they are very opinionated, you don't need to import anything, everything has a pre-defined global name, which is convenient, e.g.:

Q Q^{3}

(1)

is the 3D vector space over the rationals. This also suggests that they are quite focused on computer algebra as opposed to numerical.

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Qiskit hello world by

Ciro Santilli 37 Updated 2025-07-16

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The official hello world is documented at: qiskit.org/documentation/intro_tutorial1.html and contains a Bell state circuit.

Our version at qiskit/hello.py.

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Qiskit Aer by

Ciro Santilli 37 Updated 2025-07-16

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github.com/Qiskit/qiskit-aer

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qiskit/hello.py by

Ciro Santilli 37 Updated 2025-07-16

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Our example uses a Bell state circuit to illustrate all the fundamental Qiskit basics.

Sample program output, counts are randomized each time.

First we take the quantum state vector immediately after the

∣ 00 ⟩

input.

input:
state:
Statevector([1.+0.j, 0.+0.j, 0.+0.j, 0.+0.j],
            dims=(2, 2))
probs:
[1. 0. 0. 0.]

We understand that the first element of Statevector is

∣ 00 ⟩

, and has probability of 1.0.

Next we take the state after a Hadamard gate on the first qubit:

h:
state:
Statevector([0.70710678+0.j, 0.70710678+0.j, 0.        +0.j,
             0.        +0.j],
            dims=(2, 2))
probs:
[0.5 0.5 0.  0. ]

We now understand that the second element of the Statevector is

∣ 01 ⟩

, and now we have a 50/50 propabability split for the first bit.

Then we apply the CNOT gate:

cx:
state:
Statevector([0.70710678+0.j, 0.        +0.j, 0.        +0.j,
             0.70710678+0.j],
            dims=(2, 2))
probs:
[0.5 0.  0.  0.5]

which leaves us with the final

\frac{∣ 00 ⟩ + ∣ 11 ⟩}{2}

Then we print the circuit a bit:

qc without measure:
     ┌───┐
q_0: ┤ H ├──■──
     └───┘┌─┴─┐
q_1: ─────┤ X ├
          └───┘
c: 2/══════════

qc with measure:
     ┌───┐     ┌─┐
q_0: ┤ H ├──■──┤M├───
     └───┘┌─┴─┐└╥┘┌─┐
q_1: ─────┤ X ├─╫─┤M├
          └───┘ ║ └╥┘
c: 2/═══════════╩══╩═
                0  1
qasm:
OPENQASM 2.0;
include "qelib1.inc";
qreg q[2];
creg c[2];
h q[0];
cx q[0],q[1];
measure q[0] -> c[0];
measure q[1] -> c[1];

And finally we compile the circuit and do some sample measurements:

qct:
     ┌───┐     ┌─┐
q_0: ┤ H ├──■──┤M├───
     └───┘┌─┴─┐└╥┘┌─┐
q_1: ─────┤ X ├─╫─┤M├
          └───┘ ║ └╥┘
c: 2/═══════════╩══╩═
                0  1
counts={'11': 484, '00': 516}
counts={'11': 493, '00': 507}

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Computer science course of the University of Oxford by

Ciro Santilli 37 Updated 2025-07-16

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Public landing page: www.ox.ac.uk/admissions/undergraduate/courses/course-listing/computer-science

Course lists: www.cs.ox.ac.uk/teaching/courses/ True to form, courses appear to have identifiers, e.g. qi for the Quantum Information course of the University of Oxford rather than more arbitrary A1/A2/A3, B1/B2/B3, naming convention used by the Mathematics course of the University of Oxford and the Physics course of the University of Oxford, and URLs can either have years or not:

www.cs.ox.ac.uk/teaching/courses/qi/: no year: goes to latest
www.cs.ox.ac.uk/teaching/courses/2023-2024/qi/: has year, fixed year. Disgraceful repetition of redundant 2023-2024, but OK.

The "course materials" section of each course leads to courses.cs.ox.ac.uk/ which is paywalled by IP (accessible via Eduroam): TODO which system does it use? Some courses place their materials directly on "www.cs.ox.ac.uk", and when that is the case they are publicly accessible. So it is very much hit and miss. E.g. www.cs.ox.ac.uk/teaching/courses/2022-2023/quantum/index.html from Quantum Processes and Computation course of the University of Oxford has the assignments such as www.cs.ox.ac.uk/people/aleks.kissinger/courses/qpc2022/assignment1.pdf publicly visible, but e.g. www.cs.ox.ac.uk/teaching/courses/2022-2023/modelsofcomputation/ has nothing.

Handbook:

2022:
- general www.cs.ox.ac.uk/files/13731/CS%20Handbook%20final.pdf
- Year 1 (Prelims): www.cs.ox.ac.uk/files/13794/Handbook%202022%20Part%20C%20-%20V1.3.pdf
- Year 2/3 (Parts A/B): www.cs.ox.ac.uk/files/13793/Handbook%202022%20Parts%20A%20&%20B%20V1.3.pdf There is some mixture on which courses can be taken on year 2 or 3. This also implies that they cannot have the usual A2/B2 naming scheme. They just don't have names instead mostly. It is also the most beautiful illustration of why you shouldn't do Compute Science at university: there's no depth to the subject. You can just take random courses and you learn it all quickly. Section "The only reason for universities to exist should be the laboratories".
  - Year 2 has four mandatory core courses:
    Models of Computation
    Algorithms and Data Structures
    Compilers (mandatory for compsi, but not mathematics and computer science)
    Concurrent programming
    A only:
    Probability
  - Hilary term
    Concurrent Programming (mandatory for compsi, but not mathematics and computer science)
    Quantum information
- Year 4 (Part C): www.cs.ox.ac.uk/files/13794/Handbook%202022%20Part%20C%20-%20V1.3.pdf
  - Michaelmas term
    Bayesian Statistical Probabilistic Programming
    Concurrent Algorithms and Data Structures
    Quantum Processes and Computation
    Computational Learning Theory
    Computational Biology
    Advanced Complexity Theory
    Graph Representation Learning
  - Hilary term
    Advanced Security
    Database Systems Implementation
    Ethical Computing in Practice
    Law and Computer Science
    Quantum Software course of the University of Oxford
    Geometric Deep Learning
    Foundations of Self-Programming Agents
    Deep Learning in Healthcare

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Busy Beaver Challenge by

Ciro Santilli 37 Updated 2025-07-16

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bbchallenge.org/story

Project trying to compute BB(5) once and for all. Notably it has better presentation and organization than any other previous effort, and appears to have grouped everyone who cares about the topic as of the early 2020s.

Very cool initiative!

By 2023, they had basically decided every machine: discuss.bbchallenge.org/t/the-30-to-34-ctl-holdouts-from-bb-5/141

In June 2024 they felt that they had verified the result after a full Coq proof was published:

So now onto BB(6) I guess.

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Year 2 or 3 course of the computer science course of the University of Oxford by

Ciro Santilli 37 Updated 2025-07-16

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Quantum Information course of the University of Oxford by

Ciro Santilli 37 Updated 2025-07-16

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www.cs.ox.ac.uk/teaching/courses/qi/

2023: Jonathan Barrett

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Year 4 of the computer science course of the University of Oxford by

Ciro Santilli 37 Updated 2025-07-16

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Department of Computer Science of the University of Oxford by

Ciro Santilli 37 Updated 2025-07-16

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www.cs.ox.ac.uk

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numpy/fft.py by

Ciro Santilli 37 Updated 2025-07-16

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Output:

sin(t)
fft
real 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
imag 0 -10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 10
rfft
real 0 0 0 0 0 0 0 0 0 0 0
imag 0 -10 0 0 0 0 0 0 0 0 0

sin(t) + sin(4t)
fft
real 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
imag 0 -10 0 0 -10 0 0 0 0 0 0 0 0 0 0 0 10 0 0 10
rfft
real 0 0 0 0 0 0 0 0 0 0 0
imag 0 -10 0 0 -10 0 0 0 0 0 0

With our understanding of the discrete Fourier transform we see clearly that:

the signal is being decomposed into sinusoidal components
because we are doing the Discrete Fourier transform of a real signal, for the fft, $X_{k} = \overset{ˉ}{X_{N - k}}$ so there is redundancy in the. We also understand that rfft simply cuts off and only keeps half of the coefficients

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Quantum state vector by

Ciro Santilli 37 Updated 2025-07-16

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Tensor product in quantum computing by

Ciro Santilli 37 Updated 2025-07-16

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We don't need to understand a super generalized version of tensor products to know what they mean in basic quantum computing!

Intuitively, taking a tensor product of two qubits simply means putting them together on the same quantum system/computer.

When we write the bra-ket notation:

∣ 00 ⟩

that is the same as

∣ 0 ⟩ \otimes ∣ 0 ⟩

The tensor product is called a "product" because it distributes over addition.

E.g. consider:

(\frac{∣ 0 ⟩ + ∣ 1 ⟩}{2}) \otimes ∣ 0 ⟩ = \frac{∣ 0 ⟩ \otimes ∣ 0 ⟩ + ∣ 1 ⟩ \otimes ∣ 0 ⟩}{2} = \frac{∣ 00 ⟩ + ∣ 10 ⟩}{2}

(1)

Intuitively, in this operation we just put a Hadamard gate qubit together with a second pure

∣ 0 ⟩

qubit.

And the outcome still has the second qubit as always 0, because we haven't made them interact.

The quantum state

\frac{∣ 00 ⟩ + ∣ 10 ⟩}{2}

is called a separable state, because it can be written as a single product of two different qubits. We have simply brought two qubits together, without making them interact.

If we then add a CNOT gate to make a Bell state:

\frac{∣ 00 ⟩ + ∣ 11 ⟩}{2} = \frac{∣ 0 ⟩ \otimes ∣ 0 ⟩ + ∣ 1 ⟩ \otimes ∣ 1 ⟩}{2}

(2)

we can now see that the Bell state is non-separable: we've made the two qubits interact, and there is no way to write this state with a single tensor product. The qubits are fundamentally entangled.

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Quantum Processes and Computation course of the University of Oxford by

Ciro Santilli 37 Updated 2025-07-16

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2022 page: www.cs.ox.ac.uk/teaching/courses/2022-2023/quantum/ (archive). Assignments are available:

2022 lecturer: Aleks Kissinger

The course would be better named ZX-calculus as it appears to be the only subject covered.

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