Ciro Santilli @cirosantilli 35

Ciro Santilli 35  Updated 2025-04-24  +Created 1970-01-01

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 35  Updated 2025-04-24  +Created 1970-01-01

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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 35  Updated 2025-04-24  +Created 1970-01-01

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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 35  Updated 2025-04-24  +Created 1970-01-01

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Quantum Information course of the University of Oxford by

Ciro Santilli 35  Updated 2025-04-24  +Created 1970-01-01

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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 35  Updated 2025-04-24  +Created 1970-01-01

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Department of Computer Science of the University of Oxford by

Ciro Santilli 35  Updated 2025-04-24  +Created 1970-01-01

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www.cs.ox.ac.uk

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@cirosantilli/_file/numpy/numpy/fft.py by

Ciro Santilli 35  Updated 2025-04-24  +Created 1970-01-01

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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 35  Updated 2025-04-24  +Created 1970-01-01

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Tensor product in quantum computing by

Ciro Santilli 35  Updated 2025-04-24  +Created 1970-01-01

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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 35  Updated 2025-04-24  +Created 1970-01-01

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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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Quantum Software course of the University of Oxford by

Ciro Santilli 35  Updated 2025-04-24  +Created 1970-01-01

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2022 page: www.cs.ox.ac.uk/teaching/courses/qsoft/ Half of the problems are Jupyter Notebooks, not bad.

Like Quantum Processes and Computation course of the University of Oxford, also ZX-calculus-heavy.

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B2 Oxford physics course by

Ciro Santilli 35  Updated 2025-04-24  +Created 1970-01-01

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www-thphys.physics.ox.ac.uk/people/AndreiStarinets/sr_mt_2022.html (archive) contains 2022 problem sets and notes, well done Mr Andrei Starinets!

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B4 Oxford physics course by

Ciro Santilli 35  Updated 2025-04-24  +Created 1970-01-01

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www-pnp.physics.ox.ac.uk/~barra/teaching.shtml As of 2023, contains some good 2015 materials: web.archive.org/web/20220525094139/http://www-pnp.physics.ox.ac.uk/~barra/teaching.shtml It was called "Subatomic physics" back then.

2015 professor: Alan J. Barr.

Possible 2022 professor: Guy Wilkinson (unconfirmed): www.chch.ox.ac.uk/staff/professor-guy-wilkinson

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Bilibili by

Ciro Santilli 35  Updated 2025-04-24  +Created 1970-01-01

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Champaign-Urbana metropolitan area by

Ciro Santilli 35  Updated 2025-04-24  +Created 1970-01-01

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It is quite comical that two separate towns were founded one next to the other right in the middle of nowhere. And that both have so slightly weird names.

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