qiskit/hello.py by Ciro Santilli 37 Updated 2025-07-16
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 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 , 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 , 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 .
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}
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:
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:
Busy Beaver Challenge by Ciro Santilli 37 Updated 2025-07-16
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!
numpy/fft.py by Ciro Santilli 37 Updated 2025-07-16
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:
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: that is the same as .
The tensor product is called a "product" because it distributes over addition.
E.g. consider:
Intuitively, in this operation we just put a Hadamard gate qubit together with a second pure qubit.
And the outcome still has the second qubit as always 0, because we haven't made them interact.
The quantum state 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:
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.
2015 professor: Alan J. Barr.
Possible 2022 professor: Guy Wilkinson (unconfirmed): www.chch.ox.ac.uk/staff/professor-guy-wilkinson
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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