@cirosantilli/_file/qiskit/qiskit/qft.py by 
Ciro Santilli 35 Updated 2025-01-29 +Created 1970-01-01
Ciro Santilli 35 Updated 2025-01-29 +Created 1970-01-01This is an example of the
qiskit.circuit.library.QFT implementation of the Quantum Fourier transform function which is documented at: docs.quantum.ibm.com/api/qiskit/0.44/qiskit.circuit.library.QFTOutput:So this also serves as a more interesting example of quantum compilation, mapping the
init: [1, 0, 0, 0, 0, 0, 0, 0]
qc
┌──────────────────────────────┐┌──────┐
q_0: ┤0 ├┤0 ├
│ ││ │
q_1: ┤1 Initialize(1,0,0,0,0,0,0,0) ├┤1 QFT ├
│ ││ │
q_2: ┤2 ├┤2 ├
└──────────────────────────────┘└──────┘
transpiled qc
┌──────────────────────────────┐ ┌───┐
q_0: ┤0 ├────────────────────■────────■───────┤ H ├─X─
│ │ ┌───┐ │ │P(π/2) └───┘ │
q_1: ┤1 Initialize(1,0,0,0,0,0,0,0) ├──────■───────┤ H ├─┼────────■─────────────┼─
│ │┌───┐ │P(π/2) └───┘ │P(π/4) │
q_2: ┤2 ├┤ H ├─■─────────────■──────────────────────X─
└──────────────────────────────┘└───┘
Statevector([0.35355339+0.j, 0.35355339+0.j, 0.35355339+0.j,
0.35355339+0.j, 0.35355339+0.j, 0.35355339+0.j,
0.35355339+0.j, 0.35355339+0.j],
dims=(2, 2, 2))
init: [0.0, 0.35355339059327373, 0.5, 0.3535533905932738, 6.123233995736766e-17, -0.35355339059327373, -0.5, -0.35355339059327384]
Statevector([ 7.71600526e-17+5.22650714e-17j,
1.86749130e-16+7.07106781e-01j,
-6.10667421e-18+6.10667421e-18j,
1.13711443e-16-1.11022302e-16j,
2.16489014e-17-8.96726857e-18j,
-5.68557215e-17-1.11022302e-16j,
-6.10667421e-18-4.94044770e-17j,
-3.30200457e-16-7.07106781e-01j],
dims=(2, 2, 2))QFT gate to Qiskit Aer primitives.If we don't
transpile in this example, then running blows up with:qiskit_aer.aererror.AerError: 'unknown instruction: QFT'The second input is:and the output of that approximately:which can be defined simply as the normalized DFT of the input quantum state vector.
[0, 1j/sqrt(2), 0, 0, 0, 0, 0, 1j/sqrt(2)]From this we see that the Quantum Fourier transform is equivalent to a direct discrete Fourier transform on the quantum state vector, related: physics.stackexchange.com/questions/110073/how-to-derive-quantum-fourier-transform-from-discrete-fourier-transform-dft
Accounts:
- twitter.com/lukedashjr on Twitter. Status as of January 2024:This dude doesn't fuck around. Or perhaps he only fucks around. Either way.
father of 10 children
- www.linkedin.com/in/lukedashjr/ on LinkedIn
- bitcointalk.org/index.php?action=profile;u=3318 on bitcointalk.org
- www.reddit.com/user/luke-jr/
- github.com/sponsors/luke-jr
- freenode username:
luke-jr, mentioned e.g. at bitcointalk.org/index.php?topic=38007.0 from Section "Prayer wars"
Author of the prayer side of the Prayer wars.
Creator of Eligius pool Bitcoin mining pool.
According to LinkedIn he studied at the Benedictine College in Kansas.
TODO is his real birthname "Luke Dash Jr."?
Apparently he had his coins stolen in January 2023, then worth $3.5m: blog.cryptostars.is/luke-dashjr-an-original-bitcoin-developer-loses-all-his-btc-88421c395ce5p...
www.reddit.com/r/Buttcoin/comments/4936kw/lukejr_is_a_seriously_a_super_crazy_person_quotes/ "Luke-Jr is a seriously a super crazy person quotes gigathread." (2016) on Reddit. Apparently he has some fun views of life.
@cirosantilli/_file/qiskit/qiskit/hello.py by Ciro Santilli 35 Updated 2025-01-29 +Created 1970-01-01
Ciro Santilli 35 Updated 2025-01-29 +Created 1970-01-01Our 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.We understand that the first element of
input:
state:
Statevector([1.+0.j, 0.+0.j, 0.+0.j, 0.+0.j],
dims=(2, 2))
probs:
[1. 0. 0. 0.]Statevector is , and has probability of 1.0.Next we take the state after a Hadamard gate on the first qubit:We now understand that the second element of the
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. ]Statevector is , and now we have a 50/50 propabability split for the first bit.Then we apply the CNOT gate:which leaves us with the final .
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]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}- I opened and was confirmed or generated considerable interest
- I wrote comments pointing out a non obvious cause/fix/duplicate.
- I reviewed the patch
This shall not list bugs solved by my accepted pull requests.
Pinned article: ourbigbook/introduction-to-the-ourbigbook-project
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