Quantum algorithms tutorial using QIBO
Marek Gluza
NTU Singapore
slides.com/marekgluza
Quantum algorithms tutorial using QIBO
Marek Gluza
NTU Singapore
slides.com/marekgluza
What is a quantum algorithm?
\hat H \mapsto \hat \mathcal H_\ell = \hat \mathcal U_\ell^\dagger \hat H \hat\mathcal U_\ell
\partial_\ell \hat \mathcal H_\ell = [[A(\hat \mathcal H_\ell),B(\hat \mathcal H_\ell)], \hat \mathcal H_\ell]
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What is a quantum computer?
It's an experimental setup A which includes a quantum system B and that setup A allows to manipulate the quantum state of B.
What is a quantum algorithm?
\hat H \mapsto \hat \mathcal H_\ell = \hat \mathcal U_\ell^\dagger \hat H \hat\mathcal U_\ell
\partial_\ell \hat \mathcal H_\ell = [[A(\hat \mathcal H_\ell),B(\hat \mathcal H_\ell)], \hat \mathcal H_\ell]
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What is a universal quantum computer?
It's an experimental setup which includes a quantum system and that setup allows to manipulate its quantum state.
It's an experimental setup which includes few-level quantum systems and that setup allows to manipulate the quantum state using gates.
These gates form a universal gate set which means that if you apply sufficiently many you will be able to reach any desired quantum state.
What is our quantum computer?
\hat H \mapsto \hat \mathcal H_\ell = \hat \mathcal U_\ell^\dagger \hat H \hat\mathcal U_\ell
\partial_\ell \hat \mathcal H_\ell = [[A(\hat \mathcal H_\ell),B(\hat \mathcal H_\ell)], \hat \mathcal H_\ell]
What is a universal quantum computer?
|\psi\rangle = a | 0 \rangle + b | 1\rangle
|\psi\rangle = a | 00 \rangle + b | 10\rangle+c | 01 \rangle + b | 11\rangle
|\psi\rangle = a | 000 \rangle + b | 100\rangle+c | 010 \rangle + d | 100\rangle+
e | 011 \rangle + f | 101\rangle+g | 110 \rangle +h | 111\rangle
|\psi\rangle = a | 0000 \rangle + b | 1000\rangle+c | 0100 \rangle + d | 1000\rangle+
e | 0011 \rangle + f | 0101\rangle+g | 1010 \rangle +h | 1100\rangle + \ldots
1 qubit
2 qubits
3 qubits
4 qubits
And you get the idea lah
In the circuit model we will apply gates. Today we will see some special examples.
What are quantum gates?
|\psi\rangle = a | 0 \rangle + b | 1\rangle
|+\rangle = \frac 1 {\sqrt 2} (| 0 \rangle + | 1\rangle)
How to quantum?
What are quantum gates?
|\psi\rangle = | 0 \rangle
Z|0\rangle = | 0\rangle
How does it work again?
What are quantum gates?
|\psi\rangle = | 0 \rangle
|+\rangle = \frac 1 {\sqrt 2} (| 0 \rangle + | 1\rangle)
Use the quantum computer to transform
into
Trivial quantum algorithm solves it:
Apply the Haddamard gate
H = \frac 1 {\sqrt 2} \begin{pmatrix} 1 & 1 \\ 1 &- 1\end{pmatrix}
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H
1 qubit is boring, 10 qubits are challenging, 100 qubits are worth
the buzz
What are quantum gates?
|\psi\rangle = | 0 \rangle \otimes |0\rangle
|+\rangle \otimes |+\rangle = \frac 1 { 2} (| 0 0\rangle + | 01\rangle+|10\rangle + | 11\rangle)
Use the quantum computer to transform
into
Apply the Haddamard gate on each qubit
H\otimes H
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H
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H
What are quantum gates?
|\psi\rangle = | 0 \rangle \otimes |0\rangle
|\Phi\rangle = \frac 1 { \sqrt 2} (| 0 0\rangle + | 11\rangle)
Use the quantum computer to transform
into
Apply the Haddamard gate on each qubit
H\otimes 1
and then apply the controlled-not gate
\text{CNOT} = |0\rangle\langle 0|\otimes 1 + |1\rangle\langle1 |\otimes X
H
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What else is there?
What are quantum algorithms?
|\psi\rangle
|\langle \phi |\psi\rangle|^2
Use the quantum computer to transform
into their fidelity
|\phi\rangle
and
as an encoded in a measured expectation value
How well does it work?
What is quantum compiling?
Controlled-SWAP
Use the quantum computer to transform
into the
and
CNOT
Controlled-CNOT
New quantum algorithm for diagonalization
\hat H \mapsto \hat \mathcal H_\ell = \hat \mathcal U_\ell^\dagger \hat H \hat\mathcal U_\ell
\partial_\ell \hat \mathcal H_\ell = [[A(\hat \mathcal H_\ell),B(\hat \mathcal H_\ell)], \hat \mathcal H_\ell]
building useful quantum algorithms
new approach to preparing useful states
building useful variational circuits
tons of fun maths in the appendix
no qubit overheads
no controlled-unitaries
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Bridging the gap between theoretical quantum algorithms and experimental actualities
Next 2 years theory support for prof. Rainer Dumke as NTU PPF (super-conducting qubits, tomography zoo, proof-of-principle quantum algorithms...)
Student internships available,
I'm coordinating an undergrad study group and a graduate-level research seminar
Material science?
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Quantum processing using QIBO
By Marek Gluza
Quantum processing using QIBO
Let's look at the essential ingredients of the circuit model of a quantum computer, see how quantum gates build upon basic calculations typically covered in introductory quantum mechanics courses, explore how circuits made of quantum gates allow us to make sense of computations involving several qubits and finally get a taste for what it feels to design, compile and run algorithms performing quantum information processing. Two paradigmatic quantum circuits will be discussed: how to entangle a particular product state into a Bell state and the swap-test circuit for measuring overlaps between pure quantum states. All formulas will be accompanied with an online interactive python notebook implementing the examples using QIBO.
