Basic programming for quantum machine learning with Qiskit and - - PowerPoint PPT Presentation

Basic programming for quantum machine learning with Qiskit and PennyLane

NITheP Mini-school

Amira Abbas 08/09/2020

Applications

Logistics Finance Material science The universe

Quantum machine learning

Quantum open source foundation

qosf.org

Agenda

An introduction to variational circuits

Agenda

A simple model An introduction to variational circuits

Agenda

Circuit optimisation A simple model An introduction to variational circuits

Agenda

Circuit optimisation Build the model with PennyLane A simple model An introduction to variational circuits

Agenda

Circuit optimisation Build the model with PennyLane A simple model An introduction to variational circuits Assume basic knowledge of quantum computing ! Previous mini-school: Daniel Park; Nielsen & Chuang - Quantum computation and quantum information

f(x; θ)

f(x; θ) θ

|f(x; θ)⟩ θ

Quantum models

Quantum models

Deterministic quantum models Deutsch-Jozsa algorithm

y U |ψ⟩

Quantum models

Deterministic quantum models Deutsch-Jozsa algorithm Variational quantum models Variational quantum eigensolver Variational quantum classifier Quantum support vector machines Quantum neural networks

y U

⟨y⟩

U(θ)

|ψ⟩ |ψ⟩

Quantum machine learning

. . .

Quantum machine learning

. . .

U(x; θ)

Quantum machine learning

. . .

U(x; θ) |f(x; θ)⟩

Quantum machine learning

. . .

U(x; θ) M |f(x; θ)⟩

Quantum machine learning

̂ y

. . .

U(x; θ) M } |f(x; θ)⟩

Variational circuits

Success of variational models

Can run on near term quantum hardware Robust to noise Shows most promise in chemistry applications Can be used in many quantum machine learning models

A simple example

|0⟩

Source:https://pennylane.ai/qml/demos/tutorial_qubit_rotation.html

A simple example

|0⟩

Source:https://pennylane.ai/qml/demos/tutorial_qubit_rotation.html

|0⟩ = [ 1 0]

A simple example

|0⟩

Source:https://pennylane.ai/qml/demos/tutorial_qubit_rotation.html

|0⟩ = [ 1 0]

A simple example

|0⟩

Source:https://pennylane.ai/qml/demos/tutorial_qubit_rotation.html

|0⟩ = [ 1 0]

⟨σz⟩

A simple example

|0⟩

Source:https://pennylane.ai/qml/demos/tutorial_qubit_rotation.html

|0⟩ = [ 1 0]

⟨σz⟩

σz = [ 1 0 −1]

A simple example

|0⟩

Source:https://pennylane.ai/qml/demos/tutorial_qubit_rotation.html

|0⟩ = [ 1 0]

⟨σz⟩

⟨0 ∣ σz ∣ 0⟩

σz = [ 1 0 −1]

Calculating the expectation value:

A simple example

|0⟩

Source:https://pennylane.ai/qml/demos/tutorial_qubit_rotation.html

|0⟩ = [ 1 0]

⟨σz⟩

⟨0 ∣ σz ∣ 0⟩ = [1 0] [ 1 −1] [ 1 0]

σz = [ 1 0 −1]

Calculating the expectation value:

A simple example

|0⟩

Source:https://pennylane.ai/qml/demos/tutorial_qubit_rotation.html

|0⟩ = [ 1 0]

⟨σz⟩

⟨0 ∣ σz ∣ 0⟩ = [1 0] [ 1 −1] [ 1 0] = 1

σz = [ 1 0 −1]

Calculating the expectation value:

A simple example

|0⟩

Source:https://pennylane.ai/qml/demos/tutorial_qubit_rotation.html

|0⟩ = [ 1 0]

⟨σz⟩

⟨1 ∣ σz ∣ 1⟩

σz = [ 1 0 −1]

Calculating the expectation value:

X

X = [ 1 1 0]

A simple example

|0⟩

Source:https://pennylane.ai/qml/demos/tutorial_qubit_rotation.html

|0⟩ = [ 1 0]

⟨σz⟩

⟨1 ∣ σz ∣ 1⟩ = [0 1] [ 1 −1] [ 1] = − 1

σz = [ 1 0 −1]

Calculating the expectation value:

X

X = [ 1 1 0]

U(θ)

|0⟩⊗n

A simple example

A simple example

|0⟩

Ry(θ2) Rx(θ1)

Source:https://pennylane.ai/qml/demos/tutorial_qubit_rotation.html

⟨σz⟩

|0⟩

Ry(θ2)

Source:https://pennylane.ai/qml/demos/tutorial_qubit_rotation.html

⟨σz⟩

Rx(θ1) = cos

θ1 2

−i sin

θ1 2

−i sin

θ1 2

cos

θ1 2

Ry(θ2) = cos

θ2 2

−sin

θ2 2

sin

θ2 2

cos

θ2 2

|0⟩ = [ 1 0] σz = [ 1 −1]

A simple example

Rx(θ1)

|0⟩

Ry(θ2) Rx(θ1)

Source:https://pennylane.ai/qml/demos/tutorial_qubit_rotation.html

⟨σz⟩

Rx(θ1) = cos

θ1 2

−i sin

θ1 2

−i sin

θ1 2

cos

θ1 2

Ry(θ2) = cos

θ2 2

−sin

θ2 2

sin

θ2 2

cos

θ2 2

|0⟩ = [ 1 0] σz = [ 1 −1]

|ψ⟩ = Ry(θ2) Rx(θ1) |0⟩

State after operations:

A simple example

|0⟩

Ry(θ2) Rx(θ1)

Source:https://pennylane.ai/qml/demos/tutorial_qubit_rotation.html

⟨σz⟩

Rx(θ1) = cos

θ1 2

−i sin

θ1 2

−i sin

θ1 2

cos

θ1 2

Ry(θ2) = cos

θ2 2

−sin

θ2 2

sin

θ2 2

cos

θ2 2

|0⟩ = [ 1 0] σz = [ 1 −1]

|ψ⟩ = Ry(θ2) Rx(θ1) |0⟩

State after operations: Calculating the expectation value: ⟨ψ ∣ σz ∣ ψ⟩

A simple example

|0⟩

Ry(θ2) Rx(θ1)

Source:https://pennylane.ai/qml/demos/tutorial_qubit_rotation.html

⟨σz⟩

Rx(θ1) = cos

θ1 2

−i sin

θ1 2

−i sin

θ1 2

cos

θ1 2

Ry(θ2) = cos

θ2 2

−sin

θ2 2

sin

θ2 2

cos

θ2 2

|0⟩ = [ 1 0] σz = [ 1 −1]

Calculating the expectation value: ⟨ψ ∣ σz ∣ ψ⟩ = ⟨0 ∣ Rx(θ1)†Ry(θ2)†σz Ry(θ2)Rx(θ1) ∣ 0⟩

|ψ⟩ = Ry(θ2) Rx(θ1) |0⟩

State after operations:

A simple example

|0⟩

Ry(θ2) Rx(θ1)

Source:https://pennylane.ai/qml/demos/tutorial_qubit_rotation.html

⟨σz⟩

Rx(θ1) = cos

θ1 2

−i sin

θ1 2

−i sin

θ1 2

cos

θ1 2

Ry(θ2) = cos

θ2 2

−sin

θ2 2

sin

θ2 2

cos

θ2 2

|0⟩ = [ 1 0] σz = [ 1 −1]

Calculating the expectation value: ⟨ψ ∣ σz ∣ ψ⟩ = ⟨0 ∣ Rx(θ1)†Ry(θ2)†σz Ry(θ2)Rx(θ1) ∣ 0⟩ = cos(θ1) cos(θ2)

|ψ⟩ = Ry(θ2) Rx(θ1) |0⟩

State after operations:

A simple example

|0⟩

Ry(θ2) Rx(θ1)

Source:https://pennylane.ai/qml/demos/tutorial_qubit_rotation.html

⟨σz⟩

Rx(θ1) = cos

θ1 2

−i sin

θ1 2

−i sin

θ1 2

cos

θ1 2

Ry(θ2) = cos

θ2 2

−sin

θ2 2

sin

θ2 2

cos

θ2 2

|0⟩ = [ 1 0] σz = [ 1 −1]

Calculating the expectation value: ⟨ψ ∣ σz ∣ ψ⟩ = ⟨0 ∣ Rx(θ1)†Ry(θ2)†σz Ry(θ2)Rx(θ1) ∣ 0⟩ = cos(θ1) cos(θ2)

|ψ⟩ = Ry(θ2) Rx(θ1) |0⟩

State after operations: How do we choose the parameters?

A simple example

U(θ)

|0⟩⊗n

A simple example

U(θ)

̂ y

|0⟩⊗n

A simple example

U(θ)

̂ y

cost

|0⟩⊗n

A simple example

U(θ)

̂ y

cost update θ

|0⟩⊗n

A simple example

Classical machine learning

f(θ)

̂ y

cost update θ

data

σ(f(θ))

Source:https://pennylane.ai/qml/demos/tutorial_qubit_rotation.html

Define a cost function which we want to minimise:

A simple example

Source:https://pennylane.ai/qml/demos/tutorial_qubit_rotation.html

⟨ψ ∣ σz ∣ ψ⟩ = ⟨0 ∣ Rx(θ1)†Ry(θ2)†σz Ry(θ2)Rx(θ1) ∣ 0⟩ = cos(θ1) cos(θ2)

Define a cost function which we want to minimise:

A simple example

Source:https://pennylane.ai/qml/demos/tutorial_qubit_rotation.html

⟨ψ ∣ σz ∣ ψ⟩ = ⟨0 ∣ Rx(θ1)†Ry(θ2)†σz Ry(θ2)Rx(θ1) ∣ 0⟩ = cos(θ1) cos(θ2)

A simple example

[ 1 0 −1] [ 1 0] = 1 [1 0]

Define a cost function which we want to minimise:

Source:https://pennylane.ai/qml/demos/tutorial_qubit_rotation.html

⟨ψ ∣ σz ∣ ψ⟩ = ⟨0 ∣ Rx(θ1)†Ry(θ2)†σz Ry(θ2)Rx(θ1) ∣ 0⟩ = cos(θ1) cos(θ2)

A simple example

[ 1 0 −1] [ 1 0] = 1 [1 0] [ 1 0 −1] [ 1] = − 1 [0 1]

Define a cost function which we want to minimise:

Source:https://pennylane.ai/qml/demos/tutorial_qubit_rotation.html

⟨ψ ∣ σz ∣ ψ⟩ = ⟨0 ∣ Rx(θ1)†Ry(θ2)†σz Ry(θ2)Rx(θ1) ∣ 0⟩ = cos(θ1) cos(θ2)

A simple example

Define a cost function which we want to minimise:

Circuit optimisation

Circuit optimisation

⟨ψ ∣ σz ∣ ψ⟩ = ⟨0 ∣ Rx(θ1)†Ry(θ2)†σz Ry(θ2)Rx(θ1) ∣ 0⟩ = cos(θ1) cos(θ2)

Define a cost function:

Gradient-based methods

Gradient descent

Gradient descent

⃗ θ cost

Gradient descent

⃗ θ cost θ1

Gradient descent

⃗ θ cost θ1

Gradient descent

⃗ θ cost θ1

Gradient descent

⃗ θ cost θ1 θ* θ2

Gradient-based methods

Source:Schuld, Maria, et al. "Circuit-centric quantum classifiers." Physical Review A 101.3 (2020): 032308.

U(θ)

̂ yθ

|0⟩⊗n

Gradient-based methods

Source:Schuld, Maria, et al. "Circuit-centric quantum classifiers." Physical Review A 101.3 (2020): 032308.

U(θ + s) ̂ yθ+s |0⟩⊗n U(θ − s) ̂ yθ−s |0⟩⊗n

−

Gradient =

U(θ)

̂ yθ

|0⟩⊗n

Software frameworks

https://qosf.org/learn_quantum/

Jump to the code

Next up

Encoding data into quantum states More sophisticated models Barren plateaus

Thank you!

NITheP Mini-school

Amira Abbas @AmiraMorphism amyami187@gmail.com