Quantum Machine Learning Constructors

Besides the arbitrary Hamiltonian constructors, Qadence also provides a complete set of program constructors useful for digital-analog quantum machine learning programs.

Feature Maps

A few feature maps are directly available for feature loading,

from qadence import feature_map

n_qubits = 3

fm = feature_map(n_qubits, fm_type="fourier")

fm = feature_map(n_qubits, fm_type="chebyshev")

fm = feature_map(n_qubits, fm_type="tower")

Fourier = KronBlock(0,1,2) [tag: FM]
├── RX(0) [params: ['phi']]
├── RX(1) [params: ['phi']]
└── RX(2) [params: ['phi']]
Chebyshev KronBlock(0,1,2) [tag: FM]
├── RX(0) [params: ['2*acos(phi)']]
├── RX(1) [params: ['2*acos(phi)']]
└── RX(2) [params: ['2*acos(phi)']]
Tower KronBlock(0,1,2) [tag: FM]
├── RX(0) [params: ['2*acos(phi)']]
├── RX(1) [params: ['4*acos(phi)']]
└── RX(2) [params: ['6*acos(phi)']]

Hardware-Efficient Ansatz

Ansatze blocks for quantum machine-learning are typically built following the Hardware-Efficient Ansatz formalism (HEA). Both fully digital and digital-analog HEAs can easily be built with the hea function. By default, the digital version is returned:

from qadence import hea
from qadence.draw import display

n_qubits = 3
depth = 2

ansatz = hea(n_qubits, depth)

As seen above, the rotation layers are automatically parameterized, and the prefix "theta" can be changed with the param_prefix argument.

Furthermore, both the single-qubit rotations and the two-qubit entangler can be customized with the operations and entangler argument. The operations can be passed as a list of single-qubit rotations, while the entangler should be either CNOT, CZ, CRX, CRY, CRZ or CPHASE.

from qadence import RX, RY, CPHASE

ansatz = hea(
    n_qubits=n_qubits,
    depth=depth,
    param_prefix="phi",
    operations=[RX, RY, RX],
    entangler=CPHASE
)

Having a truly hardware-efficient ansatz means that the entangling operation can be chosen according to each device's native interactions. Besides digital operations, in Qadence it is also possible to build digital-analog HEAs with the entanglement produced by the natural evolution of a set of interacting qubits, as is natural in neutral atom devices. As with other digital-analog functions, this can be controlled with the strategy argument which can be chosen from the Strategy enum type. Currently, only Strategy.DIGITAL and Strategy.SDAQC are available. By default, calling strategy = Strategy.SDAQC will use a global entangling Hamiltonian with Ising-like NN interactions and constant interaction strength inside a HamEvo operation,

from qadence import Strategy

ansatz = hea(
    n_qubits,
    depth=depth,
    strategy=Strategy.SDAQC
)

Note that, by default, only the time-parameter is automatically parameterized when building a digital-analog HEA. However, as described in the Hamiltonians tutorial, arbitrary interaction Hamiltonians can be easily built with the hamiltonian_factory function, with both customized or fully parameterized interactions, and these can be directly passed as the entangler for a customizable digital-analog HEA.

from qadence import hamiltonian_factory, Interaction, N, Register, hea

# Build a parameterized neutral-atom Hamiltonian following a honeycomb_lattice:
register = Register.honeycomb_lattice(1, 1)

entangler = hamiltonian_factory(
    register,
    interaction=Interaction.NN,
    detuning=N,
    interaction_strength="e",
    detuning_strength="n"
)

# Build a fully parameterized Digital-Analog HEA:
n_qubits = register.n_qubits
depth = 2

ansatz = hea(
    n_qubits=register.n_qubits,
    depth=depth,
    operations=[RX, RY, RX],
    entangler=entangler,
    strategy=Strategy.SDAQC
)

Qadence also offers a out-of-the-box training routine called train_with_grad for optimizing fully-differentiable models like QNNs and QuantumModels containing either trainable and/or non-trainable parameters (i.e., inputs). Feel free to refresh your memory about different parameter types.

Machine Learning Tools

train_with_grad performs training, logging/printing loss metrics and storing intermediate checkpoints of models.

As every other training routine commonly used in Machine Learning, it requires model, data and an optimizer as input arguments. However, in addition, it requires a loss_fn and a TrainConfig. A loss_fn is required to be a function which expects both a model and data and returns a tuple of (loss, metrics: <dict>), where metrics is a dict of scalars which can be customized too.

import torch
from itertools import count
cnt = count()
criterion = torch.nn.MSELoss()

def loss_fn(model: torch.nn.Module, data: torch.Tensor) -> tuple[torch.Tensor, dict]:
    next(cnt)
    x, y = data[0], data[1]
    out = model(x)
    loss = criterion(out, y)
    return loss, {}

The TrainConfig [qadence.ml_tools.config] tells train_with_grad what batch_size should be used, how many epochs to train, in which intervals to print/log metrics and how often to store intermediate checkpoints.

from qadence.ml_tools import TrainConfig

batch_size = 5
n_epochs = 100

config = TrainConfig(
    folder="some_path/",
    max_iter=n_epochs,
    checkpoint_every=100,
    write_every=100,
    batch_size=batch_size,
)

Fitting a funtion with a QNN using ml_tools

Let's look at a complete example of how to use train_with_grad now.

from pathlib import Path
import torch
from itertools import count
from qadence.constructors import hamiltonian_factory, hea, feature_map
from qadence import chain, Parameter, QuantumCircuit, Z
from qadence.models import QNN
from qadence.ml_tools import train_with_grad, TrainConfig
import matplotlib.pyplot as plt

n_qubits = 2
fm = feature_map(n_qubits)
ansatz = hea(n_qubits=n_qubits, depth=3)
observable = hamiltonian_factory(n_qubits, detuning=Z)
circuit = QuantumCircuit(n_qubits, fm, ansatz)

model = QNN(circuit, observable, backend="pyqtorch", diff_mode="ad")
batch_size = 1
input_values = {"phi": torch.rand(batch_size, requires_grad=True)}
pred = model(input_values)

cnt = count()
criterion = torch.nn.MSELoss()
optimizer = torch.optim.Adam(model.parameters(), lr=0.1)

def loss_fn(model: torch.nn.Module, data: torch.Tensor) -> tuple[torch.Tensor, dict]:
    next(cnt)
    x, y = data[0], data[1]
    out = model(x)
    loss = criterion(out, y)
    return loss, {}

tmp_path = Path("/tmp")

n_epochs = 5

config = TrainConfig(
    folder=tmp_path,
    max_iter=n_epochs,
    checkpoint_every=100,
    write_every=100,
    batch_size=batch_size,
)

batch_size = 25

x = torch.linspace(0, 1, batch_size).reshape(-1, 1)
y = torch.sin(x)

train_with_grad(model, (x, y), optimizer, config, loss_fn=loss_fn)

plt.plot(y.numpy())
plt.plot(model(input_values).detach().numpy())

For users who want to use the low-level API of qadence, here is the example from above written without train_with_grad.

Fitting a function - Low-level API

from pathlib import Path
import torch
from itertools import count
from qadence.constructors import hamiltonian_factory, hea, feature_map
from qadence import chain, Parameter, QuantumCircuit, Z
from qadence.models import QNN
from qadence.ml_tools import train_with_grad, TrainConfig

n_qubits = 2
fm = feature_map(n_qubits)
ansatz = hea(n_qubits=n_qubits, depth=3)
observable = hamiltonian_factory(n_qubits, detuning=Z)
circuit = QuantumCircuit(n_qubits, fm, ansatz)

model = QNN(circuit, observable, backend="pyqtorch", diff_mode="ad")
batch_size = 1
input_values = {"phi": torch.rand(batch_size, requires_grad=True)}
pred = model(input_values)

criterion = torch.nn.MSELoss()
optimizer = torch.optim.Adam(model.parameters(), lr=0.1)
n_epochs=50
cnt = count()

tmp_path = Path("/tmp")

config = TrainConfig(
    folder=tmp_path,
    max_iter=n_epochs,
    checkpoint_every=100,
    write_every=100,
    batch_size=batch_size,
)

x = torch.linspace(0, 1, batch_size).reshape(-1, 1)
y = torch.sin(x)

for i in range(n_epochs):
    out = model(x)
    loss = criterion(out, y)
    loss.backward()
    optimizer.step()