QCBM algorithm

examples/QCBM/README.md

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+# Quantum Circuit Born Machine
+(Implementation by: [Gopal Ramesh Dahale](https://github.com/Gopal-Dahale))
+
+Quantum Circuit Born Machine (QCBM) [1] is a generative modeling algorithm which uses Born rule from quantum mechanics to sample from a quantum state $|\psi \rangle$ learned by training an ansatz $U(\theta)$ [1][2]. In this tutorial we show how `torchquantum` can be used to model a Gaussian mixture with QCBM.
+
+## Setup
+
+Below is the usage of `qcbm_gaussian_mixture.py` which can be obtained by running `python qcbm_gaussian_mixture.py -h`.
+
+```
+usage: qcbm_gaussian_mixture.py [-h] [--n_wires N_WIRES] [--epochs EPOCHS] [--n_blocks N_BLOCKS] [--n_layers_per_block N_LAYERS_PER_BLOCK] [--plot] [--optimizer OPTIMIZER] [--lr LR]
+
+options:
+  -h, --help            show this help message and exit
+  --n_wires N_WIRES     Number of wires used in the circuit
+  --epochs EPOCHS       Number of training epochs
+  --n_blocks N_BLOCKS   Number of blocks in ansatz
+  --n_layers_per_block N_LAYERS_PER_BLOCK
+                        Number of layers per block in ansatz
+  --plot                Visualize the predicted probability distribution
+  --optimizer OPTIMIZER
+                        optimizer class from torch.optim
+  --lr LR
+```
+
+For example:
+
+```
+python qcbm_gaussian_mixture.py --plot --epochs 100 --optimizer RMSprop --lr 0.01 --n_blocks 6 --n_layers_per_block 2 --n_wires 6
+```
+
+Using the command above gives an output similar to the plot below.
+
+<p align="center">
+<img src ='./assets/sample_output.png' width-500 alt='sample output of QCBM'>
+</p>
+
+
+## References
+
+1. Liu, Jin-Guo, and Lei Wang. “Differentiable learning of quantum circuit born machines.” Physical Review A 98.6 (2018): 062324.
+2. Gili, Kaitlin, et al. "Do quantum circuit born machines generalize?." Quantum Science and Technology 8.3 (2023): 035021.

examples/QCBM/qcbm_gaussian_mixture.py

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+import matplotlib.pyplot as plt
+import numpy as np
+import torch
+from torchquantum.algorithm import QCBM, MMDLoss
+import torchquantum as tq
+import argparse
+import os
+from pprint import pprint
+
+
+# Reproducibility
+def set_seed(seed: int = 42) -> None:
+    np.random.seed(seed)
+    torch.manual_seed(seed)
+    torch.cuda.manual_seed(seed)
+    # When running on the CuDNN backend, two further options must be set
+    torch.backends.cudnn.deterministic = True
+    torch.backends.cudnn.benchmark = False
+    # Set a fixed value for the hash seed
+    os.environ["PYTHONHASHSEED"] = str(seed)
+    print(f"Random seed set as {seed}")
+
+
+def _setup_parser():
+    parser = argparse.ArgumentParser()
+    parser.add_argument(
+        "--n_wires", type=int, default=6, help="Number of wires used in the circuit"
+    )
+    parser.add_argument(
+        "--epochs", type=int, default=10, help="Number of training epochs"
+    )
+    parser.add_argument(
+        "--n_blocks", type=int, default=6, help="Number of blocks in ansatz"
+    )
+    parser.add_argument(
+        "--n_layers_per_block",
+        type=int,
+        default=1,
+        help="Number of layers per block in ansatz",
+    )
+    parser.add_argument(
+        "--plot",
+        action="store_true",
+        help="Visualize the predicted probability distribution",
+    )
+    parser.add_argument(
+        "--optimizer", type=str, default="Adam", help="optimizer class from torch.optim"
+    )
+    parser.add_argument("--lr", type=float, default=1e-2)
+    return parser
+
+
+# Function to create a gaussian mixture
+def gaussian_mixture_pdf(x, mus, sigmas):
+    mus, sigmas = np.array(mus), np.array(sigmas)
+    vars = sigmas**2
+    values = [
+        (1 / np.sqrt(2 * np.pi * v)) * np.exp(-((x - m) ** 2) / (2 * v))
+        for m, v in zip(mus, vars)
+    ]
+    values = np.sum([val / sum(val) for val in values], axis=0)
+    return values / np.sum(values)
+
+
+def main():
+    set_seed()
+    parser = _setup_parser()
+    args = parser.parse_args()
+
+    print("Configuration:")
+    pprint(vars(args))
+
+    # Create a gaussian mixture
+    n_wires = args.n_wires
+    assert n_wires >= 1, "Number of wires must be at least 1"
+
+    x_max = 2**n_wires
+    x_input = np.arange(x_max)
+    mus = [(2 / 8) * x_max, (5 / 8) * x_max]
+    sigmas = [x_max / 10] * 2
+    data = gaussian_mixture_pdf(x_input, mus, sigmas)
+
+    # This is the target distribution that the QCBM will learn
+    target_probs = torch.tensor(data, dtype=torch.float32)
+
+    # Ansatz
+    layers = tq.RXYZCXLayer0(
+        {
+            "n_blocks": args.n_blocks,
+            "n_wires": n_wires,
+            "n_layers_per_block": args.n_layers_per_block,
+        }
+    )
+
+    qcbm = QCBM(n_wires, layers)
+
+    # To train QCBMs, we use MMDLoss with radial basis function kernel.
+    bandwidth = torch.tensor([0.25, 60])
+    space = torch.arange(2**n_wires)
+    mmd = MMDLoss(bandwidth, space)
+
+    # Optimization
+    optimizer_class = getattr(torch.optim, args.optimizer)
+    optimizer = optimizer_class(qcbm.parameters(), lr=args.lr)
+
+    for i in range(args.epochs):
+        optimizer.zero_grad(set_to_none=True)
+        pred_probs = qcbm()
+        loss = mmd(pred_probs, target_probs)
+        loss.backward()
+        optimizer.step()
+        print(i, loss.item())
+
+    # Visualize the results
+    if args.plot:
+        with torch.no_grad():
+            pred_probs = qcbm()
+
+        plt.plot(x_input, target_probs, linestyle="-.", label=r"$\pi(x)$")
+        plt.bar(x_input, pred_probs, color="green", alpha=0.5, label="samples")
+        plt.xlabel("Samples")
+        plt.ylabel("Prob. Distribution")
+
+        plt.legend()
+        plt.show()
+
+
+if __name__ == "__main__":
+    main()

test/algorithm/test_qcbm.py

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+from torchquantum.algorithm.qcbm import QCBM, MMDLoss
+import torchquantum as tq
+import torch
+
+
+def test_qcbm_forward():
+    n_wires = 3
+    n_layers = 3
+    ops = []
+    for l in range(n_layers):
+        for q in range(n_wires):
+            ops.append({"name": "rx", "wires": q, "params": 0.0, "trainable": True})
+        for q in range(n_wires - 1):
+            ops.append({"name": "cnot", "wires": [q, q + 1]})
+
+    data = torch.ones(2**n_wires)
+    qmodule = tq.QuantumModule.from_op_history(ops)
+    qcbm = QCBM(n_wires, qmodule)
+    probs = qcbm()
+    expected = torch.tensor([1.0, 0, 0, 0, 0, 0, 0, 0])
+    assert torch.allclose(probs, expected)
+
+
+def test_mmd_loss():
+    n_wires = 2
+    bandwidth = torch.tensor([0.1, 1.0])
+    space = torch.arange(2**n_wires)
+
+    mmd = MMDLoss(bandwidth, space)
+    loss = mmd(torch.zeros(4), torch.zeros(4))
+    assert torch.isclose(loss, torch.tensor(0.0), rtol=1e-5)

torchquantum/algorithm/__init__.py

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 SOFTWARE.
 """
 
-from .vqe import *
-from .hamiltonian import *
-from .qft import *
-from .grover import *
+from .vqe import VQE
+from .hamiltonian import Hamiltonian
+from .qft import QFT
+from .grover import Grover
+from .qcbm import QCBM, MMDLoss

torchquantum/algorithm/qcbm.py

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+import torch
+import torch.nn as nn
+
+import torchquantum as tq
+
+__all__ = ["QCBM", "MMDLoss"]
+
+
+class MMDLoss(nn.Module):
+    """Squared maximum mean discrepancy with radial basis function kerne"""
+
+    def __init__(self, scales, space):
+        """
+        Initialize MMDLoss object. Calculates and stores the kernel matrix.
+
+        Args:
+            scales: Bandwidth parameters.
+            space: Basis input space.
+        """
+        super().__init__()
+
+        gammas = 1 / (2 * (scales**2))
+
+        # squared Euclidean distance
+        sq_dists = torch.abs(space[:, None] - space[None, :]) ** 2
+
+        # Kernel matrix
+        self.K = sum(torch.exp(-gamma * sq_dists) for gamma in gammas) / len(scales)
+        self.scales = scales
+
+    def k_expval(self, px, py):
+        """
+        Kernel expectation value
+
+        Args:
+            px: First probability distribution
+            py: Second probability distribution
+
+        Returns:
+            Expectation value of the RBF Kernel.
+        """
+
+        return px @ self.K @ py
+
+    def forward(self, px, py):
+        """
+        Squared MMD loss.
+
+        Args:
+            px: First probability distribution
+            py: Second probability distribution
+
+        Returns:
+            Squared MMD loss.
+        """
+        pxy = px - py
+        return self.k_expval(pxy, pxy)
+
+
+class QCBM(nn.Module):
+    """
+    Quantum Circuit Born Machine (QCBM)
+
+    Attributes:
+        ansatz: An Ansatz object
+        n_wires: Number of wires in the ansatz used.
+
+    Methods:
+        __init__: Initialize the QCBM object.
+        forward: Returns the probability distribution (output from measurement).
+    """
+
+    def __init__(self, n_wires, ansatz):
+        """
+        Initialize QCBM object
+
+        Args:
+            ansatz (Ansatz): An Ansatz object
+            n_wires (int): Number of wires in the ansatz used.
+        """
+        super().__init__()
+
+        self.ansatz = ansatz
+        self.n_wires = n_wires
+
+    def forward(self):
+        """
+        Execute and obtain the probability distribution
+
+        Returns:
+            Probabilities (torch.Tensor)
+        """
+        qdev = tq.QuantumDevice(n_wires=self.n_wires, bsz=1, device="cpu")
+        self.ansatz(qdev)
+        probs = torch.abs(qdev.states.flatten()) ** 2
+        return probs