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‎examples/QCBM/README.md

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# Quantum Circuit Born Machine
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(Implementation by: [Gopal Ramesh Dahale](https://github.com/Gopal-Dahale))
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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.
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## Setup
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Below is the usage of `qcbm_gaussian_mixture.py` which can be obtained by running `python qcbm_gaussian_mixture.py -h`.
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```
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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]
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options:
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-h, --help show this help message and exit
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--n_wires N_WIRES Number of wires used in the circuit
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--epochs EPOCHS Number of training epochs
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--n_blocks N_BLOCKS Number of blocks in ansatz
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--n_layers_per_block N_LAYERS_PER_BLOCK
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Number of layers per block in ansatz
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--plot Visualize the predicted probability distribution
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--optimizer OPTIMIZER
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optimizer class from torch.optim
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--lr LR
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```
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For example:
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```
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python qcbm_gaussian_mixture.py --plot --epochs 100 --optimizer RMSprop --lr 0.01 --n_blocks 6 --n_layers_per_block 2 --n_wires 6
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```
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Using the command above gives an output similar to the plot below.
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<p align="center">
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<img src ='./assets/sample_output.png' width-500 alt='sample output of QCBM'>
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</p>
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## References
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1. Liu, Jin-Guo, and Lei Wang. “Differentiable learning of quantum circuit born machines.” Physical Review A 98.6 (2018): 062324.

‎examples/QCBM/assets/sample_output.png

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‎examples/QCBM/qcbm_gaussian_mixture.py

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import torch
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from torchquantum.algorithm import QCBM, MMDLoss
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import torchquantum as tq
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import argparse
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import os
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from pprint import pprint
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# Reproducibility
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def set_seed(seed: int = 42) -> None:
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np.random.seed(seed)
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torch.manual_seed(seed)
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torch.cuda.manual_seed(seed)
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# When running on the CuDNN backend, two further options must be set
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torch.backends.cudnn.deterministic = True
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torch.backends.cudnn.benchmark = False
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# Set a fixed value for the hash seed
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os.environ["PYTHONHASHSEED"] = str(seed)
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print(f"Random seed set as {seed}")
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def _setup_parser():
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parser = argparse.ArgumentParser()
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parser.add_argument(
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"--n_wires", type=int, default=6, help="Number of wires used in the circuit"
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)
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parser.add_argument(
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"--epochs", type=int, default=10, help="Number of training epochs"
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)
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parser.add_argument(
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"--n_blocks", type=int, default=6, help="Number of blocks in ansatz"
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)
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parser.add_argument(
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"--n_layers_per_block",
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type=int,
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default=1,
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help="Number of layers per block in ansatz",
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)
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parser.add_argument(
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"--plot",
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action="store_true",
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help="Visualize the predicted probability distribution",
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)
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parser.add_argument(
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"--optimizer", type=str, default="Adam", help="optimizer class from torch.optim"
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)
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parser.add_argument("--lr", type=float, default=1e-2)
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return parser
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# Function to create a gaussian mixture
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def gaussian_mixture_pdf(x, mus, sigmas):
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mus, sigmas = np.array(mus), np.array(sigmas)
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vars = sigmas**2
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values = [
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(1 / np.sqrt(2 * np.pi * v)) * np.exp(-((x - m) ** 2) / (2 * v))
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for m, v in zip(mus, vars)
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]
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values = np.sum([val / sum(val) for val in values], axis=0)
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return values / np.sum(values)
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# Create a gaussian mixture
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n_wires = 6
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x_max = 2**n_wires
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x_input = np.arange(x_max)
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mus = [(2 / 8) * x_max, (5 / 8) * x_max]
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sigmas = [x_max / 10] * 2
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data = gaussian_mixture_pdf(x_input, mus, sigmas)
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# This is the target distribution that the QCBM will learn
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target_probs = torch.tensor(data, dtype=torch.float32)
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# Ansatz
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layers = tq.RXYZCXLayer0({"n_blocks": 6, "n_wires": n_wires, "n_layers_per_block": 1})
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qcbm = QCBM(n_wires, layers)
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# To train QCBMs, we use MMDLoss with radial basis function kernel.
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bandwidth = torch.tensor([0.25, 60])
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space = torch.arange(2**n_wires)
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mmd = MMDLoss(bandwidth, space)
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# Optimization
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optimizer = torch.optim.Adam(qcbm.parameters(), lr=0.01)
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for i in range(100):
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optimizer.zero_grad(set_to_none=True)
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pred_probs = qcbm()
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loss = mmd(pred_probs, target_probs)
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loss.backward()
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optimizer.step()
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print(i, loss.item())
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# Visualize the results
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with torch.no_grad():
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pred_probs = qcbm()
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plt.plot(x_input, target_probs, linestyle="-.", label=r"$\pi(x)$")
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plt.bar(x_input, pred_probs, color="green", alpha=0.5, label="samples")
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plt.xlabel("Samples")
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plt.ylabel("Prob. Distribution")
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plt.legend()
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plt.show()
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mus, sigmas = np.array(mus), np.array(sigmas)
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vars = sigmas**2
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values = [
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(1 / np.sqrt(2 * np.pi * v)) * np.exp(-((x - m) ** 2) / (2 * v))
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for m, v in zip(mus, vars)
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]
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values = np.sum([val / sum(val) for val in values], axis=0)
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return values / np.sum(values)
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def main():
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set_seed()
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parser = _setup_parser()
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args = parser.parse_args()
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print("Configuration:")
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pprint(vars(args))
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# Create a gaussian mixture
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n_wires = args.n_wires
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assert n_wires >= 1, "Number of wires must be at least 1"
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x_max = 2**n_wires
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x_input = np.arange(x_max)
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mus = [(2 / 8) * x_max, (5 / 8) * x_max]
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sigmas = [x_max / 10] * 2
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data = gaussian_mixture_pdf(x_input, mus, sigmas)
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# This is the target distribution that the QCBM will learn
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target_probs = torch.tensor(data, dtype=torch.float32)
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# Ansatz
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layers = tq.RXYZCXLayer0(
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{
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"n_blocks": args.n_blocks,
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"n_wires": n_wires,
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"n_layers_per_block": args.n_layers_per_block,
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}
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)
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qcbm = QCBM(n_wires, layers)
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# To train QCBMs, we use MMDLoss with radial basis function kernel.
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bandwidth = torch.tensor([0.25, 60])
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space = torch.arange(2**n_wires)
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mmd = MMDLoss(bandwidth, space)
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# Optimization
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optimizer_class = getattr(torch.optim, args.optimizer)
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optimizer = optimizer_class(qcbm.parameters(), lr=args.lr)
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for i in range(args.epochs):
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optimizer.zero_grad(set_to_none=True)
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pred_probs = qcbm()
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loss = mmd(pred_probs, target_probs)
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loss.backward()
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optimizer.step()
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print(i, loss.item())
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# Visualize the results
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if args.plot:
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with torch.no_grad():
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pred_probs = qcbm()
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plt.plot(x_input, target_probs, linestyle="-.", label=r"$\pi(x)$")
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plt.bar(x_input, pred_probs, color="green", alpha=0.5, label="samples")
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plt.xlabel("Samples")
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plt.ylabel("Prob. Distribution")
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plt.legend()
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plt.show()
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if __name__ == "__main__":
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main()

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