|
| 1 | +import torch |
| 2 | +import torchquantum as tq |
| 3 | +import torchquantum.functional as tqf |
| 4 | + |
| 5 | +import random |
| 6 | +import numpy as np |
| 7 | + |
| 8 | +from torchquantum.functional import mat_dict |
| 9 | + |
| 10 | +from torchquantum.plugins import tq2qiskit, qiskit2tq |
| 11 | +from torchquantum.measurement import expval_joint_analytical |
| 12 | + |
| 13 | +seed = 0 |
| 14 | +random.seed(seed) |
| 15 | +np.random.seed(seed) |
| 16 | +torch.manual_seed(seed) |
| 17 | + |
| 18 | +class MAXCUT(tq.QuantumModule): |
| 19 | + """computes the optimal cut for a given graph. |
| 20 | + outputs: the most probable bitstring decides the set {0 or 1} each |
| 21 | + node belongs to. |
| 22 | + """ |
| 23 | + |
| 24 | + def __init__(self, n_wires, input_graph, n_layers): |
| 25 | + super().__init__() |
| 26 | + |
| 27 | + self.n_wires = n_wires |
| 28 | + |
| 29 | + self.input_graph = input_graph # list of edges |
| 30 | + self.n_layers = n_layers |
| 31 | + self.n_edges = len(input_graph) |
| 32 | + |
| 33 | + self.betas = torch.nn.Parameter(0.01 * torch.rand(self.n_layers)) |
| 34 | + self.gammas = torch.nn.Parameter(0.01 * torch.rand(self.n_layers)) |
| 35 | + |
| 36 | + self.reset_shift_param() |
| 37 | + |
| 38 | + def mixer(self, qdev, beta, layer_id): |
| 39 | + """ |
| 40 | + Apply the single rotation and entangling layer of the QAOA ansatz. |
| 41 | + mixer = exp(-i * beta * sigma_x) |
| 42 | + """ |
| 43 | + |
| 44 | + for wire in range(self.n_wires): |
| 45 | + if self.shift_param_name == 'beta' and self.shift_wire == wire and layer_id == self.shift_layer: |
| 46 | + degree = self.shift_degree |
| 47 | + else: |
| 48 | + degree = 0 |
| 49 | + qdev.rx( |
| 50 | + wires=wire, |
| 51 | + params=(beta.unsqueeze(0) + degree), |
| 52 | + ) # type: ignore |
| 53 | + |
| 54 | + def entangler(self, qdev, gamma, layer_id): |
| 55 | + """ |
| 56 | + Apply the single rotation and entangling layer of the QAOA ansatz. |
| 57 | + entangler = exp(-i * gamma * (1 - sigma_z * sigma_z)/2) |
| 58 | + """ |
| 59 | + for edge_id, edge in enumerate(self.input_graph): |
| 60 | + if self.shift_param_name == 'gamma' and edge_id == self.shift_edge_id and layer_id == self.shift_layer: |
| 61 | + degree = self.shift_degree |
| 62 | + else: |
| 63 | + degree = 0 |
| 64 | + qdev.cx( |
| 65 | + [edge[0], edge[1]], |
| 66 | + ) # type: ignore |
| 67 | + qdev.rz( |
| 68 | + wires=edge[1], |
| 69 | + params=(gamma.unsqueeze(0) + degree), |
| 70 | + ) # type: ignore |
| 71 | + qdev.cx( |
| 72 | + [edge[0], edge[1]], |
| 73 | + ) # type: ignore |
| 74 | + |
| 75 | + def set_shift_param(self, layer, wire, param_name, degree, edge_id): |
| 76 | + """ |
| 77 | + set the shift parameter for the parameter shift rule |
| 78 | + """ |
| 79 | + self.shift_layer = layer |
| 80 | + self.shift_wire = wire |
| 81 | + self.shift_param_name = param_name |
| 82 | + self.shift_degree = degree |
| 83 | + self.shift_edge_id = edge_id |
| 84 | + |
| 85 | + def reset_shift_param(self): |
| 86 | + """ |
| 87 | + reset the shift parameter |
| 88 | + """ |
| 89 | + self.shift_layer = None |
| 90 | + self.shift_wire = None |
| 91 | + self.shift_param_name = None |
| 92 | + self.shift_degree = None |
| 93 | + self.shift_edge_id = None |
| 94 | + |
| 95 | + def edge_to_PauliString(self, edge): |
| 96 | + # construct pauli string |
| 97 | + pauli_string = "" |
| 98 | + for wire in range(self.n_wires): |
| 99 | + if wire in edge: |
| 100 | + pauli_string += "Z" |
| 101 | + else: |
| 102 | + pauli_string += "I" |
| 103 | + return pauli_string |
| 104 | + |
| 105 | + def circuit(self, qdev): |
| 106 | + """ |
| 107 | + execute the quantum circuit |
| 108 | + """ |
| 109 | + # print(self.betas, self.gammas) |
| 110 | + for wire in range(self.n_wires): |
| 111 | + qdev.h( |
| 112 | + wires=wire, |
| 113 | + ) # type: ignore |
| 114 | + |
| 115 | + for i in range(self.n_layers): |
| 116 | + self.mixer(qdev, self.betas[i], i) |
| 117 | + self.entangler(qdev, self.gammas[i], i) |
| 118 | + |
| 119 | + def forward(self, measure_all=False): |
| 120 | + """ |
| 121 | + Apply the QAOA ansatz and only measure the edge qubit on z-basis. |
| 122 | + Args: |
| 123 | + if edge is None |
| 124 | + """ |
| 125 | + qdev = tq.QuantumDevice(n_wires=self.n_wires, device=self.betas.device) |
| 126 | + |
| 127 | + self.circuit(qdev) |
| 128 | + # print(tq.measure(qdev, n_shots=1024)) |
| 129 | + # compute the expectation value |
| 130 | + # print(qdev.get_states_1d()) |
| 131 | + if measure_all is False: |
| 132 | + expVal = 0 |
| 133 | + for edge in self.input_graph: |
| 134 | + pauli_string = self.edge_to_PauliString(edge) |
| 135 | + expv = expval_joint_analytical(qdev, observable=pauli_string) |
| 136 | + expVal += 0.5 * expv |
| 137 | + # print(pauli_string, expv) |
| 138 | + # print(expVal) |
| 139 | + return expVal |
| 140 | + else: |
| 141 | + return tq.measure(qdev, n_shots=1024, draw_id=0) |
| 142 | + |
| 143 | +def main(): |
| 144 | + # create a input_graph |
| 145 | + input_graph = [(0, 1), (0, 3), (1, 2), (2, 3)] |
| 146 | + n_wires = 4 |
| 147 | + n_layers = 3 |
| 148 | + model = MAXCUT(n_wires=n_wires, input_graph=input_graph, n_layers=n_layers) |
| 149 | + # model.to("cuda") |
| 150 | + # model.to(torch.device("cuda")) |
| 151 | + # circ = tq2qiskit(tq.QuantumDevice(n_wires=4), model) |
| 152 | + # print(circ) |
| 153 | + # print("The circuit is", circ.draw(output="mpl")) |
| 154 | + # circ.draw(output="mpl") |
| 155 | + # use backprop |
| 156 | + # backprop_optimize(model, n_steps=300, lr=0.01) |
| 157 | + # use parameter shift rule |
| 158 | + param_shift_optimize(model, n_steps=500, step_size=0.01) |
| 159 | + |
| 160 | +def shift_and_run(model, use_qiskit=False): |
| 161 | + # flatten the parameters into 1D array |
| 162 | + |
| 163 | + grad_betas = [] |
| 164 | + grad_gammas = [] |
| 165 | + n_layers = model.n_layers |
| 166 | + n_wires = model.n_wires |
| 167 | + n_edges = model.n_edges |
| 168 | + |
| 169 | + for i in range(n_layers): |
| 170 | + grad_gamma = 0 |
| 171 | + for k in range(n_edges): |
| 172 | + model.set_shift_param(i, None, 'gamma', np.pi * 0.5, k) |
| 173 | + out1 = model(use_qiskit) |
| 174 | + model.reset_shift_param() |
| 175 | + |
| 176 | + model.set_shift_param(i, None, 'gamma', -np.pi * 0.5, k) |
| 177 | + out2 = model(use_qiskit) |
| 178 | + model.reset_shift_param() |
| 179 | + |
| 180 | + grad_gamma += 0.5 * (out1 - out2).squeeze().item() |
| 181 | + grad_gammas.append(grad_gamma) |
| 182 | + |
| 183 | + grad_beta = 0 |
| 184 | + for j in range(n_wires): |
| 185 | + model.set_shift_param(i, j, 'beta', np.pi * 0.5, None) |
| 186 | + out1 = model(use_qiskit) |
| 187 | + model.reset_shift_param() |
| 188 | + |
| 189 | + model.set_shift_param(i, j, 'beta', -np.pi * 0.5, None) |
| 190 | + out2 = model(use_qiskit) |
| 191 | + model.reset_shift_param() |
| 192 | + |
| 193 | + grad_beta += 0.5 * (out1 - out2).squeeze().item() |
| 194 | + grad_betas.append(grad_beta) |
| 195 | + |
| 196 | + return model(use_qiskit), [grad_betas, grad_gammas] |
| 197 | + |
| 198 | + |
| 199 | +def param_shift_optimize(model, n_steps=10, step_size=0.1): |
| 200 | + """finds the optimal cut where parameter shift rule is used to compute the gradient""" |
| 201 | + # optimize the parameters and return the optimal values |
| 202 | + # print( |
| 203 | + # "The initial parameters are betas = {} and gammas = {}".format( |
| 204 | + # *model.parameters() |
| 205 | + # ) |
| 206 | + # ) |
| 207 | + n_layers = model.n_layers |
| 208 | + for step in range(n_steps): |
| 209 | + with torch.no_grad(): |
| 210 | + loss, grad_list = shift_and_run(model) |
| 211 | + # param_list = list(model.parameters()) |
| 212 | + # print( |
| 213 | + # "The initial parameters are betas = {} and gammas = {}".format( |
| 214 | + # *model.parameters() |
| 215 | + # ) |
| 216 | + # ) |
| 217 | + # param_list = torch.cat([param.flatten() for param in param_list]) |
| 218 | + |
| 219 | + # print("The shape of the params", len(param_list), param_list[0].shape, param_list) |
| 220 | + # print("") |
| 221 | + # print("The shape of the grad_list = {}, 0th elem shape = {}, grad_list = {}".format(len(grad_list), grad_list[0].shape, grad_list)) |
| 222 | + # print(grad_list, loss, model.betas, model.gammas) |
| 223 | + print(loss) |
| 224 | + with torch.no_grad(): |
| 225 | + for i in range(n_layers): |
| 226 | + model.betas[i].copy_(model.betas[i] - step_size * grad_list[0][i]) |
| 227 | + model.gammas[i].copy_(model.gammas[i] - step_size * grad_list[1][i]) |
| 228 | + |
| 229 | + # for param, grad in zip(param_list, grad_list): |
| 230 | + # modify the parameters and ensure that there are no multiple views |
| 231 | + # param.copy_(param - step_size * grad) |
| 232 | + # if step % 5 == 0: |
| 233 | + # print("Step: {}, Cost Objective: {}".format(step, loss.item())) |
| 234 | + |
| 235 | + # print( |
| 236 | + # "The updated parameters are betas = {} and gammas = {}".format( |
| 237 | + # *model.parameters() |
| 238 | + # ) |
| 239 | + # ) |
| 240 | + return model(measure_all=True) |
| 241 | + |
| 242 | +""" |
| 243 | +Notes: |
| 244 | +1. input_graph = [(0, 1), (3, 0), (1, 2), (2, 3)], mixer 1st & entangler 2nd, n_layers >= 2, answer is correct. |
| 245 | +
|
| 246 | +""" |
| 247 | + |
| 248 | +if __name__ == "__main__": |
| 249 | + # import pdb |
| 250 | + # pdb.set_trace() |
| 251 | + |
| 252 | + main() |
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