def solve_model(expression):
# 制約もつけられる
model = IsingQuadraticModel(*expression)
solver = Solver(client)
result = solver.solve(model)
print("energy: ", result[0].energy)
# print("time(ms): ", solver.client_result.annealing_time_ms)
return result[0].values
def by_amplify(qubits, model, token, timeout=5000):
client = FixstarsClient()
client.token = token
client.parameters.timeout = timeout
solver = Solver(client)
solver.filter_solution = False
result = solver.solve(model)
values = result[0].values
q_values = decode_solution(qubits, values, 1)
return np.where(np.array(q_values) == 1)[1]
def solve(self):
q = gen_symbols(BinaryPoly, *self.board.get_size(), len(self.pieces),
8)
# 制約(a) 重複する置き方のピースは除外する
for y in range(self.board.get_size()[0]):
for x in range(self.board.get_size()[1]):
for i in range(len(self.pieces)):
for j in range(self.pieces[i].placement_count, 8):
q[y][x][i][j] = BinaryPoly(0)
# 制約(b) ピースはボードから外に出ない
for y in range(self.board.get_size()[0]):
for x in range(self.board.get_size()[1]):
for i in range(len(self.pieces)):
for j in range(self.pieces[i].placement_count):
if len(self.pieces[i].get_blocks(j, (x, y)) -
self.board.get_blocks()) > 0:
q[y][x][i][j] = BinaryPoly(0)
# 制約(c) ピース同士は重ならずボードを全て埋める
s = dict()
for b in self.board.get_blocks():
s[b] = BinaryPoly()
for y in range(self.board.get_size()[0]):
for x in range(self.board.get_size()[1]):
for i in range(len(self.pieces)):
for j in range(self.pieces[i].placement_count):
for p in self.pieces[i].get_blocks(
j, (x, y)) & self.board.get_blocks():
s[p] += q[y][x][i][j]
board_constraints = [equal_to(q, 1) for q in s.values()]
# 制約(d) 全てのピースは一度ずつ使われる
piece_constraints = [
equal_to(
sum(q[y][x][i][j] for y in range(self.board.get_size()[0])
for x in range(self.board.get_size()[1])
for j in range(8)), 1) for i in range(len(self.pieces))
]
constraints = (sum(board_constraints) + sum(piece_constraints))
solver = Solver(self.client)
model = BinaryQuadraticModel(constraints)
result = solver.solve(model)
if len(result) == 0:
raise RuntimeError("Any one of constaraints is not satisfied.")
solution = result[0]
values = solution.values
q_values = decode_solution(q, values)
Visualizer().visualize(self.pieces, self.board, q_values)
def solve_problem(model):
# set client and parameters
client = FixstarsClient()
client.token = "lJLkgFpKzukTUGnr8F3tjrPJZlO8N0bX"
client.parameters.timeout = 5000
# set solver
solver = Solver(client)
# get result
result = solver.solve(model)
# extract value of objective function and binary variables
obj, values = result[0].energy, result[0].values
# get values of constraints
broken = model.check_constraints(values)
return obj, values, broken
def solve(self,
c_weight: float = 3,
timeout: int = 1000,
num_unit_step: int = 10) -> Setlist:
"""
Args:
c_weight (float): 時間制約の強さ
timeout (int, optional): Fixstars AE のタイムアウト[ms] (デフォルト: 10000)
num_unit_step (int, optional): Fixstars AE のステップ数 (デフォルト: 10)
Returns:
Setlist: セットリスト
"""
self.q = gen_symbols(BinaryPoly, self.num_tracks)
energy_function = self.energy(c_weight)
model = BinaryQuadraticModel(energy_function)
fixstars_client = FixstarsClient()
fixstars_client.token = os.environ.get("FIXSTARS_API_TOKEN")
fixstars_client.parameters.timeout = timeout
fixstars_client.parameters.num_unit_steps = num_unit_step
amplify_solver = Solver(fixstars_client)
amplify_solver.filter_solution = False
result = amplify_solver.solve(model)
q_values = decode_solution(self.q, result[0].values)
tracks = [self.candidates[i] for i, v in enumerate(q_values) if v == 1]
total_time = 0
user_scores = np.zeros(self.num_users)
for track in tracks:
user_scores += np.array(track.p)
total_time += track.duration_ms
return Setlist(tracks=tracks,
scores=user_scores.tolist(),
score_sum=user_scores.sum(),
score_avg=user_scores.mean(),
score_var=user_scores.var(),
total_time=total_time)
# クライアント設定
client = HitachiClient()
client.token = get_token()
client.parameters.num_executions = 1
client.parameters.outputs.energies = False
client.parameters.outputs.spins = True
client.parameters.outputs.execution_time = False
client.parameters.outputs.num_outputs = 1
client.parameters.temperature_num_steps = 10
client.parameters.temperature_step_length = 100
client.parameters.temperature_initial = 100.0
client.parameters.temperature_target = 0.02
# ソルバー生成
solver = Solver(client)
# 重み変更してアニーリング実行
w_step = 0.1 # 重み変更幅
num_steps = 10 # 重み変更回数
num_execution = 100 # アニーリング実行回数
print('N, w_a, w_b, optimal_answer_percentage[%], time[s]')
# 結果出力用ファイルを開く
f = open('result_{0}.txt'.format(N), 'w')
for i in range(1, num_steps + 1):
w_a = i * w_step
for j in range(1, num_steps + 1):
w_b = j * w_step
# 最終的なエネルギー関数
# len(A): 変数の数
n = len(A)
# イジング変数を生成
s = gen_symbols(IsingPoly, n)
# 目的関数の構築: イジング
f = IsingPoly()
for i in range(n):
f += s[i] * A[i]
f = f ** 2
# ソルバーの構築
solver = Solver(client)
# 問題を入力してマシンを実行
result = solver.solve(f)
# 解が得られなかった場合、len(result) == 0
if len(result) == 0:
raise RuntimeError("No solution was found")
print("Number of results = ",len(result))
energy = result[0].energy
values = result[0].values
partitions = set()
decode_solution,
)
from amplify.constraint import (
equal_to,
penalty,
)
from amplify.client import FixstarsClient
import numpy as np
import japanmap as jm
import matplotlib.pyplot as plt
client = FixstarsClient()
client.token = "i5G6Ei3DKlGv2n6hsWBSBzWrmffLN4vn" #20210011まで有効
client.parameters.timeout = 5000 # タイムアウト5秒
solver = Solver(client)
# 四色の定義
colors = ["red", "green", "blue", "yellow"]
num_colors = len(colors)
num_region = len(jm.pref_names) - 1 # 都道府県数を取得
# 都道府県数 x 色数 の変数を作成
q = gen_symbols(BinaryPoly, num_region, num_colors)
# 各領域に対する制約
# 一つの領域に一色のみ（one-hot）
# sum_{c=0}^{C-1} q_{i,c} = 1 for all i
reg_constraints = [
equal_to(sum_poly([q[i][c] for c in range(num_colors)]), 1)
for i in range(num_region)
def quantum_solver_approx(N, M,
query): # solve with Amplify (approximate version)
q = gen_symbols(BinaryPoly, M, N, N) # represent the solution
########## constraints ##########
# each layer doesn't have 2+ same values
one_hot_constraints_layer = [
# m -> layer
# n -> qubit
# v -> value of qubit
equal_to(sum(q[m][n][v] for n in range(N)), 1) for m in range(M)
for v in range(N)
]
# each qubit doesn't have 2+ values
one_hot_constraints_num = [
# m -> layer
# n -> qubit
# v -> value of qubit
equal_to(sum(q[m][n][v] for v in range(N)), 1) for m in range(M)
for n in range(N)
]
# every CX gate must be applied for 2 adjacent qubits
CXgate_constraints = []
for m in range(M):
for g0 in range(0, len(query[m]), 2):
v0, v1 = query[m][g0], query[m][g0 + 1]
# v0 and v1 must be adjacent each other
for i in range(N):
for j in range(i + 2, N):
CXgate_constraints.append(
penalty(q[m][i][v0] * q[m][j][v1]))
CXgate_constraints.append(
penalty(q[m][i][v1] * q[m][j][v0]))
constraints = (sum(one_hot_constraints_layer) +
sum(one_hot_constraints_num) + sum(CXgate_constraints))
cost = sum_poly(
M - 1, lambda m: sum_poly(
N, lambda i: sum_poly(
N, lambda j: sum_poly(N, lambda v: q[m][i][v] * q[m + 1][j][v])
* ((N - 1) * (i + j) - 2 * i * j) / N)))
########## solve ##########
solver = Solver(client)
model = BinaryQuadraticModel(constraints * constraintWeight + cost)
result = solver.solve(model)
if len(result) == 0:
raise RuntimeError("Any one of constraints is not satisfied.")
values = result[0].values
q_values = decode_solution(q, values, 1)
# print(q_values_main)
########## decode the result into string ##########
ans = [[-1 for n in range(N)] for m in range(M)]
for m in range(M):
for n in range(N):
for v in range(N):
if (q_values[m][n][v] > 0.5):
ans[m][n] = v
cost = 0
for m in range(M - 1):
cost += calcCost(ans[m], ans[m + 1])
return cost, ans
def quantum_solver_strict(N, M, query): # solve by Amplify (strict version)
q_all = gen_symbols(BinaryPoly,
M * N * N + (M - 1) * N * N * N + (M - 1) * N * N)
q = q_all[:M * N * N] # represent the solution
q_sub = q_all[M * N * N:M * N * N + (M - 1) * N * N *
N] # q_sub[m][i][j][v] = q[m][i][v] * q[m+1][j][v]
q_C_matrix = q_all[
M * N * N + (M - 1) * N * N *
N:] # q_C_matrix[m][i][j] = sum(q_sub[m][i][j][v] for v)
########## constraints ##########
# each layer doesn't have 2+ same values
one_hot_constraints_layer = [
# m -> layer
# n -> physical qubit
# v -> logical qubit
equal_to(sum(q[(m * N + n) * N + v] for n in range(N)), 1)
for m in range(M) for v in range(N)
]
# each qubit doesn't have 2+ values
one_hot_constraints_num = [
# m -> layer
# n -> physical qubit
# v -> logical qubit
equal_to(sum(q[(m * N + n) * N + v] for v in range(N)), 1)
for m in range(M) for n in range(N)
]
# every CX gate must be applied for 2 adjacent qubits
CXgate_constraints = []
for m in range(M):
for g0 in range(0, len(query[m]), 2):
v0, v1 = query[m][g0], query[m][g0 + 1]
# v0 and v1 must be adjacent each other
for i in range(N):
for j in range(i + 2, N):
CXgate_constraints.append(
penalty(q[(m * N + i) * N + v0] *
q[(m * N + j) * N + v1]))
CXgate_constraints.append(
penalty(q[(m * N + i) * N + v1] *
q[(m * N + j) * N + v0]))
# q_sub[m][i][j][v] = q[m][i][v] * q[m+1][j][v]
sub_gate_constraints = []
for _idx in range((M - 1) * N**3):
idx = _idx
m = idx // (N**3)
idx %= N**3
i = idx // (N**2)
idx %= N**2
j = idx // N
idx %= N
v = idx
sub_gate_constraints.append(
penalty(3 * q_sub[((m * N + i) * N + j) * N + v] +
q[(m * N + i) * N + v] * q[((m + 1) * N + j) * N + v] -
2 * q_sub[((m * N + i) * N + j) * N + v] *
(q[(m * N + i) * N + v] + q[((m + 1) * N + j) * N + v])))
# q_C_matrix[m][i][j] = sum(q_sub[m][i][j][v] for v)
C_matrix_sum_constraints = []
for _idx in range((M - 1) * N**2):
idx = _idx
m = idx // (N**2)
idx %= N**2
i = idx // N
idx %= N
j = idx
C_matrix_sum_constraints.append(
equal_to(
q_C_matrix[(m * N + i) * N + j] -
sum(q_sub[((m * N + i) * N + j) * N + v] for v in range(N)),
0))
constraints = (sum(one_hot_constraints_layer) +
sum(one_hot_constraints_num) + sum(CXgate_constraints) +
sum(sub_gate_constraints) + sum(C_matrix_sum_constraints))
cost = []
for m in range(M - 1):
for i1 in range(N):
for j1 in range(i1): # i1 > j1
for i2 in range(N):
for j2 in range(i2 + 1, N): # i2 < j2
cost.append(q_C_matrix[(m * N + i1) * N + j1] *
q_C_matrix[(m * N + i2) * N + j2])
for j1 in range(i1 + 1, N): # i1 < j1
for i2 in range(N):
for j2 in range(i2): # i2 > j2
cost.append(q_C_matrix[(m * N + i1) * N + j1] *
q_C_matrix[(m * N + i2) * N + j2])
# print(constraints)
# print(cost)
########## solve ##########
solver = Solver(client)
model = BinaryQuadraticModel(constraints * constraintWeight + sum(cost))
result = solver.solve(model)
if len(result) == 0:
raise RuntimeError("Any one of constraints is not satisfied.")
values = result[0].values
q_values = decode_solution(q_all, values, 1)
# print(q_values_main)
########## decode the result into string ##########
ans = [[-1 for n in range(N)] for m in range(M)]
for m in range(M):
for n in range(N):
for v in range(N):
if (q_values[(m * N + n) * N + v] > 0.5):
ans[m][n] = v
cost = 0
for m in range(M - 1):
cost += calcCost(ans[m], ans[m + 1])
return cost, ans
# len(A): 変数の数
n = len(A)
# Isinbg 変数を生成
s = gen_symbols(IsingPoly, n)
# 目的関数の構築
f = IsingPoly()
for i in range(n):
f += s[i] * A[i]
f = f**2
# ソルバーの構築
solver = Solver(client) # ソルバーに使用するクライアントを設定
# 問題を入力してマシンを実行
result = solver.solve(f) # 問題を入力してマシンを実行
# 解が得られなかった場合、len(result) == 0
if len(result) == 0:
raise RuntimeError("No solution was found")
partitions = set()
for sol in result:
solution = decode_solution(s, sol.values)
A0 = tuple(sorted([A[idx] for idx, val in enumerate(solution)
if val != 1]))
from amplify import BinaryPoly, Solver, sum_poly, gen_symbols, decode_solution
from amplify.constraint import clamp, equal_to, greater_equal, less_equal, penalty
from amplify.client import FixstarsClient
# クライアントの設定
client = FixstarsClient() # Fixstars Optigan
client.parameters.timeout = 1000 # タイムアウト1秒
client.token = "i5G6Ei3DKlGv2n6hsWBSBzWrmffLN4vn" #20210011まで有効
client.parameters.outputs.duplicate = True # 同じエネルギー値の解を列挙するオプション
client.parameters.outputs.num_outputs = 0 # 見つかったすべての解を出力
# ソルバーの構築
solver = Solver(client) # ソルバーに使用するクライアントを設定
# バイナリ変数：要素数2
q = gen_symbols(BinaryPoly, 2)
###########################################################
# NAND制約を与える多項式
g_NAND = q[0] * q[1]
# NAND制約をペナルティ制約条件に変換
p_NAND = penalty(g_NAND)
print("NAND")
print(f"p_NAND = {p_NAND}")
# 制約条件を満たす解を求める
result = solver.solve(p_NAND)
for sol in result:
energy = sol.energy