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parameter_utils.py
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parameter_utils.py
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###############################################################################
# // SPDX-License-Identifier: Apache-2.0
# // Copyright : JP Morgan Chase & Co
###############################################################################
# Utilities for parameter initialization
from __future__ import annotations
import numpy as np
from pathlib import Path
import pandas as pd
from importlib_resources import files
from enum import Enum
from typing import Callable
def from_fourier_basis(u, v):
"""Convert u,v parameterizing QAOA in the Fourier basis
to beta, gamma in standard parameterization
following https://arxiv.org/abs/1812.01041
Parameters
----------
u : list-like
v : list-like
QAOA parameters in Fourier basis
Returns
-------
beta, gamma : np.array
QAOA parameters in standard parameterization
(used e.g. by qaoa_qiskit.py)
"""
assert len(u) == len(v)
p = len(u)
gamma = np.zeros(p)
beta = np.zeros(p)
for i in range(p):
for j in range(p):
gamma[i] += u[j] * np.sin(((j + 1) - 0.5) * ((i + 1) - 0.5) * np.pi / p)
beta[i] += v[j] * np.cos(((j + 1) - 0.5) * ((i + 1) - 0.5) * np.pi / p)
return beta, gamma
def to_fourier_basis(gamma, beta):
"""Convert gamma,beta standard parameterizing QAOA to the Fourier basis
of u, v in standard parameterization
following https://arxiv.org/abs/1812.01041
Parameters
----------
gamma : list-like
beta : list-like
QAOA parameters in standard basis
Returns
-------
u, v : np.array
QAOA parameters in fourier parameterization
(used e.g. by qaoa_qiskit.py)
"""
assert len(gamma) == len(beta)
p = len(gamma)
A = np.zeros((p, p))
B = np.zeros((p, p))
# Build matrix for linear system solving
for i in range(p):
for j in range(p):
A[i][j] = np.sin(((j + 1) - 0.5) * ((i + 1) - 0.5) * np.pi / p)
B[i][j] = np.cos(((j + 1) - 0.5) * ((i + 1) - 0.5) * np.pi / p)
u = np.linalg.solve(A, gamma)
v = np.linalg.solve(B, beta)
if np.allclose(np.dot(A, u), gamma) == True & np.allclose(np.dot(B, v), beta) == True:
return u, v
else:
raise ValueError("Linear solving was incorrect")
def extrapolate_parameters_in_fourier_basis(u, v, p, step_size):
"""Extrapolate the parameters u, v from p to p+step_size
Parameters
----------
u : list-like
v : list-like
QAOA parameters in Fourier basis
p : int
QAOA depth
step_size : int
Target QAOA depth for extrapolation
Returns
-------
u, v : np.array
QAOA parameters in Fourier basis
for depth p+step_size
"""
u_next = np.zeros(p)
v_next = np.zeros(p)
u_next[: p - step_size] = u
v_next[: p - step_size] = v
u_next[p - step_size :] = 0
v_next[p - step_size :] = 0
return u_next, v_next
class QAOAParameterization(Enum):
"""
Enum class to specify the parameterization of the QAOA parameters
"""
THETA = "theta"
GAMMA_BETA = "gamma beta"
FREQ = "freq"
U_V = "u v"
def convert_to_gamma_beta(*args, parameterization: QAOAParameterization | str):
"""
Convert QAOA parameters to gamma, beta parameterization
"""
parameterization = QAOAParameterization(parameterization)
if parameterization == QAOAParameterization.THETA:
assert len(args) == 1, "theta parameterization requires a single argument"
theta = args[0]
p = int(len(theta) / 2)
gamma = theta[:p]
beta = theta[p:]
elif parameterization == QAOAParameterization.FREQ:
assert len(args) == 1, "freq parameterization requires two arguments"
freq = args[0]
p = int(len(freq) / 2)
u = freq[:p]
v = freq[p:]
beta, gamma = from_fourier_basis(u, v)
elif parameterization == QAOAParameterization.GAMMA_BETA:
assert len(args) == 2, "gamma beta parameterization requires two arguments"
gamma, beta = args
elif parameterization == QAOAParameterization.U_V:
assert len(args) == 2, "u v parameterization requires two arguments"
u, v = args
beta, gamma = from_fourier_basis(u, v)
else:
raise ValueError("Invalid parameterization")
return gamma, beta
def get_sk_gamma_beta(p, parameterization: QAOAParameterization | str = "gamma beta"):
"""
Load the look-up table for initial points from
https://arxiv.org/pdf/2110.14206.pdf
"""
if p == 1:
gamma = np.array([0.5])
beta = np.array([np.pi / 8])
elif p == 2:
gamma = np.array([0.3817, 0.6655])
beta = np.array([0.4960, 0.2690])
elif p == 3:
gamma = np.array([0.3297, 0.5688, 0.6406])
beta = np.array([0.5500, 0.3675, 0.2109])
elif p == 4:
gamma = np.array([0.2949, 0.5144, 0.5586, 0.6429])
beta = np.array([0.5710, 0.4176, 0.3028, 0.1729])
elif p == 5:
gamma = np.array([0.2705, 0.4804, 0.5074, 0.5646, 0.6397])
beta = np.array([0.5899, 0.4492, 0.3559, 0.2643, 0.1486])
elif p == 6:
gamma = np.array([0.2528, 0.4531, 0.4750, 0.5146, 0.5650, 0.6392])
beta = np.array([0.6004, 0.4670, 0.3880, 0.3176, 0.2325, 0.1291])
elif p == 7:
gamma = np.array([0.2383, 0.4327, 0.4516, 0.4830, 0.5147, 0.5686, 0.6393])
beta = np.array([0.6085, 0.4810, 0.4090, 0.3534, 0.2857, 0.2080, 0.1146])
elif p == 8:
gamma = np.array([0.2268, 0.4162, 0.4332, 0.4608, 0.4818, 0.5179, 0.5717, 0.6393])
beta = np.array([0.6151, 0.4906, 0.4244, 0.3780, 0.3224, 0.2606, 0.1884, 0.1030])
elif p == 9:
gamma = np.array([0.2172, 0.4020, 0.4187, 0.4438, 0.4592, 0.4838, 0.5212, 0.5754, 0.6398])
beta = np.array([0.6196, 0.4973, 0.4354, 0.3956, 0.3481, 0.2973, 0.2390, 0.1717, 0.0934])
elif p == 10:
gamma = np.array([0.2089, 0.3902, 0.4066, 0.4305, 0.4423, 0.4604, 0.4858, 0.5256, 0.5789, 0.6402])
beta = np.array([0.6235, 0.5029, 0.4437, 0.4092, 0.3673, 0.3246, 0.2758, 0.2208, 0.1578, 0.0855])
elif p == 11:
gamma = np.array([0.2019, 0.3799, 0.3963, 0.4196, 0.4291, 0.4431, 0.4611, 0.4895, 0.5299, 0.5821, 0.6406])
beta = np.array([0.6268, 0.5070, 0.4502, 0.4195, 0.3822, 0.3451, 0.3036, 0.2571, 0.2051, 0.1459, 0.0788])
elif p == 12:
gamma = np.array([0.1958, 0.3708, 0.3875, 0.4103, 0.4185, 0.4297, 0.4430, 0.4639, 0.4933, 0.5343, 0.5851, 0.6410])
beta = np.array([0.6293, 0.5103, 0.4553, 0.4275, 0.3937, 0.3612, 0.3248, 0.2849, 0.2406, 0.1913, 0.1356, 0.0731])
elif p == 13:
gamma = np.array([0.1903, 0.3627, 0.3797, 0.4024, 0.4096, 0.4191, 0.4290, 0.4450, 0.4668, 0.4975, 0.5385, 0.5878, 0.6414])
beta = np.array([0.6315, 0.5130, 0.4593, 0.4340, 0.4028, 0.3740, 0.3417, 0.3068, 0.2684, 0.2260, 0.1792, 0.1266, 0.0681])
elif p == 14:
gamma = np.array([0.1855, 0.3555, 0.3728, 0.3954, 0.4020, 0.4103, 0.4179, 0.4304, 0.4471, 0.4703, 0.5017, 0.5425, 0.5902, 0.6418])
beta = np.array([0.6334, 0.5152, 0.4627, 0.4392, 0.4103, 0.3843, 0.3554, 0.3243, 0.2906, 0.2535, 0.2131, 0.1685, 0.1188, 0.0638])
elif p == 15:
gamma = np.array([0.1811, 0.3489, 0.3667, 0.3893, 0.3954, 0.4028, 0.4088, 0.4189, 0.4318, 0.4501, 0.4740, 0.5058, 0.5462, 0.5924, 0.6422])
beta = np.array([0.6349, 0.5169, 0.4655, 0.4434, 0.4163, 0.3927, 0.3664, 0.3387, 0.3086, 0.2758, 0.2402, 0.2015, 0.1589, 0.1118, 0.0600])
elif p == 16:
gamma = np.array([0.1771, 0.3430, 0.3612, 0.3838, 0.3896, 0.3964, 0.4011, 0.4095, 0.4197, 0.4343, 0.4532, 0.4778, 0.5099, 0.5497, 0.5944, 0.6425])
beta = np.array([0.6363, 0.5184, 0.4678, 0.4469, 0.4213, 0.3996, 0.3756, 0.3505, 0.3234, 0.2940, 0.2624, 0.2281, 0.1910, 0.1504, 0.1056, 0.0566])
elif p == 17:
gamma = np.array(
[0.1735, 0.3376, 0.3562, 0.3789, 0.3844, 0.3907, 0.3946, 0.4016, 0.4099, 0.4217, 0.4370, 0.4565, 0.4816, 0.5138, 0.5530, 0.5962, 0.6429]
)
beta = np.array(
[0.6375, 0.5197, 0.4697, 0.4499, 0.4255, 0.4054, 0.3832, 0.3603, 0.3358, 0.3092, 0.2807, 0.2501, 0.2171, 0.1816, 0.1426, 0.1001, 0.0536]
)
else:
raise ValueError(f"p={p} not supported, try lower p")
parameterization = QAOAParameterization(parameterization)
if parameterization == QAOAParameterization.THETA:
return np.concatenate((4 * gamma, beta), axis=0)
elif parameterization == QAOAParameterization.GAMMA_BETA:
return 4 * gamma, beta
def get_fixed_gamma_beta(d, p, return_AR=False):
"""
Returns the parameters for QAOA for MaxCut on regular graphs from arXiv:2107.00677
Parameters
----------
d : int
Degree of the graph
p : int
QAOA depth
return_AR : bool
return the guaranteed approximation ratio
Returns
-------
gamma, beta : (list, list)
Parameters as two separate lists in a tuple
AR : float
Only returned is flag return_AR is raised
"""
df = pd.read_json(str(files("qokit.assets.maxcut_datasets").joinpath("fixed_angles_for_regular_graphs.json")), orient="index")
row = df[(df["d"] == d) & (df["p"] == p)]
if len(row) != 1:
raise ValueError(f"Failed to retrieve fixed angles for d={d}, p={p}")
row = row.squeeze()
if return_AR:
return row["gamma"], row["beta"], row["AR"]
else:
return row["gamma"], row["beta"]
def get_best_known_parameters_for_LABS_wrt_overlap(N: int) -> pd.DataFrame:
"""
Loads best known LABS QAOA parameters with respect to overlap with ground state.
Note that these parameters may be different from optimal
parameters w.r.t expectation value of the cost hamiltonian.
The scaling of parameters with N is taken from arXiv:1411.4028.
Parameters
----------
N : int
Number of qubits
Returns
-------
df : pd.DataFrame DataFrame with all known values
"""
df = pd.read_json(str(files("qokit.assets").joinpath("best_LABS_QAOA_parameters_wrt_overlap.json")), orient="index")
df = df[df["N"] == N]
return df
def get_best_known_parameters_for_LABS_wrt_overlap_for_p(N: int, p: int) -> tuple[list[float], list[float]]:
"""
Loads best known LABS QAOA parameters with respect to overlap with ground state.
Note that these parameters may be different from optimal
parameters w.r.t expectation value of the cost hamiltonian.
Parameters
----------
N : int
Number of qubits.
p : int
Number of QAOA layers.
Returns
-------
gamma, beta : list[float] QAOA parameters for fixed p if specified
"""
df = get_best_known_parameters_for_LABS_wrt_overlap(N)
if p > int(df["p"].max()):
raise ValueError(f"QAOA values for p={p} is not known for N={N}")
row = df[df["p"] == p].squeeze()
gamma = [float(x) for x in row["gamma"]]
beta = [float(x) for x in row["beta"]]
return gamma, beta