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############################ | ||
# define spin Hamiltonians | ||
############################ | ||
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import numpy as np | ||
from qiskit.quantum_info import SparsePauliOp | ||
import random | ||
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class Nearest_Neighbour_1d: | ||
def __init__(self, n: int, Jx=1, Jy=1, Jz=1, hx=0.2, hy=0, hz=0, pbc=False, verbose=False, rand_field=[]): | ||
self.n = n | ||
self.xx_tuples = [('XX', [i, i + 1], Jx) for i in range(0, n-1)] | ||
self.yy_tuples = [('YY', [i, i + 1], Jy) for i in range(0, n-1)] | ||
self.zz_tuples = [('ZZ', [i, i + 1], Jz) for i in range(0, n-1)] | ||
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if len(rand_field) == 0: | ||
self.rand_field = [0]*n | ||
elif len(rand_field) >= n: | ||
self.rand_field = rand_field[:n] | ||
else: | ||
raise ValueError(f'Length of random field should be at least {n}!') | ||
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self.x_tuples = [('X', [i], (self.rand_field[i]+1)*hx) for i in range(0, n)] | ||
self.y_tuples = [('Y', [i], (self.rand_field[i]+1)*hy) for i in range(0, n)] | ||
self.z_tuples = [('Z', [i], (self.rand_field[i]+1)*hz) for i in range(0, n)] | ||
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if pbc: | ||
self.xx_tuples.append(('XX', [n-1, 0], Jx)) | ||
self.yy_tuples.append(('YY', [n-1, 0], Jy)) | ||
self.zz_tuples.append(('ZZ', [n-1, 0], Jz)) | ||
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self.ham = SparsePauliOp.from_sparse_list([*self.xx_tuples, *self.yy_tuples, *self.zz_tuples, *self.x_tuples, *self.y_tuples, *self.z_tuples], num_qubits=n).simplify() | ||
self.xyz_group() | ||
self.par_group() | ||
if verbose: | ||
print('The Hamiltonian: \n', self.ham) | ||
print('The xyz grouping: \n', self.ham_xyz) | ||
print('The parity grouping: \n', self.ham_par) | ||
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def xyz_group(self): | ||
self.x_terms = SparsePauliOp.from_sparse_list([*self.xx_tuples, *self.x_tuples], num_qubits=self.n).simplify() | ||
self.y_terms = SparsePauliOp.from_sparse_list([*self.yy_tuples, *self.y_tuples], num_qubits=self.n).simplify() | ||
self.z_terms = SparsePauliOp.from_sparse_list([*self.zz_tuples, *self.z_tuples], num_qubits=self.n).simplify() | ||
self.ham_xyz = [self.x_terms, self.y_terms, self.z_terms] | ||
self.ham_xyz = [item for item in self.ham_xyz if not np.all(abs(item.coeffs) == 0)] | ||
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def par_group(self): | ||
self.even_terms = SparsePauliOp.from_sparse_list([*self.xx_tuples[::2], *self.yy_tuples[::2], *self.zz_tuples[::2], *self.x_tuples[::2], *self.y_tuples[::2], *self.z_tuples[::2]], num_qubits=self.n).simplify() | ||
self.odd_terms = SparsePauliOp.from_sparse_list([*self.xx_tuples[1::2], *self.yy_tuples[1::2], *self.zz_tuples[1::2], *self.x_tuples[1::2], *self.y_tuples[1::2], *self.z_tuples[1::2]], num_qubits=self.n).simplify() | ||
self.ham_par = [self.even_terms, self.odd_terms] | ||
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# def lc_group(self, right, left, step): | ||
# self.ham_lc = [] | ||
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class Power_Law: | ||
def __init__(self, n: int, alpha=4, Jx=1, Jy=1, Jz=1, hx=0.0, hy=0.0, hz=0.2, pbc=False, verbose=False): | ||
self.n, self.alpha = n, alpha | ||
self.xx_tuples = [('XX', [i, j], Jx*abs(i-j)**(-alpha)) for i in range(0, n-1) for j in range(i+1, n)] | ||
self.yy_tuples = [('YY', [i, j], Jy*abs(i-j)**(-alpha)) for i in range(0, n-1) for j in range(i+1, n)] | ||
self.zz_tuples = [('ZZ', [i, j], Jz*abs(i-j)**(-alpha)) for i in range(0, n-1) for j in range(i+1, n)] | ||
self.x_tuples = [('X', [i], hx) for i in range(0, n)] | ||
self.y_tuples = [('Y', [i], hy) for i in range(0, n)] | ||
self.z_tuples = [('Z', [i], hz) for i in range(0, n)] | ||
if pbc: | ||
# self.xx_tuples.append(('XX', [n-1, 0], Jx)) | ||
# self.yy_tuples.append(('YY', [n-1, 0], Jy)) | ||
# self.zz_tuples.append(('ZZ', [n-1, 0], Jz)) | ||
raise ValueError(f'PBC is not defined!') | ||
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self.ham = SparsePauliOp.from_sparse_list([*self.xx_tuples, *self.yy_tuples, *self.zz_tuples, *self.x_tuples, *self.y_tuples, *self.z_tuples], num_qubits=n).simplify() | ||
if verbose: print('The Hamiltonian: \n', self.ham) | ||
self.xyz_group() | ||
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def xyz_group(self): | ||
self.x_terms = SparsePauliOp.from_sparse_list([*self.xx_tuples, *self.x_tuples], self.n).simplify() | ||
self.y_terms = SparsePauliOp.from_sparse_list([*self.yy_tuples, *self.y_tuples], self.n).simplify() | ||
self.z_terms = SparsePauliOp.from_sparse_list([*self.zz_tuples, *self.z_tuples], self.n).simplify() | ||
self.ham_xyz = [self.x_terms, self.y_terms, self.z_terms] | ||
self.ham_xyz = [item for item in self.ham_xyz if not np.all(abs(item.coeffs) == 0)] | ||
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# def parity_group(self): | ||
# print('todo') | ||
# return self.ham.to_matrix().todense() | ||
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# class TF_Ising_1d: | ||
# def __init__(self, n: int, J=1, h=0.2, g=0.0, pbc=False, verbose=False): | ||
# self.n = n | ||
# self.zz_tuples = [('ZZ', [i, i + 1], -J) for i in range(0, n-1)] | ||
# self.x_tuples = [('X', [i], -h) for i in range(0, n)] | ||
# self.z_tuples = [('Z', [i], -g) for i in range(0, n)] | ||
# if pbc: self.zz_tuples.append(('ZZ', [n-1, 0], -J)) | ||
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# self.ham = SparsePauliOp.from_sparse_list([*self.zz_tuples, *self.x_tuples, *self.z_tuples], num_qubits=n).simplify() | ||
# if verbose: print('The Hamiltonian: \n', self.ham) | ||
# self.parity_group() | ||
# self.xyz_group() | ||
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# def parity_group(self): | ||
# # return self.ham.to_matrix().todense() | ||
# self.ham_parity = [SparsePauliOp.from_sparse_list([*self.zz_tuples[::2], *self.x_tuples[::2], *self.z_tuples[::2]], num_qubits=self.n).simplify(), SparsePauliOp.from_sparse_list([*self.zz_tuples[1::2], *self.x_tuples[1::2], *self.z_tuples[1::2]], num_qubits=self.n).simplify()] | ||
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# def xyz_group(self): | ||
# self.ham_xyz = [SparsePauliOp.from_sparse_list([*self.zz_tuples, *self.z_tuples], num_qubits=self.n).simplify(), SparsePauliOp.from_sparse_list([*self.x_tuples], num_qubits=self.n)] | ||
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# class Heisenberg_1d: | ||
# def __init__(self, n: int, Jx=1, Jy=1, Jz=1, h=0.2, pbc=False, verbose=False): | ||
# self.xx_tuples = [('XX', [i, i + 1], -Jx) for i in range(0, n-1)] | ||
# self.yy_tuples = [('YY', [i, i + 1], -Jy) for i in range(0, n-1)] | ||
# self.zz_tuples = [('ZZ', [i, i + 1], -Jz) for i in range(0, n-1)] | ||
# self.x_tuples = [('X', [i], -h) for i in range(0, n)] | ||
# if pbc: | ||
# self.xx_tuples.append(('XX', [n-1, 0], -Jx)) | ||
# self.yy_tuples.append(('YY', [n-1, 0], -Jy)) | ||
# self.zz_tuples.append(('ZZ', [n-1, 0], -Jz)) | ||
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# self.ham = SparsePauliOp.from_sparse_list([*self.xx_tuples, *self.yy_tuples, *self.zz_tuples, *self.x_tuples], num_qubits=n) | ||
# if verbose: print('The Hamiltonian: \n', self.ham) | ||
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# def parity_group(self): | ||
# print('todo') | ||
# return self.ham.to_matrix().todense() |
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