Source code for

# Copyright 2022 Xanadu Quantum Technologies Inc.

# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at


# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# See the License for the specific language governing permissions and
# limitations under the License.
"""Continuous-variable operations, states, and noise models."""

# pylint: disable=import-outside-toplevel,too-many-instance-attributes

import numpy as np
from scipy.linalg import block_diag
import scipy.sparse as sp
from thewalrus.symplectic import expand, beam_splitter

[docs]def invert_permutation(p): """Invert the permutation associated with p.""" p_inverted = np.empty(p.size, p.dtype) p_inverted[p] = np.arange(p.size) return p_inverted
[docs]def SCZ_mat(adj, sparse=True): """Return a symplectic matrix corresponding to CZ gate application. Give the 2N by 2N symplectic matrix for CZ gate application based on the adjacency matrix adj. Assumes quadrature-like convention: (q1, ..., qN, p_1, ..., p_N). Args: adj (array): N by N binary symmetric matrix. If modes i and j are linked by a CZ, then entry ij and ji is equal to the weight of the edge (1 by default); otherwise 0. sparse (bool): whether to return a sparse or dense array when adj input is a sparse array. Returns: np.array or sp.sparse.csr_matrix: 2N by 2N symplectic matrix. sparse if the adjacency matrix is sparse. """ # Number of modes N = adj.shape[0] if isinstance(adj, np.ndarray): identity = np.eye(N, dtype=np.int8) zeros = np.zeros((N, N), dtype=np.int8) block_func = np.block else: identity = sp.identity(N, dtype=np.int8) zeros = sp.csr_matrix((N, N), dtype=np.int8) block_func = sp.bmat # Construct symplectic symplectic = block_func([[identity, zeros], [adj, identity]]) if not sparse and isinstance(symplectic, sp.coo_matrix): return symplectic.toarray() return symplectic
[docs]def SCZ_apply(adj, quads, one_shot=True): """Apply SCZ matrix to one- or two-dimensional array quads. If one-shot is True, use SCZ_mat to apply a symplectic CZ matrix to a matrix or vector of quadratures. Otherwise, take advantage of the block structure of a symplectic SCZ matrix for a more memory- efficient matrix multiplication. """ N = quads.shape[0] // 2 if len(quads.shape) == 1: if one_shot: new_quads = SCZ_mat(adj).dot(quads) else: old_qs = quads[:N] old_ps = quads[N:] new_quads = np.empty(2 * N, quads.dtype) new_quads[:N] = old_qs new_quads[N:] = + old_ps if len(quads.shape) == 2: if one_shot: SCZ = SCZ_mat(adj) new_quads = else: c1, c2, c3, c4 = quads[:N, :N], quads[:N, N:], quads[N:, :N], quads[N:, N:] block2 = ( + c2 block3 = + c3 block4 = c4 + + ( + new_quads = np.block([[c1, block2], [block3, block4]]) return new_quads
[docs]def splitter_symp(n=4): """Return the symplectic matrix of a four-splitter. Return the symplectic matrix of the beamsplitters connecting the four micronodes in each macronode. `n` refers to the total number of modes (so n >= 4). If n = 4, return the matrix in the 'all q's first' convention; otherwise, return a large block-diagonal matrix in the 'q1p1, ..., qnpn' convention. Args: n (int, optional): the total number of modes on which the beamsplitters apply (n must be >= 4). Returns: numpy.array: the sympletic matrix of the four-splitter. """ # 50/50 beamsplitter in the 'all q's first' convention. bs5050 = beam_splitter(np.pi / 4, 0) bs1 = expand(bs5050, [1, 0], 4) bs2 = expand(bs5050, [3, 2], 4) bs3 = expand(bs5050, [2, 0], 4) bs4 = expand(bs5050, [3, 1], 4) bs_network = (bs4 @ bs3 @ bs2 @ bs1).astype(np.single) if n == 4: return bs_network if n > 4: # Permutation away from 'all q's first' convention for matrices of # with dimension 4 and the network spanning all the macronoes. perm_out_4 = [0, 4, 1, 5, 2, 6, 3, 7] bs_perm = bs_network[:, perm_out_4][perm_out_4, :] # Symplectic corresponding to the beasmplitter network spanning # the whole lattice. bs_full = block_diag(*[bs_perm] * (n // 4)) return bs_full else: print("Total number of modes cannot be less than 4.") raise Exception




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