Python Qobj.permute方法代码示例

# 需要导入模块: from qutip.qobj import Qobj [as 别名]
# 或者: from qutip.qobj.Qobj import permute [as 别名]
def rand_super_bcsz(N=2, enforce_tp=True, rank=None, dims=None):
    """
    Returns a random superoperator drawn from the Bruzda
    et al ensemble for CPTP maps [BCSZ08]_. Note that due to
    finite numerical precision, for ranks less than full-rank,
    zero eigenvalues may become slightly negative, such that the
    returned operator is not actually completely positive.


    Parameters
    ----------
    N : int
        Square root of the dimension of the superoperator to be returned.
    enforce_tp : bool
        If True, the trace-preserving condition of [BCSZ08]_ is enforced;
        otherwise only complete positivity is enforced.
    rank : int or None
        Rank of the sampled superoperator. If None, a full-rank
        superoperator is generated.
    dims : list
        Dimensions of quantum object.  Used for specifying
        tensor structure. Default is dims=[[[N],[N]], [[N],[N]]].

    Returns
    -------
    rho : Qobj
        A superoperator acting on vectorized dim × dim density operators,
        sampled from the BCSZ distribution.
    """
    if dims is not None:
        # TODO: check!
        pass
    else:
        dims = [[[N], [N]], [[N], [N]]]

    if rank is None:
        rank = N ** 2
    if rank > N ** 2:
        raise ValueError("Rank cannot exceed superoperator dimension.")

    # We use mainly dense matrices here for speed in low
    # dimensions. In the future, it would likely be better to switch off
    # between sparse and dense matrices as the dimension grows.

    # We start with a Ginibre uniform matrix X of the appropriate rank,
    # and use it to construct a positive semidefinite matrix X X⁺.
    X = randnz((N ** 2, rank), norm="ginibre")

    # Precompute X X⁺, as we'll need it in two different places.
    XXdag = np.dot(X, X.T.conj())

    if enforce_tp:
        # We do the partial trace over the first index by using dense reshape
        # operations, so that we can avoid bouncing to a sparse representation
        # and back.
        Y = np.einsum("ijik->jk", XXdag.reshape((N, N, N, N)))

        # Now we have the matrix 𝟙 ⊗ Y^{-1/2}, which we can find by doing
        # the square root and the inverse separately. As a possible improvement,
        # iterative methods exist to find inverse square root matrices directly,
        # as this is important in statistics.
        Z = np.kron(np.eye(N), sqrtm(la.inv(Y)))

        # Finally, we dot everything together and pack it into a Qobj,
        # marking the dimensions as that of a type=super (that is,
        # with left and right compound indices, each representing
        # left and right indices on the underlying Hilbert space).
        D = Qobj(np.dot(Z, np.dot(XXdag, Z)))
    else:
        D = N * Qobj(XXdag / np.trace(XXdag))

    D.dims = [
        # Left dims
        [[N], [N]],
        # Right dims
        [[N], [N]],
    ]

    # Since [BCSZ08] gives a row-stacking Choi matrix, but QuTiP
    # expects a column-stacking Choi matrix, we must permute the indices.
    D = D.permute([[1], [0]])

    D.dims = dims

    # Mark that we've made a Choi matrix.
    D.superrep = "choi"

    return sr.to_super(D)