Python Qobj.superrep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 superrep [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)

# 需要导入模块: from qutip.qobj import Qobj [as 别名]
# 或者: from qutip.qobj.Qobj import superrep [as 别名]
def liouvillian(H, c_ops=[], data_only=False, chi=None):
    """Assembles the Liouvillian superoperator from a Hamiltonian
    and a ``list`` of collapse operators. Like liouvillian, but with an
    experimental implementation which avoids creating extra Qobj instances,
    which can be advantageous for large systems.

    Parameters
    ----------
    H : qobj
        System Hamiltonian.

    c_ops : array_like
        A ``list`` or ``array`` of collapse operators.

    Returns
    -------
    L : qobj
        Liouvillian superoperator.

    """

    if chi and len(chi) != len(c_ops):
        raise ValueError('chi must be a list with same length as c_ops')

    if H is not None:
        if H.isoper:
            op_dims = H.dims
            op_shape = H.shape
        elif H.issuper:
            op_dims = H.dims[0]
            op_shape = [np.prod(op_dims[0]), np.prod(op_dims[0])]
        else:
            raise TypeError("Invalid type for Hamiltonian.")
    else:
        # no hamiltonian given, pick system size from a collapse operator
        if isinstance(c_ops, list) and len(c_ops) > 0:
            c = c_ops[0]
            if c.isoper:
                op_dims = c.dims
                op_shape = c.shape
            elif c.issuper:
                op_dims = c.dims[0]
                op_shape = [np.prod(op_dims[0]), np.prod(op_dims[0])]
            else:
                raise TypeError("Invalid type for collapse operator.")
        else:
            raise TypeError("Either H or c_ops must be given.")

    sop_dims = [[op_dims[0], op_dims[0]], [op_dims[1], op_dims[1]]]
    sop_shape = [np.prod(op_dims), np.prod(op_dims)]

    spI = sp.identity(op_shape[0], format='csr')

    if H:
        if H.isoper:
            data = -1j * (sp.kron(spI, H.data, format='csr')
                          - sp.kron(H.data.T, spI, format='csr'))
        else:
            data = H.data
    else:
        data = sp.csr_matrix((sop_shape[0], sop_shape[1]), dtype=complex)

    for idx, c_op in enumerate(c_ops):
        if c_op.issuper:
            data = data + c_op.data
        else:
            cd = c_op.data.T.conj()
            c = c_op.data
            if chi:
                data = data + np.exp(1j * chi[idx]) * sp.kron(cd.T, c,
                                                              format='csr')
            else:
                data = data + sp.kron(cd.T, c, format='csr')
            cdc = cd * c
            data = data - 0.5 * sp.kron(spI, cdc, format='csr')
            data = data - 0.5 * sp.kron(cdc.T, spI, format='csr')

    if data_only:
        return data
    else:
        L = Qobj()
        L.dims = sop_dims
        L.data = data
        L.isherm = False
        L.superrep = 'super'
        return L

# 需要导入模块: from qutip.qobj import Qobj [as 别名]
# 或者: from qutip.qobj.Qobj import superrep [as 别名]
def tensor(*args):
    """Calculates the tensor product of input operators.

    Parameters
    ----------
    args : array_like
        ``list`` or ``array`` of quantum objects for tensor product.

    Returns
    -------
    obj : qobj
        A composite quantum object.

    Examples
    --------
    >>> tensor([sigmax(), sigmax()])
    Quantum object: dims = [[2, 2], [2, 2]], \
shape = [4, 4], type = oper, isHerm = True
    Qobj data =
    [[ 0.+0.j  0.+0.j  0.+0.j  1.+0.j]
     [ 0.+0.j  0.+0.j  1.+0.j  0.+0.j]
     [ 0.+0.j  1.+0.j  0.+0.j  0.+0.j]
     [ 1.+0.j  0.+0.j  0.+0.j  0.+0.j]]
    """

    if not args:
        raise TypeError("Requires at least one input argument")

    if len(args) == 1 and isinstance(args[0], (list, np.ndarray)):
        # this is the case when tensor is called on the form:
        # tensor([q1, q2, q3, ...])
        qlist = args[0]

    elif len(args) == 1 and isinstance(args[0], Qobj):
        # tensor is called with a single Qobj as an argument, do nothing
        return args[0]

    else:
        # this is the case when tensor is called on the form:
        # tensor(q1, q2, q3, ...)
        qlist = args

    if not all([isinstance(q, Qobj) for q in qlist]):
        # raise error if one of the inputs is not a quantum object
        raise TypeError("One of inputs is not a quantum object")

    out = Qobj()

    if qlist[0].issuper:
        out.superrep = qlist[0].superrep
        if not all([q.superrep == out.superrep for q in qlist]):
            raise TypeError("In tensor products of superroperators, all must" +
                            "have the same representation")

    out.isherm = True
    for n, q in enumerate(qlist):
        if n == 0:
            out.data = q.data
            out.dims = q.dims
        else:
            out.data = sp.kron(out.data, q.data, format='csr')
            out.dims = [out.dims[0] + q.dims[0], out.dims[1] + q.dims[1]]

        out.isherm = out.isherm and q.isherm

    if not out.isherm:
        out._isherm = None

    return out.tidyup() if qutip.settings.auto_tidyup else out