qubiter.OneQubitGate module

class qubiter.OneQubitGate.OneQubitGate

Bases: object

This class has no attributes or constructor. It is simply a collection of static methods, all of which return a complex 2 by 2 matrix (numpy array or array from some other tensor library). In cases where the entries of the matrix are all real, an is_quantum bool option is given to choose between a float or complex array.

All gates have a tensor library lib option. lib equals ‘np’ for numpy, ‘tf’ for tensorflow

static P_0(is_quantum=True, lib='np')

Returns projection operator P_0 = |0><0| = nbar, where |0> = [ 1, 0]^T and |1> = [0, 1]^T, T = transpose

Parameters:

• is_quantum (bool) –
• lib (str) –

Returns:

Return type:

np.ndarray

static P_0_phase_fac(ang_rads, lib='np')

Returns

exp(1j*ang_rads*P_0) = [[x, 0],[0, 1]] with x = exp(1j*ang_rads)

Parameters:

• ang_rads (float) –
• lib (str) –

Returns:

Return type:

np.ndarray

static P_1(is_quantum=True, lib='np')

Returns projection operator P_1 = |1><1| = n, where |0> = [1, 0]^T and |1> = [0, 1]^T, T = transpose

Parameters:

• is_quantum (bool) –
• lib (str) –

Returns:

Return type:

np.ndarray

static P_1_phase_fac(ang_rads, lib='np')

Returns

exp(1j*ang_rads*P_1) = [[1, 0],[0, x]] with x = exp(1j*ang_rads)

Parameters:

• ang_rads (float) –
• lib (str) –

Returns:

Return type:

np.ndarray

static const_dict(x)

Returns dictionary with all values equal to x. Dict is destined to fill a future 2-dim matrix.

Parameters:x – Returns: Return type:dict

static get_fun(lib, fun_name, lib_to_fun_name=None)

If lib is ‘np’, this method returns eval(lib + ‘.’ + fun_name). Else, if lib is not ‘np’ then: if lib_to_fun_name is None, it returns eval(lib + ‘.’ + fun_name), but if lib_to_fun_name is not None, it returns eval(lib + ‘.’ + lib_to_fun_name[lib]). It aborts if lib_to_fun_name[ lib] doesn’t exist.

Parameters:

• lib (str) – tensor library, either ‘np’ for numpy or ‘tp’ for tensorflow
• fun_name (str) – function name
• lib_to_fun_name (dict[str, str]) – dictionary mapping lib to fun_name. For example {‘tf’: ‘cos’}

Returns:

Return type:

function

static get_mat(lib, mat_dict, dtype=None)

Internal function that creates a tensor of type lib, based on a dict mat_dict.

Parameters:

• lib (str) –
• mat_dict (dict) –
• dtype (dtype | None) –

Returns:

Return type:

np.ndarray

static had2(is_quantum=True, lib='np')

Returns 2 dimensional Hadamard matrix (sigma_x + sigma_z)/sqrt(2).

Parameters:

• is_quantum (bool) –
• lib (str) –

Returns:

Return type:

np.ndarray

static mat_S(herm=False, lib='np')

Returns

[[1, 0],[0, x*sign]] where x=exp(j*pi/2)=j

where sign = 1 if herm=False and sign = -1 if herm=True.

Parameters:

• herm (bool) –
• lib (str) –

Returns:

Return type:

np.ndarray

static mat_Sdag(lib='np')

returns S^\dag.

Parameters:lib (str) – Returns: Return type:np.ndarray

static mat_T(herm=False, lib='np')

Returns

[[1, 0],[0, exp(j*pi/4*sign)]]

where sign = 1 if herm=False and sign = -1 if herm=True.

Parameters:

• herm (bool) –
• lib (str) –

Returns:

Return type:

np.ndarray

static mat_Tdag(lib='np')

returns T^\dag.

Parameters:lib (str) – Returns: Return type:np.ndarray

static phase_fac(ang_rads, lib='np')

Returns

exp(1j*ang_rads*I_2) = [[x, 0],[0, x]] with x = exp(1j*ang_rads)

Parameters:

• ang_rads (float) –
• lib (str) –

Returns:

Return type:

np.ndarray

static rot(rad_ang_x, rad_ang_y, rad_ang_z, lib='np')

Returns

exp(1j*(rad_ang_x*sig_x + rad_ang_y*sig_y + rad_ang_z*sig_z))

where rad_ang_x is an angle in radians and sig_x is the x Pauli matrix, etc.

Parameters:

• rad_ang_x (float) –
• rad_ang_y (float) –
• rad_ang_z (float) –
• lib (str) –

Returns:

Return type:

np.ndarray

static rot_ax(rad_ang, axis, lib='np')

Returns

exp(1j*rad_ang*sig_n)

where n = x if axis = 1, n = y if axis = 2 and n = z if axis = 3

Parameters:

• rad_ang (float) –
• axis (int) –
• lib (str) –

Returns:

Return type:

np.ndarray

static sigx(is_quantum=True, lib='np')

Returns sigma_x Pauli matrix.

Parameters:

• is_quantum (bool) –
• lib (str) –

Returns:

Return type:

np.ndarray

static sigy(lib='np')

Returns sigma_y Pauli matrix.

Parameters:lib (str) – Returns: Return type:np.ndarray

static sigz(is_quantum=True, lib='np')

Returns sigma_z Pauli matrix.

Parameters:

• is_quantum (bool) –
• lib (str) –

Returns:

Return type:

np.ndarray

static u2(rads0, rads1, rads2, rads3, lib='np')

Returns arbitrary 2-dim unitary matrix (U(2) group) parametrized as follows:

exp(1j*(rads0 + rads1*sig_x + rads2*sig_y + rads3*sig_z))

where rads1 is an angle in radians and sig_x is the x Pauli matrix, etc.

Parameters:

• rads0 (float) –
• rads1 (float) –
• rads2 (float) –
• rads3 (float) –
• lib (str) –

Returns:

Return type:

np.ndarray