qml.equal

equal(op1, op2, check_interface=True, check_trainability=True, rtol=1e-05, atol=1e-09)

Function for determining operator, measurement, and tape equality.

Warning

The qml.equal function is based on a comparison of the types and attributes of the measurements or operators, not their mathematical representations. While mathematical comparisons between some classes, such as Tensor and Hamiltonian, are supported, mathematically equivalent operators defined via different classes may return False when compared via qml.equal. To be more thorough would require the matrix forms to be calculated, which may drastically increase runtime.

Warning

The interfaces and trainability of data within some observables including Tensor, Hamiltonian, Prod, Sum are sometimes ignored, regardless of what the user specifies for check_interface and check_trainability.

Parameters

• op1 (Operator or MeasurementProcess or QuantumTape) – First object to compare

• op2 (Operator or MeasurementProcess or QuantumTape) – Second object to compare

• check_interface (bool, optional) – Whether to compare interfaces. Default: True.

• check_trainability (bool, optional) – Whether to compare trainability status. Default: True.

• rtol (float, optional) – Relative tolerance for parameters.

• atol (float, optional) – Absolute tolerance for parameters.

Returns

True if the operators, measurement processes, or tapes are equal, else False

Return type

bool

Example

Given two operators or measurement processes, qml.equal determines their equality.

>>> op1 = qml.RX(np.array(.12), wires=0)
>>> op2 = qml.RY(np.array(1.23), wires=0)
>>> qml.equal(op1, op1), qml.equal(op1, op2)
(True, False)

>>> T1 = qml.X(0) @ qml.Y(1)
>>> T2 = qml.Y(1) @ qml.X(0)
>>> T3 = qml.X(1) @ qml.Y(0)
>>> qml.equal(T1, T2), qml.equal(T1, T3)
(True, False)

>>> T = qml.X(0) @ qml.Y(1)
>>> H = qml.Hamiltonian([1], [qml.X(0) @ qml.Y(1)])
>>> qml.equal(T, H)
True

>>> H1 = qml.Hamiltonian([0.5, 0.5], [qml.Z(0) @ qml.Y(1), qml.Y(1) @ qml.Z(0) @ qml.Identity("a")])
>>> H2 = qml.Hamiltonian([1], [qml.Z(0) @ qml.Y(1)])
>>> H3 = qml.Hamiltonian([2], [qml.Z(0) @ qml.Y(1)])
>>> qml.equal(H1, H2), qml.equal(H1, H3)
(True, False)

>>> qml.equal(qml.expval(qml.X(0)), qml.expval(qml.X(0)))
True
>>> qml.equal(qml.probs(wires=(0,1)), qml.probs(wires=(1,2)))
False
>>> qml.equal(qml.classical_shadow(wires=[0,1]), qml.classical_shadow(wires=[0,1]))
True
>>> tape1 = qml.tape.QuantumScript([qml.RX(1.2, wires=0)], [qml.expval(qml.Z(0))])
>>> tape2 = qml.tape.QuantumScript([qml.RX(1.2 + 1e-6, wires=0)], [qml.expval(qml.Z(0))])
>>> qml.equal(tape1, tape2, tol=0, atol=1e-7)
False
>>> qml.equal(tape1, tape2, tol=0, atol=1e-5)
True

Usage Details

You can use the optional arguments to get more specific results:

>>> op1 = qml.RX(torch.tensor(1.2), wires=0)
>>> op2 = qml.RX(jax.numpy.array(1.2), wires=0)
>>> qml.equal(op1, op2)
False

>>> qml.equal(op1, op2, check_interface=False, check_trainability=False)
True

>>> op3 = qml.RX(np.array(1.2, requires_grad=True), wires=0)
>>> op4 = qml.RX(np.array(1.2, requires_grad=False), wires=0)
>>> qml.equal(op3, op4)
False

>>> qml.equal(op3, op4, check_trainability=False)
True

>>> qml.equal(Controlled(op3, control_wires=1), Controlled(op4, control_wires=1))
False

>>> qml.equal(Controlled(op3, control_wires=1), Controlled(op4, control_wires=1), check_trainability=False)
True

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