Implement a Cliffordness checker

[ica574]

What should we add?

Qiskit should have a Cliffordness checker where the API allows you to pass a quantum circuit as an argument to a function called is_clifford() which returns True if the circuit is Clifford. As a proof of concept, I've added a small function that tries to build a Clifford circuit with the Clifford class. If the circuit is NOT Clifford, the function handles an exception which leads to a False result. However, it would be more appropriate to have a proper Cliffordness checking algorithm.

[ica574]

What would be the best way to do this?

[Cryoris]

This is already possible within a few lines, as you outlined in the PR. Is there strong motivation to add this as circuit method? We generally don't like to arbitrarily extend the interface since it's already massive.

[ica574]

Would be really helpful if this could be added as a circuit method. It isn't straightforward for someone to come up with this hack, and IMO it isn't quite intuitive to use this way.

It already works as is. But it doesn't seem like a good practice to make the Cliffordness checker rely on exceptions to work. Correct me if I'm wrong of course. I was thinking of something (maybe with Pauli propagation) to verify that an arbitrary (and parameterized) circuit is Clifford. Because some circuits are only Clifford for some rotations, not all.

[alexanderivrii]

This is similar to a private method _is_qiskit_circuit in basic_simulator.py, which however treats a circuit as Clifford even if it has measurement instructions. Hence a question: should we consider a circuit with measurements as Clifford or not?

Actually, what is your definition of a Clifford circuit: circuit with only Clifford gates? circuit with every gate equivalent to a Clifford gate? circuit whose unitary matrix is Clifford? For instance, consider a circuit with RX(0.1) followed by RX(-0.1) on the same qubit. The two RX gates obviously cancel out, so the circuit is equivalent to identity (which is Clifford), however your function would not detect it. Is this the expected behavior?

Imho, given the uncertainty of defining a Clifford circuit, I don't think we should expose this method.

[ica574]

Perhaps, in order to avoid confusion, it would be a good idea to have one method which evaluates the circuit as a whole called is_clifford(circuit), and another one which evaluates whether every instruction is clifford is_every_clifford(circuit). The two will be useful in different situations. is_every_clifford(circuit) could account for the first two cases that @alexanderivrii mentioned, and is_clifford(circuit) could account for the latter. Any thoughts?

[alexanderivrii]

I listed three possible options (and there are probably some more):

• Every gate in the circuit is Clifford: e.g. CX, S, H. If the circuit contains a gate that is equivalent to a Clifford gate but not defined as a Clifford gate, the circuit will not considered to be Clifford. Performance-wise, this would be the fastest option by far.
• Every gate is equivalent to a Clifford gate, via Clifford.from_circuit (as implemented in your PR). If I remember correctly, this may attempt to construct an Operator from a gate and then check if it's Clifford. There is probably also a cut-off parameter on the maximum number of qubits to consider.
• The whole circuit is equivalent to a Clifford gate. Unfortunately constructing an operator will not work for circuits with many qubits.

I also asked whether you consider circuits with measurements as Clifford? Actually, what about barriers?

[ShellyGarion]

These functions can be also useful for certain cases to check if a circuit is Clifford:

• get_clifford_gate_names - one can check if all the operations in the circuit are pure Clifford operations.

• SubstitutePi4Rotations - substitute pi/4 rotations gates into Clifford + T + Tdg gates. In particular, pi/2 rotation gates (e.g. RZ(pi/2), RX(3*pi/2), RZZ(-pi), etc.) will be converted to purely Clifford gates. One can run this pass, and then check with the get_clifford_gate_names that the circuit contains only Clifford gates.

• Use the Clifford.from_matrix function for an arbitrary unitary matrix. However, note that this function takes exponentially long time w.r.t. the number of qubits.

• We suggested to add a more efficient Clifford.from_operation method in Add Clifford.from_operation to shortcut checking matrix representation #9576, but haven't yet implemented it.

[ica574]

I listed three possible options (and there are probably some more):

• Every gate in the circuit is Clifford: e.g. CX, S, H. If the circuit contains a gate that is equivalent to a Clifford gate but not defined as a Clifford gate, the circuit will not considered to be Clifford. Performance-wise, this would be the fastest option by far.
• Every gate is equivalent to a Clifford gate, via Clifford.from_circuit (as implemented in your PR). If I remember correctly, this may attempt to construct an Operator from a gate and then check if it's Clifford. There is probably also a cut-off parameter on the maximum number of qubits to consider.
• The whole circuit is equivalent to a Clifford gate. Unfortunately constructing an operator will not work for circuits with many qubits.

I also asked whether you consider circuits with measurements as Clifford? Actually, what about barriers?

I suppose that circuits with measurements aren't Clifford because they are non-unitary. Not sure about barriers because that's a compiler directive. What would be the best way forward from here?

[RahulShastri003]

Is this issue still open? I would like to work on it quickly!

[Cryoris]

@RahulShastri003 as you can see from the thread above, we're still discussing whether and how to pursue this.