Default optimization level does not perform self-inverse gate cancellations

[nonhermitian]

Information

• Qiskit Terra version: latest
• Python version:
• Operating system:

What is the current behavior?

qc= QuantumCircuit(2)
qc.h(range(2))
qc.cz(0,1)
qc.draw()

     ┌───┐   
q_0: ┤ H ├─■─
     ├───┤ │ 
q_1: ┤ H ├─■─
     └───┘   

transpile(qc, basis_gates=['h', 'cx']).draw()

     ┌───┐               
q_0: ┤ H ├───────■───────
     ├───┤┌───┐┌─┴─┐┌───┐
q_1: ┤ H ├┤ H ├┤ X ├┤ H ├
     └───┘└───┘└───┘└───┘

Steps to reproduce the problem

What is the expected behavior?

I would expect the default level of optimization to remove trivial things like repeated H gates.

Suggested solutions

[kdk]

Work was recently started in this direction by @vadebayo49 (see #6855 and #6576 ) but there is still some work to be done before this can be utilized by the default optimization levels, namely a way to identify (either through gate annotations or a library) which gates and gate pairs are inverse.

[mtreinish]

This is caused by the OneQubitEulerDecomposer not knowing how to simplify things in terms of h (you can see a list of the basis it can work in here: https://qiskit.org/documentation/stubs/qiskit.quantum_info.OneQubitEulerDecomposer.html#qiskit.quantum_info.OneQubitEulerDecomposer). The level 1 optimization level doesn't contain any passes that know how to cancel two consecutive h gates. I think higher optimizations definitely will though.

I think we need to re-evaluate which passes we include in the different optimization levels because I think we can get away with more optimization in level 1 than we have right now.

[nonhermitian]

It does work at level 2 and higher. However, given that the vast majority of users just do execute at the default level, perhaps level 1 should be beefed up some as you suggest.