Fix reverse permutation for transpiled circuits in Operator.from_circuit

[mtreinish]

Summary

This commit fixes a bug in the Operator.from_circuit() constructor method for Layout's generated by transpile(). The transpiler would set the _layout property for an output circuit to be the mapping from the input circuit's virtual qubits to the physical qubits (also the output circuit's qubit index). This is useful for visualization and visually tracking the permutation assuming you have the original circuit. However for the Operator.from_circuit() constructor method which will reverse the permutation caused by layout in the generated matrix this is not sufficient information since we need to order of the original circuits qubits. To fix this issue this commit changes the _layout attribute of the QuantumCircuit class to store both the initial layout as before and also a mapping of qubit objects to indices from the original circuit. Using this extra information we can reliably handle the qubit permutation in the constructor.

Details and comments

Fixes #8800

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[coveralls]

Pull Request Test Coverage Report for Build 3189095581

• 27 of 29 (93.1%) changed or added relevant lines in 10 files are covered.
• 31 unchanged lines in 2 files lost coverage.
• Overall coverage decreased (-0.02%) to 84.674%

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Changes Missing Coverage	Covered Lines	Changed/Added Lines	%
qiskit/visualization/circuit/matplotlib.py	2	3	66.67%
qiskit/visualization/gate_map.py	2	3	66.67%

Files with Coverage Reduction	New Missed Lines	%
src/sabre_swap/mod.rs	2	95.05%
src/results/marginalization.rs	29	68.97%

Totals
Change from base Build 3188378760:	-0.02%
Covered Lines:	61662
Relevant Lines:	72823

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💛 - Coveralls

[alexanderivrii]

@mtreinish, one quick question, to see if I understand things correctly: with this PR we would be able to reliably check equivalence of the original and the transpiled circuits by checking Operator(circuit).equiv(result), even if the transpiler chose a non-trivial initial layout and introduced swaps. However, the above equivalence check would not work if ancillas were allocated. (And of course if the number of qubits is sufficiently large, something like 20, but I don't recall the exact numbers, the Operator cannot be constructed either).

[mtreinish]

@alexanderivrii Yeah, that's the basic idea of this (except it's Operator.from_circuit(result), assuming result is the post transpiled circuit). If ancillas are added this doesn't factor that in currently but maybe we can add a ignore_idle_qubits argument in a follow up PR (for 0.23.0) to look at enabling that. As for the max size it will depend on memory but for larger number of qubits the memory requires are quite large 17 qubits requires 128GB of memory to allocate the array.

[jakelishman]

A minor comment about potentially changing the type of the _layout attribute, but mostly this looks fine to me.

[jakelishman]

Looks good to me, and good to get the bug fixed!

[alexanderivrii]

Sorry for the delayed reply -- it took me some time to understand the intricacies of this issue and why the original layout alone is not sufficient to fully reconstruct the operator from the transpiled circuit. And, indeed, Layout stores a mapping from indices of physical qubits to things like Qubit(QuantumRegister(3, 'q2'), 2) (corresponding to virtual qubits in the original circuit), but does not store the indices of these Qubit(QuantumRegister(3, 'q2'), 2) virtual qubits in the original circuit. The current PR addresses this by defining TranspilerLayout that contains both the layout and these indices (called input_qubit_mapping). The Operator.from_circuit has been modified to factor this input_qubit_mapping into construction. Overall, this LGTM and constitutes an important step to enable checking the equivalence of the original and the transpiled circuits.

However, things are still a bit trickier than described, and more work is needed to fully check the equivalence of the original and the transpiled circuits. For one, the layout also contains things like Qubit(QuantumRegister(1, 'ancilla'), 0) (corresponding to auxiliary qubits not present in the original circuit). On the positive side, input_qubit_mapping has these as well (mapping these to indices outside of the range of the original qubits). Not all of these ancilla qubits are in general idle, so possibly the equivalence check has to be done for the [original circuit extended with the appropriate number of ancilla qubits] vs. the [transpiled circuit]. But possibly completely idle qubits can be removed from the analysis. For two, as far as I can tell, we might still be missing the final permutation, for instance RemoveSwapsBeforeMeasure can remove the trailing swaps in the circuit and this information is not reflected in TranspilerLayout.

[mtreinish]

Right, this alone is not sufficient to fully reverse the permutation caused by the transpiler in Operator.from_circuit.This PR is about fixing the initial layout support that already existed in .from_circuit, #8597 is intended to deal with the output permutation caused by swap mapping. That change depends on this pr now, I split this out as to fix the initial layout handling became more involved than what I should integrate into that pr. As for ancilla handling we'll have to do that in a follow-up to #8597 since I think it will require a bit more work than what I have scoped in that pr.