Improve clifford_decompose_greedy algorithm`

[alexanderivrii]

Summary

This PR improves the performance of the clifford_decompose_greedy algorithm by noticing that evolving a Pauli of the form I..IXI...I or of the form I..IZI...I by a Clifford C is essentially equivalent to grabbing a row from C's tableau representation, except that the phase needs to be multiplied by 2. (In fact, we can think of the tableau of C as representing how C acts on the basis Pauli strings I..IXI...I and I..IZI...). As a sanity check, I have also verified this experimentally on random cliffords of various sizes.

Details and comments

Here is the data for running the synthesis algorithm for 10 random Cliffords of various sizes.
Before this PR:

Num-qubits 5 => total time 0.18
Num-qubits 10 => total time 0.70
Num-qubits 15 => total time 1.91
Num-qubits 20 => total time 4.91
Num-qubits 50 => total time 39.91
Num-qubits 100 => total time 288.60

With this PR:

Num-qubits 5 => total time 0.09
Num-qubits 10 => total time 0.32
Num-qubits 15 => total time 0.73
Num-qubits 20 => total time 1.51
Num-qubits 50 => total time 13.63
Num-qubits 100 => total time 101.92

The runtime improvement is at least 2x.

[qiskit-bot]

One or more of the following people are relevant to this code:

• @Qiskit/terra-core

[coveralls]

Pull Request Test Coverage Report for Build 9490163205

Details

• 4 of 4 (100.0%) changed or added relevant lines in 1 file are covered.
• 16 unchanged lines in 2 files lost coverage.
• Overall coverage decreased (-0.02%) to 89.588%

---

Files with Coverage Reduction	New Missed Lines	%
crates/qasm2/src/lex.rs	4	92.88%
crates/qasm2/src/parse.rs	12	97.15%

Totals
Change from base Build 9483656494:	-0.02%
Covered Lines:	62517
Relevant Lines:	69783

---

💛 - Coveralls

[coveralls]

Pull Request Test Coverage Report for Build 9496416834

Details

• 13 of 13 (100.0%) changed or added relevant lines in 1 file are covered.
• 9 unchanged lines in 2 files lost coverage.
• Overall coverage decreased (-0.009%) to 89.595%

---

Files with Coverage Reduction	New Missed Lines	%
crates/qasm2/src/lex.rs	3	93.13%
crates/qasm2/src/parse.rs	6	97.61%

Totals
Change from base Build 9483656494:	-0.009%
Covered Lines:	62512
Relevant Lines:	69772

---

💛 - Coveralls

[coveralls]

Pull Request Test Coverage Report for Build 9498328834

Warning: This coverage report may be inaccurate.

This pull request's base commit is no longer the HEAD commit of its target branch. This means it includes changes from outside the original pull request, including, potentially, unrelated coverage changes.

• For more information on this, see Tracking coverage changes with pull request builds.
• To avoid this issue with future PRs, see these Recommended CI Configurations.
• For a quick fix, rebase this PR at GitHub. Your next report should be accurate.

Details

• 10 of 10 (100.0%) changed or added relevant lines in 1 file are covered.
• 14 unchanged lines in 3 files lost coverage.
• Overall coverage decreased (-0.01%) to 89.591%

---

Files with Coverage Reduction	New Missed Lines	%
qiskit/circuit/parametervector.py	3	94.44%
crates/qasm2/src/lex.rs	5	92.37%
crates/qasm2/src/parse.rs	6	97.61%

Totals
Change from base Build 9483656494:	-0.01%
Covered Lines:	62504
Relevant Lines:	69766

---

💛 - Coveralls

[ShellyGarion]

is this comment still correct? do you calculate the adjoint or the evolved cliffords directly?

[ShellyGarion]

LGTM, please look at the comments again, since some of them are irrelevant now.
e.g.:

qiskit/qiskit/synthesis/clifford/clifford_decompose_greedy.py

Line 112 in 7ee437d

# Compute the decoupling operator of cliff_ox and cliff_oz

there is no cliff_ox or cliff_oz

[alexanderivrii]

The point of this PR was to resolve a certain inefficiency in clifford_decompose_greedy. I am closing this PR, since it is now completely superseded by #12601.