IQP as circuit library function (and in Rust)

[Cryoris]

Summary

Part of #13046. Moves IQP (instantaneous quantum polytime) circuits to be a function, and ports the internals to Rust.

Details and comments

• This also adds the feature of creating random IQP circuits by just setting the number of qubits, without explicitly requiring the interactions matrix.
• The speedup from porting to Rust is more noticeable for large circuits (100+ qubits), where it is ~55x faster. See the table below for more numbers 🙂

IQP timings

-- n = 10, speedup 4.48x
main: 0.001 +- 0.000
this: 0.000 +- 0.000

-- n = 20, speedup 12.59x
main: 0.002 +- 0.000
this: 0.000 +- 0.000

-- n = 50, speedup 45.07x
main: 0.009 +- 0.000
this: 0.000 +- 0.000

-- n = 100, speedup 58.98x
main: 0.034 +- 0.002
this: 0.001 +- 0.000

-- n = 200, speedup 58.45x
main: 0.133 +- 0.004
this: 0.002 +- 0.001

-- n = 500, speedup 51.41x
main: 0.862 +- 0.037
this: 0.017 +- 0.010

[qiskit-bot]

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

• @Cryoris
• @Qiskit/terra-core
• @ajavadia

[coveralls]

Pull Request Test Coverage Report for Build 11590872936

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.
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• For a quick fix, rebase this PR at GitHub. Your next report should be accurate.

Details

• 111 of 114 (97.37%) changed or added relevant lines in 5 files are covered.
• 104 unchanged lines in 7 files lost coverage.
• Overall coverage decreased (-0.003%) to 88.699%

---

Changes Missing Coverage	Covered Lines	Changed/Added Lines	%
qiskit/circuit/library/iqp.py	20	21	95.24%
crates/accelerate/src/circuit_library/iqp.rs	87	89	97.75%
<!--	Total:	111	114

Files with Coverage Reduction	New Missed Lines	%
crates/accelerate/src/two_qubit_decompose.rs	1	92.09%
qiskit/transpiler/passes/synthesis/unitary_synthesis.py	2	58.05%
crates/qasm2/src/lex.rs	4	92.48%
crates/qasm2/src/parse.rs	6	97.62%
qiskit/synthesis/two_qubit/xx_decompose/decomposer.py	7	90.77%
qiskit/quantum_info/operators/symplectic/base_pauli.py	30	88.55%
crates/accelerate/src/sparse_observable.rs	54	95.42%
<!--	Total:	104

Totals
Change from base Build 11584707253:	-0.003%
Covered Lines:	75504
Relevant Lines:	85124

---

💛 - Coveralls

[Cryoris]

As discussed offline I split the iqp function into iqp and random_iqp to have a separate function for the random generation of IQP circuits 🙂