This commit is a rewrite of the core swap trials functionality in the
StochasticSwap transpiler pass. Previously this core routine was written
using Cython (see Qiskit#1789) which had great performance, but that
implementation was single threaded. The core of the stochastic swap
algorithm by it's nature is well suited to be executed in parallel, it
attempts a number of random trials and then picks the best result
from all the trials and uses that for that layer. These trials can
easily be run in parallel as there is no data dependency between the
trials (there are shared inputs but read-only). As the algorithm
generally scales exponentially the speed up from running the trials in
parallel can offset this and improve the scaling of the pass. Running
the pass in parallel was previously tried in Qiskit#4781 using Python
multiprocessing but the overhead of launching an additional process and
serializing the input arrays for each trial was significantly larger
than the speed gains. To run the algorithm efficiently in parallel
multithreading is needed to leverage shared memory on shared inputs.

This commit rewrites the cython routine using rust. This was done for
two reasons. The first is that rust's safety guarantees make dealing
with and writing parallel code much easier and safer. It's also
multiplatform because the rust language supports native threading
primatives in language. The second is while writing parallel cython
code using open-mp there are limitations with it, mainly on windows. In
practice it was also difficult to write and maintain parallel cython
code as it has very strict requirements on python and c code
interactions. It was much faster and easier to port it to rust and the
performance for each iteration (outside of parallelism) is the same (in
some cases marginally faster) in rust. The implementation here reuses
the data structures that the previous cython implementation introduced
(mainly flattening all the terra objects into 1d or 2d numpy arrays for
efficient access from C).

The speedups from this PR can be significant, calling transpile() on a
400 qubit (with a depth of 10) QV model circuit targetting a 409 heavy
hex coupling map goes from ~200 seconds with the single threaded cython
to ~60 seconds with this PR locally on a 32 core system, When transpiling
a 1000 qubit (also with a depth of 10) QV model circuit targetting a 1081
qubit heavy hex coupling map goes from taking ~6500 seconds to ~720
seconds.

The tradeoff with this PR is for local qiskit-terra development a rust
compiler needs to be installed. This is made trivial using rustup
(https://rustup.rs/), but it is an additional burden and one that we
might not want to make. If so we can look at turning this PR into a
separate repository/package that qiskit-terra can depend on. The
tradeoff here is that we'll be adding friction to the api boundary
between the pass and the core swap trials interface. But, it does ease
the dependency on development for qiskit-terra.

This commit fixes how we package the compiled rust module in
qiskit-terra. As a single rust project only gives us a single compiled
binary output we can't use the same scheme we did previously with cython
with a separate dynamic lib file for each module. This shifts us to
making the rust code build a `qiskit._accelerate` module and in that we
have submodules for everything we need from compiled code. For this PR
there is only one submodule, `stochastic_swap`, so for example the
parallel swap_trials routine can be imported from
`qiskit._accelerate.stochastic_swap.swap_trials`. In the future we can
have additional submodules for other pieces of compiled code in qiskit.
For example, the likely next candidate is the pauli expectation value
cython module, which we'll likely port to rust and also make parallel
(for sufficiently large number of qubits). In that case we'd add a new
submodule for that functionality.

This commit corrects the use of the normal distribution to have the mean
set to 1.0. Previously we were doing this out of band for each value by
adding 1 to the random value which wasn't necessary because we could
just generate it with a mean of 1.0.

This commit removes an unecessary extra scope around the locked read for
where we store the best solution. The scope was previously there to
release the lock after we check if there is a solution or not. However
this wasn't actually needed as we can just do the check inline and the
lock will release after the condition block.

Co-authored-by: Jake Lishman <jake@binhbar.com>

Previously the swap_trials() function had an explicit lifetime
annotation `'p` which wasn't necessary because the compiler can
determine this on it's own. Normally when dealing with numpy views and a
Python object (i.e. a GIL handle) we need a lifetime annotation to tell
the rust compiler the numpy view and the python gil handle will have the
same lifetime. But since swap_trials doesn't take a gil handle and
operates purely in rust we don't need this lifetime and the rust
compiler can deal with the lifetime of the numpy views on their own.

This commit fixes the python lint failures and also updates the ci
configuration for the lint job to also run rust's style and lint
enforcement.

This commit fixes the output list from the `layout_mapping()`
method of `NLayout`. Previously, it incorrectly would return the
wrong indices it should be a list of virtual -> physical to
qubit pairs. This commit corrects this error

Co-authored-by: georgios-ts <45130028+georgios-ts@users.noreply.github.com>

This commit makes the parallelization of the swap_trials() configurable.
This is dones in two ways, first a new argument parallel_threshold is
added which takes an optional int which is the number of qubits to
switch between a parallel and serial version. The second is that it
takes into account the the state of the QISKIT_IN_PARALLEL environment
variable. This variable is set to TRUE by parallel_map() when we're
running in a multiprocessing context. In those cases also running
stochastic swap in parallel will likely just cause too much load as
we're potentially oversubscribing work to the number of available CPUs.
So, if QISKIT_IN_PARALLEL is set to True we run swap_trials serially.

…wap-in-rust

This reverts commit 57790c8. That
commit attempted to sovle some issues in test running, mainly around
multiple parallel dispatch causing exceess load. But in practice it was
broken and caused more issues than it fixed. We'll investigate and add
control for the parallelization in a future commit separately after all
the tests are passing so we have a good baseline.

Previously, in the case of circuits that had multiple best possible
depth == 1 solutions for a layer, there was a race condition in the fast
exit path between the threads which could lead to a non-deterministic
result even with a fixed seed. The output was always valid, but which
result was dependent on which parallel thread with an ideal solution
finished last and wrote to the locked best result last. This was causing
weird non-deterministic test failures for some tests because of Qiskit#1794 as
the exact match result would change between runs. This could be a bigger
issue because user expectations are that with a fixed seed set on the
transpiler that the output circuit will be deterministically
reproducible.

To address this is issue this commit trades off some performance to
ensure we're always returning a deterministic result in this case. This
is accomplished by updating/checking if a depth==1 solution has been
found in another trial thread we only act (so either exit early or
update the already found depth == 1 solution) if that solution already
found has a trial number that is less than this thread's trial number.
This does limit the effectiveness of the fast exit, but in practice it
should hopefully not effect the speed too much.

As part of this commit some tests are updated because the new
deterministic behavior is slightly different from the previous results
from the cython serial implementation. I manually verified that the
new output circuits are still valid (it also looks like the quality
of the results in some of those cases improved, but this is strictly
anecdotal and shouldn't be taken as a general trend with this PR).

Co-authored-by: georgios-ts <45130028+georgios-ts@users.noreply.github.com>

This was only a for local testing to prove it was a bad idea and was
accidently included in the branch. We should not nest the parallel
execution like this.

This commit eliminates the short circuit fast return in swap_trial()
when another trial thread has found an ideal solution. Trying to do this
in a parallel context is tricky to make deterministic because in cases
of >1 depth == 1 solutions there is an inherent race condition between
the threads for writing out their depth == 1 result to the shared
location. Different strategies were tried to make this reliably
deterministic but there wa still a race condition. Since this was just a
performance optimization to avoid doing unnecessary work this commit
removes this step. Weighing improved performance against repeatability
in the output of the compiler, the reproducible results are more
important. After we've adopted a multithreaded stochastic swap we can
investigate adding this back as a potential future optimization.

This reverts commit c510764. The
removal there was premature and we had a fix for the non-determinism in
place, ignoring a typo which was preventing it from working.

Co-Authored-By: Georgios Tsilimigkounakis <45130028+georgios-ts@users.noreply.github.com>

This commit disables the multiprocessing based parallelism when running
unittest jobs in CI. We historically have defaulted the use of
multiprocessing in environments only where the "fork" start method is
available because this has the best performance and has no caveats
around how it is used by users (you don't need an
`if __name__ == "__main__"` guard). However, the use of the "fork"
method isn't always 100% reliable (see
https://bugs.python.org/issue40379), which we saw on Python 3.9 Qiskit#6188.
In unittest CI (and tox) by default we use stestr which spawns (not using
fork) parallel workers to run tests in parallel. With this PR this means
in unittest we're now running multiple test runner subprocesses, which
are executing parallel dispatched code using multiprocessing's fork
start method, which is executing multithreaded rust code. This three layers
of nesting is fairly reliably hanging as Python's fork doesn't seem to
be able to handle this many layers of nested parallelism. There are 2
ways I've been able to fix this, the first is to change the start method
used by `parallel_map()` to either "spawn" or "forkserver" either of
these does not suffer from random hanging. However, doing this in the
unittest context causes significant overhead and slows down test
executing significantly. The other is to just disable the
multiprocessing which fixes the hanging and doesn't impact runtime
performance signifcantly (and might actually help in CI so we're not
oversubscribing the limited resources.

As I have not been able to reproduce `parallel_map()` hanging in
a standalone context with multithreaded stochastic swap this commit opts
for just disabling multiprocessing in CI and documenting the known issue
in the release notes as this is the simpler solution. It's unlikely that
users will nest parallel processes as it typically hurts performance
(and parallel_map() actively guards against it), we only did it in
testing previously because the tests which relied on it were a small
portion of the test suite (roughly 65 tests) and typically did not have
a significant impact on the total throughput of the test suite.

In an earlier commit we disabled the use of parallel dispatch in
parallel_map() to avoid a bug in cpython associated with their fork()
based subprocess launch. Doing this works around the bug which was
reliably triggered by running multiprocessing in parallel subprocesses.
It also has the side benefit of providing a ~2x speed up for test suite
execution in CI. However, this meant we lost our test coverage in CI for
running parallel_map() with actual multiprocessing based parallel
dispatch. To ensure we don't inadvertandtly regress this code path
moving forward this commit adds a dedicated test script which runs a
simple transpilation in parallel and verifies that everything works as
expected with the default parallelism settings.

This commit adds a switch on running between a single threaded and a
multithreaded variant of the swap_trials loop based on whether the
QISKIT_IN_PARALLEL flag is set. If QISKIT_IN_PARALLEL is set to TRUE
this means the `parallel_map()` function is running in the outer python
context and we're running in multiprocessing already. This means we do
not want to be running in multiple threads generally as that will lead
to potential resource exhaustion by spawn n processes each potentially
running with m threads where `n` is `min(num_phys_cpus, num_tasks)` and
`m` is num_logical_cpus (although only
`min(num_logical_cpus, num_trials)` will be active) which on the typical
system there aren't enough cores to leverage both multiprocessing and
multithreading. However, in case a user does have such an environment
they can set the `QISKIT_FORCE_THREADS` env variable to `TRUE` which
will use threading regardless of the status of `QISKIT_IN_PARALLEL`.

Co-authored-by: Jake Lishman <jake@binhbar.com>

This commits fixes some minor details found during code review. It
expands the section on building from source to explain how to build a
release optimized binary with editable mode, makes the QISKIT_PARALLEL
env variable usage consistent across all jobs, and adds a missing
shebang to the `install_rush.sh` script which is used to install rust in
the manylinux container environment.

…wap-in-rust

In earlier commits the tox configuration was changed to try and fix the
docs CI job by going to great effort to try and enforce that
setuptools-rust was installed in all situations, even before it was
actually needed. However, the problem with the docs ci job was unrelated
to the tox configuration and this reverts the configuration to something
that works with more versions of tox and setuptools-rust.