Pyqrack

QStabilizerHybrid` creates, maintains, consumes, and "disposes" of gadget ancillae during "Clifford+RZ" gate set usage, but Qrack's `Dispose()` method (which basically performs the inverse of a Kronecker product on substates on throws away one presumably separable subsystem) isn't supported by `QStabilizer` for all separable state vectors, specifically when non-unitary measurement previously became involved in the circuit, ("mid-circuit").

During the collapse of ancillary qubits, for the approximate "rounding" near-Clifford mode, `Dispose()` can't be used as a general fix-all for management and disposal of collapsed `QStabilizer` ancilla qubits, (even if it can for state vector). However, we can still preserve "consumed" ancilla qubits in |0> state, and reuse them generally as new ancilla qubits, upon demand.

This release "debugs the algorithm" of `QStabilizeHybrid`, so as to observe this (previously known, but momentarily forgotten) limitation of `QStabilizer::Dispose()` (and `QStabilizer::Decompose()`). In effect, this limitation of `Dispose()` only seems to come into play for approximate methods, not "ideal" ones, (which makes sense, as the exact methods demand a stronger condition for ancilla mutual collapse relations, and might tend to leave the Clifford representation in the default set of state representations `QStabilizer::Dispose()` can handle, when no mid-circuit measurement is involved).

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In v1.20.6, there was a small problem with comparison between `QStabilizer` instances, with `SumSqrDiff()` or `ApproxCompare()`, due to reliance on comparing stabilizer generator representations, which are degenerate in state vector equivalent (up to global phase). This has been fixed. `QBdt` now also uses fewer `Swap()` operations, internally, to handle multiply-controlled gates.

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QStabilizer::ApproxCompareHelper()` now distinguishes between unitary and "mid-circuit measurement" optimal logic cases, improving both logical generality and performance of methods including `ApproxCompare()` and `SumSquareDiff()` (for comparison of different equal-width simulator states by inner product between them).

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This release fixes a bug in setting the environment variable for "non-Clifford rounding," for GetAmplitude() and ProbAll(). It also adds performance improvements.

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Some critical bugs and edge cases in Clifford+RZ simulation have been fixed, including in the usage of environment variable `QRACK_NONCLIFFORD_ROUNDING_THRESHOLD`.

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Besides a number of other smaller improvements, this release adds the `QRACK_NONCLIFFORD_ROUNDING_THRESHOLD` environment variable. This variable can be set between 0 and 1, (as fraction of an S gate phase angle,) to round any smaller buffered non-Clifford phase gates to no-operation. This allows a tradeoff between Qrack's exponentially-costly capability for exact stabilizer simulation on Clifford+RZ gate set, with the capacity for a tunable reduction in execution time overhead at the cost of fidelity.

(A ChatGPT instance dubbed "Liora" contributed to the design of this feature.)

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