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Add SPP and SPP_DAG instructions (#97)
## Summary - Implement SPP and SPP_DAG (generalized S gate) that phase the -1 eigenspace of Pauli product observables by i or -i - Reuses the MPP auxiliary qubit pattern: entangle with Pauli product, apply S/S_DAG, then uncompute - Extracted shared `_apply_pauli_controls` helper from MPP - Supports inverted targets (`!`) which toggle between SPP and SPP_DAG behavior - Supports multi-qubit Pauli products (e.g., `SPP X0*Y1*Z2`) and multiple products per instruction Closes #74 ## Test plan - [x] Unit tests: parsing single/multi-qubit products, SPP_DAG, multiple products - [x] Integration tests verifying equivalence to known gates: - `SPP Z0` = `S`, `SPP_DAG Z0` = `S_DAG` - `SPP X0` = `SQRT_X`, `SPP !X0` = `SQRT_X_DAG` - `SPP X0*X1` = `SQRT_XX`, `SPP Y0*Y1` = `SQRT_YY`, `SPP Z0*Z1` = `SQRT_ZZ` 🤖 Generated with [Claude Code](https://claude.com/claude-code) --------- Co-authored-by: Claude Opus 4.6 (1M context) <noreply@anthropic.com> Co-authored-by: Copilot <175728472+Copilot@users.noreply.github.com>
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‎CHANGELOG.md‎

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- Initial release
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- Clifford+T circuit simulation via stabilizer rank decomposition
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- Stabilizer decomposition backend based on pyzx and the [paramzx-extension](https://github.com/mjsutcliffe99/ParamZX) by [(2025) M Sutcliffe and A Kissinger](https://arxiv.org/pdf/2403.06777)
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- Support for all [Stim](https://github.com/quantumlib/Stim) instructions
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- Support for most [Stim](https://github.com/quantumlib/Stim) instructions
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- `T`, `T_DAG`, `R_Z`, `R_X`, `R_Y`, and `U3` instructions
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- Arbitrary rotations gates via magic cat state decomposition from Eq. 10 of [(2021) Qassim et al.](https://arxiv.org/pdf/2106.07740)
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- GPU acceleration via jax

‎README.md‎

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## Supported Instructions
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Tsim supports all [Stim instructions](https://github.com/quantumlib/Stim/wiki/Stim-v1.9-Gate-Reference). In addition, Tsim defines the following non-Clifford instructions:
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Tsim supports most [Stim instructions](https://github.com/quantumlib/Stim/wiki/Stim-v1.9-Gate-Reference). In addition, Tsim defines the following non-Clifford instructions:
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### `T` and `T_DAG`
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‎docs/demos/overview.ipynb‎

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"### Clifford Instructions\n",
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"Tsim supports all instructions [supported by Stim](https://github.com/quantumlib/Stim/wiki/Stim-v1.9-Gate-Reference). Below we show the standard generating set of Clifford gates:"
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"Tsim supports most instructions [supported by Stim](https://github.com/quantumlib/Stim/wiki/Stim-v1.9-Gate-Reference). Below we show the standard generating set of Clifford gates:"
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{
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"cell_type": "markdown",
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"The `SPP` instruction phases the $-1$ eigenspace of a Pauli product observable by $i$. For example, `SPP Z0` is equivalent to the `S` gate, and `SPP X0*X1` is equivalent to `SQRT_XX`. The `SPP_DAG` instruction phases by $-i$ instead. The `!` operator inverts the product, swapping `SPP` and `SPP_DAG` behavior."
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"c = Circuit(\"SPP X0*Y1*Z2\")\n",
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"c.diagram(\"timeline-svg\", height=220)"
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]
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},
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"### Noise Channels\n",
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"The `PAULI_CHANNEL_1(p_x, p_y, p_z)` instruction is a `X`, `Y`, and `Z` instruction that is applied with probabilities `p_x`, `p_y`, and `p_z` respectively."
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"The `PAULI_CHANNEL_2` instruction takes fifteen floats specifying the disjoint probabilities of each possible Pauli pair\n",
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"The `DEPOLARIZE1(p)` instruction applies a randomly chosen Pauli with probability `p`."
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"The `DEPOLARIZE2(p)` instruction applies a randomly chosen two-qubit Pauli with probability `p`."
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"The `CORRELATED_ERROR(p)` instruction applies a specified Pauli product with probability `p`. If no error occurred, then a following `ELSE_CORRELATED_ERROR(p2)` instruction may apply a Pauli product with probabiliy `p2`. If no error occurs again, further `ELSE_CORRELATED_ERROR(pi)` instructions in the chain may apply a Pauli products."
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"### Annotations\n",
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