Optimize Wigner Function and Improve make_grid with @njit for Better Performance and Memory Efficiency

[JakeKitchen]

User description

Optimized Wigner Function Iterative Computation

Context:

The _wigner_discretized_iterative function calculates the Wigner function iteratively, which is essential for simulating quantum states in continuous variable quantum mechanics. The original implementation had redundant operations, recalculations, and excessive memory allocations, leading to performance bottlenecks. The make_grid function was also optimized with @njit to further enhance performance. This update improves both mathematical efficiency and memory management.

Description of the Change:

1. Precompute Exponential Terms: The exponential grid is computed only once and reused to avoid redundant calculations in each iteration.
2. Precompute Square Roots: All square roots required for the computation are calculated at the beginning and stored in an array. This reduces overhead inside nested loops.
3. Efficient Matrix Swapping: Instead of creating new matrices in every loop iteration, the function reuses memory by swapping matrices, which reduces memory allocations.
4. Optimized make_grid Function:
   • The make_grid function was updated to use @njit to accelerate its performance.
   • Memory allocations for the Q and P coordinate matrices are optimized to reduce overhead.
   • A precomputed sqrt_factor is used to avoid redundant calculations inside nested loops.
   • By leveraging @njit, the function is now compliant with Numba’s JIT compilation, allowing faster and more efficient execution.

Benefits:

1. Improved Mathematical Efficiency:

   • The function minimizes the number of floating-point operations inside loops by precomputing values such as exponential terms and square roots.
   • The iterative Wigner calculation avoids recalculating these values multiple times, making the function more computationally efficient.
   • Memory-intensive operations are reduced by swapping matrices rather than allocating new ones, ensuring cache-friendlier execution.

2. Better Performance:

   • Memory Reuse: By reusing the same memory blocks with matrix swapping, the function avoids costly memory allocations, improving speed.
   • Optimized make_grid: Using @njit in make_grid improves both speed and memory efficiency, enabling seamless integration with the rest of the optimized functions.

3. Numba Compliance:

   • The optimized function ensures type safety and alignment with Numba’s @njit constraints, avoiding common type-related issues.

Possible Drawbacks:

• Increased Memory Usage at Startup: Precomputing the square roots and exponential grid slightly increases memory usage at the beginning, but this is offset by performance gains during execution.

Related GitHub Issues:

NA

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PR Type

enhancement, bug_fix

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Description

• Optimized the Wire class in tensors.py by using field for attribute initialization and improved dictionary comprehensions for better performance.
• Simplified the shape calculation process by removing unnecessary sorting functions and directly combining shapes.
• Enhanced the make_grid function in wigner.py by preallocating arrays and optimizing the computation of coordinate matrices.
• Improved the _wigner_discretized_iterative function by precomputing exponential terms and square roots, reducing redundant calculations, and reusing matrices to enhance memory efficiency.

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Changes walkthrough 📝

Relevant files

Enhancement

tensors.py Optimize tensor network wire and shape handling                    mrmustard/math/tensor_networks/tensors.py Improved initialization of Wire class attributes using field. Optimized wire dictionary initialization with dictionary comprehensions. Simplified shape calculation by removing unnecessary function. Converted keys to lists in AdjointView and DualView initializations. +31/-44  wigner.py Enhance Wigner function computation efficiency                      mrmustard/physics/wigner.py Optimized make_grid function with preallocated arrays. Precomputed exponential terms and square roots in _wigner_discretized_iterative. Improved memory efficiency by reusing matrices. +34/-20

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⏱️ Estimated effort to review: 3 🔵🔵🔵⚪⚪

🏅 Score: 92

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⚡ Recommended focus areas for review Performance Optimization Verify that the optimizations in the `_wigner_discretized_iterative` function, including precomputation of exponential terms and square roots, and matrix reuse, actually improve performance without introducing numerical instability. Code Refactoring Review the changes in the `shape` method of the `Tensor` class to ensure that the new implementation correctly handles all possible input scenarios and maintains the expected behavior.

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PR Code Suggestions ✨

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Category	Suggestion	Score
Performance	Use NumPy's vectorized operations to improve performance in grid creation ___ **Consider using NumPy's vectorized operations instead of nested loops in the make_grid function to improve performance. This can be achieved by using np.meshgrid to create the coordinate matrices.** [mrmustard/physics/wigner.py [29-48]](https://github.com/XanaduAI/MrMustard/pull/504/files#diff-133da5e283683fe9f83202a7fc05ff614f84cdf71682d7622a9a5ae5c3deb6e7R29-R48) ```diff @njit def make_grid(q_vec: np.ndarray, p_vec: np.ndarray, hbar: float): r"""Returns two coordinate matrices `Q` and `P` from coordinate vectors `q_vec` and `p_vec`, along with the grid over which Wigner functions can be discretized. """ - n_q = q_vec.size - n_p = p_vec.size - Q = np.empty((n_q, n_p), dtype=np.float64) - P = np.empty((n_q, n_p), dtype=np.float64) + Q, P = np.meshgrid(q_vec, p_vec, indexing='ij') sqrt_factor = 1.0 / np.sqrt(2.0 * hbar) - - for i in range(n_q): - q = q_vec[i] - for j in range(n_p): - p = p_vec[j] - Q[i, j] = q - P[i, j] = p - grid = (Q + 1j * P) * sqrt_factor return Q, P, grid ``` - [ ] **Apply this suggestion** Suggestion importance[1-10]: 9 Why: The suggestion to use NumPy's `meshgrid` function instead of nested loops significantly improves performance by leveraging vectorized operations, which is a well-known optimization technique in numerical computing.	9
	Use in-place operations and preallocate arrays to reduce memory allocations and improve performance ___ **Consider using in-place operations and preallocating arrays to reduce memory allocations and improve performance in the _wigner_discretized_iterative function.** [mrmustard/physics/wigner.py [155-169]](https://github.com/XanaduAI/MrMustard/pull/504/files#diff-133da5e283683fe9f83202a7fc05ff614f84cdf71682d7622a9a5ae5c3deb6e7R155-R169) ```diff @njit def _wigner_discretized_iterative(rho, q_vec, p_vec, hbar): # pragma: no cover """Optimized iterative computation of the Wigner function.""" cutoff = len(rho) Q, P, grid = make_grid(q_vec, p_vec, hbar) Wmat = np.zeros((2, cutoff) + grid.shape, dtype=np.complex128) # Precompute the exponential term to avoid recalculating it. - exp_grid = np.exp(-2.0 * np.abs(grid) ** 2) / np.pi + np.exp(-2.0 * np.abs(grid) ** 2, out=Wmat[0, 0]) + Wmat[0, 0] /= np.pi - # Initialize Wmat and W with the |0><0| component. - Wmat[0, 0] = exp_grid - W = rho[0, 0].real * Wmat[0, 0].real + # Initialize W with the |0><0| component. + W = np.real(rho[0, 0] * Wmat[0, 0]) # Precompute square roots to avoid repetitive calculations. - sqrt_n = np.array([np.sqrt(n) for n in range(cutoff)], dtype=np.float64) + sqrt_n = np.sqrt(np.arange(cutoff, dtype=np.float64)) ``` - [ ] **Apply this suggestion** Suggestion importance[1-10]: 9 Why: The suggestion to use in-place operations and preallocate arrays is a strong optimization strategy that reduces memory allocations and enhances performance, particularly in computationally intensive functions like `_wigner_discretized_iterative`.	9
	Utilize NumPy's broadcasting to simplify computations and improve performance ___ **Consider using NumPy's broadcasting capabilities to simplify the computation of Wmat elements and improve performance in the _wigner_discretized_iterative function.** [mrmustard/physics/wigner.py [172-183]](https://github.com/XanaduAI/MrMustard/pull/504/files#diff-133da5e283683fe9f83202a7fc05ff614f84cdf71682d7622a9a5ae5c3deb6e7R172-R183) ```diff -for n in range(1, cutoff): - Wmat[0, n] = (2.0 * grid * Wmat[0, n - 1]) / sqrt_n[n] - W += 2 * np.real(rho[0, n] * Wmat[0, n]) +# Compute Wmat[0] for all n at once +Wmat[0, 1:] = (2.0 * grid * Wmat[0, :-1].T / sqrt_n[1:]).T +W += 2 * np.real(np.sum(rho[0, 1:] * Wmat[0, 1:], axis=0)) # Compute the remaining coefficients and accumulate the Wigner function. for m in range(1, cutoff): - Wmat[1, m] = (2 * np.conj(grid) * Wmat[0, m] - sqrt_n[m] * Wmat[0, m - 1]) / sqrt_n[m] - W += rho[m, m].real * Wmat[1, m].real + Wmat[1, m:] = ((2 * np.conj(grid) * Wmat[0, m:].T - sqrt_n[m] * Wmat[0, m-1:].T) / sqrt_n[m:]).T + W += rho[m, m].real * Wmat[1, m].real + 2 * np.real(np.sum(rho[m, m+1:] * Wmat[1, m+1:], axis=0)) - for n in range(m + 1, cutoff): - Wmat[1, n] = (2 * grid * Wmat[1, n - 1] - sqrt_n[m] * Wmat[0, n - 1]) / sqrt_n[n] - W += 2 * np.real(rho[m, n] * Wmat[1, n]) - ``` - [ ] **Apply this suggestion** Suggestion importance[1-10]: 8 Why: This suggestion effectively uses NumPy's broadcasting capabilities to simplify and optimize the computation of `Wmat` elements, which can lead to performance improvements in the `_wigner_discretized_iterative` function.	8
	✅ Use tuples instead of lists for storing modes to improve performance and reduce memory usage ___ Suggestion Impact: The commit changed the initialization of modes in the AdjointView class to use keys() directly, which returns a view object similar to a tuple, instead of converting them to lists. This aligns with the suggestion to use more efficient data structures. code diff: ```diff + modes_in_ket=self._original.input.bra.keys(), + modes_out_ket=self._original.output.bra.keys(), + modes_in_bra=self._original.input.ket.keys(), + modes_out_bra=self._original.output.ket.keys(), ) def value(self, shape: tuple[int]): @@ -397,7 +405,12 @@ ComplexTensor: the unitary matrix in Fock representation """ # converting the given shape into a shape for the original tensor - shape_in_ket, shape_out_ket, shape_in_bra, shape_out_bra = self._original.unpack_shape(shape) + ( + shape_in_ket, + shape_out_ket, + shape_in_bra, + shape_out_bra, + ) = self._original.unpack_shape(shape) shape_ret = shape_in_bra + shape_out_bra + shape_in_ket + shape_out_ket ret = math.conj(math.astensor(self._original.value(shape_ret))) @@ -413,10 +426,10 @@ self._original = tensor super().__init__( name=self._original.name, - modes_in_ket=list(self._original.output.ket.keys()), - modes_out_ket=list(self._original.input.ket.keys()), - modes_in_bra=list(self._original.output.bra.keys()), - modes_out_bra=list(self._original.input.bra.keys()), + modes_in_ket=self._original.output.ket.keys(), + modes_out_ket=self._original.input.ket.keys(), + modes_in_bra=self._original.output.bra.keys(), + modes_out_bra=self._original.input.bra.keys(), ``` ___ **Consider using a more efficient data structure, such as a tuple or a frozen set, for storing the modes in the Tensor class initialization to improve performance and reduce memory usage.** [mrmustard/math/tensor_networks/tensors.py [186-191]](https://github.com/XanaduAI/MrMustard/pull/504/files#diff-c37f10f883a6d5dca46cceb10fc281d137fc78db80c19ed8362a1858aeb7d614R186-R191) ```diff def __init__( self, name: str, - modes_in_ket: list[int] | None = None, - modes_out_ket: list[int] | None = None, - modes_in_bra: list[int] | None = None, - modes_out_bra: list[int] | None = None, + modes_in_ket: tuple[int, ...] | None = None, + modes_out_ket: tuple[int, ...] | None = None, + modes_in_bra: tuple[int, ...] | None = None, + modes_out_bra: tuple[int, ...] | None = None, ): self._name = name self._update_modes(modes_in_ket, modes_out_ket, modes_in_bra, modes_out_bra) def _update_modes( self, - modes_in_ket: list[int] | None = None, - modes_out_ket: list[int] | None = None, - modes_in_bra: list[int] | None = None, - modes_out_bra: list[int] | None = None, + modes_in_ket: tuple[int, ...] | None = None, + modes_out_ket: tuple[int, ...] | None = None, + modes_in_bra: tuple[int, ...] | None = None, + modes_out_bra: tuple[int, ...] | None = None, ): - self._modes_in_ket = modes_in_ket if modes_in_ket else [] - self._modes_out_ket = modes_out_ket if modes_out_ket else [] - self._modes_in_bra = modes_in_bra if modes_in_bra else [] - self._modes_out_bra = modes_out_bra if modes_out_bra else [] + self._modes_in_ket = modes_in_ket if modes_in_ket else () + self._modes_out_ket = modes_out_ket if modes_out_ket else () + self._modes_in_bra = modes_in_bra if modes_in_bra else () + self._modes_out_bra = modes_out_bra if modes_out_bra else () ``` - [ ] **Apply this suggestion** Suggestion importance[1-10]: 7 Why: Changing from lists to tuples for storing modes can improve performance and reduce memory usage due to the immutability and fixed size of tuples, making this a reasonable suggestion for optimization. However, the impact might be less significant compared to other suggestions.	7

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Codecov Report

Attention: Patch coverage is 7.14286% with 13 lines in your changes missing coverage. Please review.

Project coverage is 89.61%. Comparing base (3a1d8bb) to head (e55355f).

Files with missing lines	Patch %	Lines
mrmustard/physics/wigner.py	7.14%	13 Missing :warning:

Additional details and impacted files

```diff @@ Coverage Diff @@ ## develop #504 +/- ## =========================================== - Coverage 89.77% 89.61% -0.16% =========================================== Files 92 92 Lines 6072 6087 +15 =========================================== + Hits 5451 5455 +4 - Misses 621 632 +11 ``` | [Files with missing lines](https://app.codecov.io/gh/XanaduAI/MrMustard/pull/504?dropdown=coverage&src=pr&el=tree&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=XanaduAI) | Coverage Δ | | |---|---|---| | [mrmustard/math/tensor\_networks/tensors.py](https://app.codecov.io/gh/XanaduAI/MrMustard/pull/504?src=pr&el=tree&filepath=mrmustard%2Fmath%2Ftensor_networks%2Ftensors.py&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=XanaduAI#diff-bXJtdXN0YXJkL21hdGgvdGVuc29yX25ldHdvcmtzL3RlbnNvcnMucHk=) | `94.11% <ø> (ø)` | | | [mrmustard/physics/wigner.py](https://app.codecov.io/gh/XanaduAI/MrMustard/pull/504?src=pr&el=tree&filepath=mrmustard%2Fphysics%2Fwigner.py&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=XanaduAI#diff-bXJtdXN0YXJkL3BoeXNpY3Mvd2lnbmVyLnB5) | `50.00% <7.14%> (-50.00%)` | :arrow_down: | ... and [1 file with indirect coverage changes](https://app.codecov.io/gh/XanaduAI/MrMustard/pull/504/indirect-changes?src=pr&el=tree-more&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=XanaduAI) ------ [Continue to review full report in Codecov by Sentry](https://app.codecov.io/gh/XanaduAI/MrMustard/pull/504?dropdown=coverage&src=pr&el=continue&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=XanaduAI). > **Legend** - [Click here to learn more](https://docs.codecov.io/docs/codecov-delta?utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=XanaduAI) > `Δ = absolute (impact)`, `ø = not affected`, `? = missing data` > Powered by [Codecov](https://app.codecov.io/gh/XanaduAI/MrMustard/pull/504?dropdown=coverage&src=pr&el=footer&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=XanaduAI). Last update [3a1d8bb...e55355f](https://app.codecov.io/gh/XanaduAI/MrMustard/pull/504?dropdown=coverage&src=pr&el=lastupdated&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=XanaduAI). Read the [comment docs](https://docs.codecov.io/docs/pull-request-comments?utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=XanaduAI).