Refactoring of synthesis of division and modulo operations

[TooMuchDakka]

Description

The current implementation of the synthesis of the division and modulo operations did not create the correct gate sequence and lead to a missmatch between the expected and actual output values when simulating the synthesized circuits. With this PR the implementation of both operations is replaced with the restoring division algorithm defined in Quantum Circuit Designs of Integer Division Optimizing T-count and T-depth. This caused the following changes:

• Both operands now need 2*N ancillary qubits to store the values of the quotient and remainder for each operation.
• The internal SyrecSynthesis interface for the division and modulo operations had to be updated since both
  the quotient and remainder qubits need to be provided for both operations.
• The transistor cost of both operations increased.

Note that the referenced paper also defines a non-restoring division algorithm that requires less transistors to synthesize. At the moment we are not sure whether any of the two division algorithms could be refactored to only require N ancillary qubits (to store the quotient in the division/remainder in the modulo operation) to synthesis.

Fixes #302

Checklist:

• The pull request only contains commits that are related to it.
• I have added appropriate tests and documentation.
• I have made sure that all CI jobs on GitHub pass.
• The pull request introduces no new warnings and follows the project's style guidelines.

[burgholzer]

LGTM

[Copilot]

Pull Request Overview

This PR refactors the synthesis of division and modulo operations by replacing the existing implementation with the restoring division algorithm from "Quantum Circuit Designs of Integer Division Optimizing T-count and T-depth". The changes address a mismatch between expected and actual output values in synthesized circuits.

• Updates division and modulo synthesis to use the restoring division algorithm with proper quotient and remainder calculations
• Modifies the SyrecSynthesis interface to require both quotient and remainder qubits for both operations
• Adds comprehensive test coverage for division and modulo operations with updated cost expectations

Reviewed Changes

Copilot reviewed 6 out of 6 changed files in this pull request and generated 5 comments.

Show a summary per file

File	Description
src/algorithms/synthesis/syrec_synthesis.cpp	Implements new restoring division algorithm for both division and modulo operations
include/algorithms/synthesis/syrec_synthesis.hpp	Updates function signatures to include quotient and remainder parameters
test/unittests/simulation/test_synthesis_basic_operations.cpp	Adds new test cases for division and modulo operations
test/unittests/simulation/data/test_synthesis_of_basic_operations.json	Provides test data with expected input/output pairs for division and modulo
test/configs/circuits_line_aware_synthesis.json	Updates expected circuit metrics for affected test circuits
test/configs/circuits_cost_aware_synthesis.json	Updates expected circuit metrics for affected test circuits

[codecov]

Codecov Report

Attention: Patch coverage is 92.85714% with 2 lines in your changes missing coverage. Please review.

Files with missing lines	Patch %	Lines
src/algorithms/synthesis/syrec_synthesis.cpp	92.8%	0 Missing and 2 partials ⚠️

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