[FEATURE] Implement Circuit Segmentation via `.segment()` Method

[TheGupta2012]

Feature Description

• Introduce a .segment() method to pyqasm.QasmModule that partitions quantum circuits into independent segments where no entanglement exists between segments.

• Each segment is returned as a standalone QasmModule object containing:

  • Remapped qubit registers (e.g., PYQASM_SEGMENT_0[i])
  • Gates acting exclusively on the segment's qubits

• Key constraints:

  • We use entangling gates to define an "independently executable segment". Raises an error if the circuit contains measurements or classical controls (unsupported in v1).
  • Qubit order in new registers follows first occurrence in the original circuit.

Motivation

• Parallel Execution: Enables independent segment execution across multiple QPUs.
• Resource Optimization: Splits large circuits for execution on smaller devices.
• Error Containment: Isolates quantum errors to individual segments.

Implementation (Optional)

Preprocessing:

• Validate absence of measurements/classical controls.

• Construct a qubit connectivity graph using multi-qubit gates (edges connect interacting qubits).

Segmentation Algorithm:

• Identify connected components in the graph → segments. Should essentially be a disjoint set union amongst all the qubits present in our program. Inspired by the BlockSplitter in qiskit's dag_circuit.collect_blocks

• For each segment:

  • Create a new register qubit[N] __PYQASM_SEGMENT_<idx>__ (N = segment qubit count).

  • Remap original qubits to new register indices ordered by first gate occurrence.

Module Generation:

• Clone original module headers (OPENQASM 3.0, includes).
• Replace original gates with remapped operations.
• Preserve gate order within segments.

Edge Cases:

• All Single-qubit gates → Divide into a default segment count (say 10) as all qubits are disjoint
• Empty circuits → No OP

Example flow

from pyqasm import loads

qasm_code = """
OPENQASM 3.0;
qubit[4] q;
h q[0]; 
cx q[0], q[1];
h q[2];
cx q[2], q[3];
"""

module = loads(qasm_code)
segments = module.segment()  # Returns 2 QasmModules

print(segments[0])
# Output:
# OPENQASM 3.0;
# qubit[2] __PYQASM_SEGMENT_0__;
# h __PYQASM_SEGMENT_0__[0];
# cx __PYQASM_SEGMENT_0__[0], __PYQASM_SEGMENT_0__[1];

print(segments[1])
# Output:
# OPENQASM 3.0;
# qubit[2] __PYQASM_SEGMENT_1__;
# h __PYQASM_SEGMENT_1__[0];
# cx __PYQASM_SEGMENT_1__[0], __PYQASM_SEGMENT_1__[1];

This is a first draft where we return a list of modules but can potentially be changed in-place addition of these segments to existing module