rqm-optimize

rqm-optimize is an optional, backend-adjacent SU(2)-aware compression layer for the RQM ecosystem. It compresses contiguous single-qubit gate runs into shorter equivalent forms, reducing unnecessary depth while preserving circuit behavior up to global phase. It operates on Qiskit QuantumCircuit objects after the compiler and lowering stages — it is not the primary optimization stage and does not own the public circuit schema.

Standard-Compatible Quaternion Coordinates

A complete quaternion and a complete conventional complex/SU(2) or matrix representation carry the same transformation information. RQM uses quaternions because they make ordered rotation composition, inverses, normalization, sign handling, residuals, canonicalization, and lowering explicit in one structured coordinate system.

Any claimed benefit must come from a measured implementation or workflow—not from additional physics or information in the representation. This package does not claim quantum-state compression, unique measurement, lower hardware error, or universal compiler superiority.

Purpose

rqm-optimize is a practical SU(2)-aware compression layer for backend-native circuits. It operates after the circuit has already been lowered to a Qiskit QuantumCircuit — that is, after rqm-compiler optimization and rqm-qiskit lowering have already run.

It accepts a Qiskit QuantumCircuit, scans it for contiguous single-qubit gate runs, fuses those runs into minimal SU(2)-equivalent operations, and returns a simplified circuit that is unitary-equivalent to the original up to global phase.

rqm-optimize is complementary to rqm-compiler, not a replacement for it:

• rqm-compiler optimizes in its own internal circuit model, before lowering to a backend.
• rqm-optimize compresses in backend-native / Qiskit circuit space, after lowering.

Use rqm-optimize when you want an extra 1-qubit compression pass after the compiler and lowering stages.

The canonical external/public circuit IR lives in rqm-circuits upstream. rqm-optimize does not consume or define the public wire format — it works on QuantumCircuit objects only.

Stack placement

rqm-core      → math foundation (quaternion / SU(2) / Bloch)
rqm-circuits  → canonical external/public circuit IR
rqm-compiler  → internal optimization / rewriting engine
rqm-qiskit    → Qiskit lowering / execution bridge
rqm-braket    → Braket lowering / execution bridge
rqm-optimize  → optional backend-adjacent optimization / compression layer  ← this package

rqm-optimize is downstream of rqm-circuits, rqm-compiler, and usually rqm-qiskit. It is an optional later-stage pass — the rest of the stack functions without it.

Typical data flow

Studio / API / SDK
    ↓
rqm-circuits payload  (public circuit IR — parsed/validated upstream)
    ↓
rqm-compiler          (internal optimization / rewriting)
    ↓
rqm-qiskit            (lowering to Qiskit QuantumCircuit)
    ↓
rqm-optimize          (optional: backend-adjacent 1-qubit compression)
    ↓
backend run

Some users also call rqm-optimize directly on a hand-written Qiskit QuantumCircuit without going through the full stack — that is a fully supported and practical mode of use.

What rqm-optimize owns / does not own

Owns:

• Backend-adjacent single-qubit compression in Qiskit circuit space
• SU(2)-aware fusion of contiguous one-qubit runs
• Optional native-basis preferences for emitted decompositions (ibm, zyz)
• Optimization metadata about that compression step (OptimizationResult)

Does NOT own:

• Canonical external/public circuit schema → rqm-circuits
• Compiler rewrite / canonicalization logic → rqm-compiler
• Quaternion / SU(2) / Bloch / spinor math primitives → rqm-core
• API wire format → rqm-api
• Studio payload format → Studio + rqm-api

Installation

pip install rqm-optimize

Or from source:

git clone https://github.com/RQM-Technologies-dev/rqm-optimize.git
cd rqm-optimize
pip install -e ".[dev]"

Quickstart

This example shows direct backend-native usage — passing a hand-written Qiskit QuantumCircuit directly to optimize. This is a real and useful mode, though not the canonical ecosystem entry point (which starts at an rqm-circuits payload parsed upstream).

from qiskit import QuantumCircuit
from rqm_optimize import optimize

qc = QuantumCircuit(1)
qc.rx(0.5, 0)
qc.ry(0.3, 0)
qc.rz(0.2, 0)
qc.h(0)
qc.s(0)
qc.t(0)

result = optimize(qc, return_metadata=True)

print("original gates:", result.original_gate_count)    # 6
print("optimized gates:", result.optimized_gate_count)  # 1
print("fused runs:", result.fused_runs)                 # 1
print("original depth:", result.original_depth)         # 6
print("optimized depth:", result.optimized_depth)       # 1
print(result.circuit)

Compiler-path integration

API and Studio users typically originate in rqm-circuits upstream. By the time rqm-optimize is called, the circuit has already crossed the public IR boundary (parsed from an rqm-circuits payload) and the compiler boundary (rqm-compiler optimization). rqm-optimize is a later-stage, backend-adjacent compression pass applied after rqm-qiskit lowering:

public circuit (rqm-circuits) → optimize in compiler space (rqm-compiler)
    → lower to Qiskit (rqm-qiskit) → optional backend-native compression (rqm-optimize) → run

If you are using rqm-compiler to construct circuits and rqm-qiskit to lower them to Qiskit, pass the lowered circuit directly to optimize:

# public IR → compile → lower → optional compress → run
from rqm_qiskit import to_qiskit       # rqm-qiskit lowering bridge
from rqm_optimize import optimize

qiskit_circuit = to_qiskit(compiled_circuit)   # your rqm-compiler output
optimized = optimize(qiskit_circuit)
# submit optimized to your backend of choice

Native-basis preference

Request IBM-native decomposition (rz + sx) to produce circuits that map directly to common superconducting hardware gate sets:

result = optimize(qc, native_basis="ibm", return_metadata=True)
# output gates are rz and sx — no transpilation step needed for IBM backends

Supported native_basis values:

What v0.1 does

• Detects contiguous single-qubit gate runs on each qubit.
• Fuses each run into a single SU(2)-equivalent gate using matrix multiplication followed by Qiskit's OneQubitEulerDecomposer.
• Supports native-basis preference so fused runs can be emitted directly as IBM-native (rz/sx) or analytic ZYZ gates.
• Skips fusion when the decomposition would produce more gates than the original (i.e., only applies optimizations that reduce or maintain gate count).
• Preserves barriers, measurements, resets, and multi-qubit gates exactly as hard boundaries.
• Never mutates the input circuit.
• Returns deterministic output.
• Reports rich metadata: total gate count, circuit depth, single-qubit gate count, fused run count — both before and after.

Supported gates in v0.1

rx, ry, rz, u, u3, u2, u1, p, x, y, z, h, s, sdg, t, tdg, id, sx, sxdg, r, and any generic single-qubit UnitaryGate whose matrix can be extracted.

What v0.1 does not yet do

• Backend-aware native-axis alignment using calibration data (planned for v0.2).
• Quaternionic error metrics and drift-aware path selection (planned).
• Braket circuit support (planned).
• Two-qubit gate optimization.

OptimizationResult fields

Architecture

src/rqm_optimize/
├── __init__.py         # Public API: optimize, OptimizationResult
├── optimizer.py        # Type dispatch, strategy validation, result packaging
├── fusion.py           # Single-qubit run identification and matrix fusion
├── geometry.py         # SU(2) / global-phase normalization helpers
├── metrics.py          # Gate count, depth, 1q gate count, matrix error norms
├── qiskit_adapter.py   # Qiskit instruction inspection, matrix extraction, Euler emission
└── py.typed            # PEP 561 marker

The public surface area is intentionally minimal: optimize() and OptimizationResult. All internal helpers are private.

Development and testing

# Install with dev dependencies.
pip install -e ".[dev]"

# Run tests.
pytest

# Run the example.
python examples/basic_optimize.py

Tests cover:

• Public API importability and __all__ contract.
• Fusion correctness (runs compressed, boundaries respected, equivalence up to global phase).
• Integration tests comparing unitaries using qiskit.quantum_info.Operator.
• Measurement / barrier / multi-qubit structure preservation.
• Metadata fields (original_depth, optimized_depth, original_1q_gate_count, optimized_1q_gate_count) and determinism.
• native_basis parameter: IBM (rz/sx) and ZYZ decomposition paths.

Product ladder

rqm-optimize     → improves circuits today
rqm-calibration  → backend / drift / native-axis intelligence  (future)
rqm-noise        → quaternionic noise and error modeling        (future)

License

Apache License 2.0 — see LICENSE.