---
title: 'SEQC: Stratify-Elaborate Quantum Compiler'
url: https://www.emergentmind.com/topics/stratify-elaborate-quantum-compiler-seqc
type: topic
---

# SEQC: Stratify-Elaborate Quantum Compiler

The Stratify-Elaborate Quantum Compiler (SEQC) is a hierarchical, parallelized compilation framework designed for chiplet-based quantum architectures. As the field transitions toward modular quantum devices composed of multiple interconnected chiplets, SEQC addresses the critical scalability challenge posed by heterogeneous inter-chiplet connectivity, highly variable gate fidelities, and the need for efficient cross-chiplet allocation and routing. The compiler decomposes large circuits into chiplet-local subcircuits, compiles them in parallel, and optimizes both for end-to-end fidelity and compilation throughput, establishing itself as an effective strategy for scalable modular quantum computation [2501.08478].

## 1. Hierarchical Pipeline Structure

SEQC divides the compilation process into two distinct stages optimized for chiplet-based hardware:

1. **Stratification** (one-time per device topology): An input $n$-qubit circuit $\mathcal{C}$ is partitioned into a set of subcircuits $\{\mathcal{C}_1, \ldots, \mathcal{C}_m\}$, each mapped to at most $k$ qubits, where $k$ is the chiplet size. The partition aims to minimize future inter-chiplet communication by grouping densely interacting qubits.
2. **Elaboration** (per compilation): Each subcircuit $\mathcal{C}_\ell$ is compiled independently onto its assigned chiplet. The process encompasses qubit placement and routing, basis translation into native gate sets, and localized, parallel circuit-level optimizations.

This stratified approach confines high-cost optimization steps to chiplet-local subcircuits, reducing the per-chiplet complexity from $O(n^2)$ to $O(k^2)$, which considerably accelerates compilation for large-scale designs.

## 2. Qubit Assignment and Partitioning Algorithms

During stratification, SEQC employs a parallelized simulated-annealing heuristic to partition logical qubits into subcircuits:

- **Cost Graph Construction**: Nodes represent logical qubits; edges connect $(q_i, q_j)$ weighted by the count $w_{i,j}$ of two-qubit gates between them.
- **Partition Objective**:
  \[
  C_{\rm cut} = \sum_{\substack{i < j\\ q_i, q_j\text{ in different blocks}}} w_{i,j}
  \]
- Multiple independent annealing trials run in parallel. Each annealing step swaps qubits between blocks if it reduces $C_{\rm cut}$. The minimum-cost solution is selected.

Subcircuit-to-chiplet assignment then adapts SABRE-like heuristics for the chiplet supergraph, introducing three classes of SWAP operations: symbiotic (benefits two cross-chiplet edges), commensalistic (helps one without harming others), and parasitic (adverse effect). Candidate layouts are ranked by fidelity-weighted shortest paths, giving preference to high-fidelity, low-latency links between chiplets.

## 3. Subcircuit Compilation and Optimization

Once mapping is fixed, each subcircuit $\mathcal{C}_\ell$ undergoes an elaboration pipeline:

1. **Placement**: Selects an injective mapping $\pi: \{q_0, \ldots, q_{k-1}\} \rightarrow \{Q_0, \ldots, Q_{k-1}\}$ maximizing an estimated gate fidelity via SABRE-style lookahead:
   \[
   H_{\rm look}(\pi) = \sum_{g\in\text{next }\Delta\text{ gates}}\left[(d_\pi(g)+1) - \alpha\ln f_g\right]
   \]
2. **Routing**: For non-adjacent two-qubit gates, inserts a minimal-weight path of SWAPs, with cost per edge $w_e = -\ln f_e + \gamma t_e$, balancing fidelity $f_e$ and latency $t_e$.
3. **Basis Translation**: Decomposes logical gates to the chiplet’s native gate set using polynomial-time algorithms and caches for small unitaries.
4. **Circuit Optimization**: Commutation-and-cancellation is applied in parallel within each chiplet subcircuit. Due to strict partitioning, no cross-chiplet optimizations are needed post-stratification.

## 4. Handling Inter-Chiplet Links

SEQC differentiates between intra-chiplet and inter-chiplet connections, modeling them as distinct edge sets:

- **Resource Heterogeneity**: Typically, intra-chiplet gates demonstrate higher fidelity ($f_{\rm intra} \gg f_{\rm inter}$) and lower duration ($t_{\rm intra} \ll t_{\rm inter}$).
- **Pre-stratification Routing**: Gates necessitating cross-chiplet communication are assigned to “halo” qubits at the chiplet periphery to minimize interaction range.
- **Immutable Cross-Chiplet SWAPs**: Inter-chiplet routes established during stratification remain fixed during elaboration; all subsequent placement/routing cost functions respect the true $f_e$ and $t_e$ values to discourage unnecessary high-cost inter-chiplet operations.

## 5. Performance Metrics and Experimental Results

SEQC benchmarking utilizes circuits from the Supermarq suite (BitCode, PhaseCode, GHZ, VQE, Hamiltonian-Simulation), scaled up to 1000 qubits. The chiplet model assumes a grid of heavy-hexagon 10-qubit chiplets with the following native parameters: intra-chiplet CZ fidelity 99.4%, duration 34 ns; inter-chiplet SWAP fidelity 89.8%, duration 1400 ns.

| Metric                       | SEQC Result                    | Comparison                   |
|------------------------------|-------------------------------|------------------------------|
| Avg. circuit fidelity gain   | +9.3% (up to +49.99%)         | Qiskit “peephole” baseline   |
| Avg. compile speedup         | $3.27\times$ (max $6.74\times$)| Chiplet-unaware Qiskit       |
| Execution time per shot      | $1.92\times$ lower             |                              |
| Stratification cost          | $\sim$ baseline single-run     | Zero overhead on reuse       |

A Qiskit 1.2.4 “peephole” routine, modified for chiplet-unaware baseline comparison, introduces SWAPs post hoc, but does not support fidelity- or latency-aware optimization.

## 6. Parallelization and Scalability

SEQC exploits parallelism at two tiers:

- **Stratification stage**: Each annealing chain is processed in a separate OS thread/process, yielding a pool of independent solutions.
- **Elaboration stage**: Subcircuits are mapped and optimized independently, enabling chiplet-level parallel compilation. For $m$ chiplets of size $k\ll n$, this reduces overall complexity from $O(n^2)$ to $mO(k^2)$.
- Resulting speedups are empirically observed between $3\times$ and $7\times$, with elaboration dominating efficiency gains in large circuits.

## 7. Flexibility and Hyperparameter Tuning

SEQC hyperparameters and objective weights can be tuned for various topologies and device constraints:

- The qubit-to-subcircuit annealer’s schedule and weights are retargetable to accommodate different chiplet numbers and non-uniform or evolving hardware graphs.
- Routing cost weights $(\lambda_{\mathrm{lat}}, \lambda_{\mathrm{err}}, \gamma)$ enable balancing between minimal latency and maximum circuit fidelity.
- For exotic modular topologies, including those with nonuniform or routed interconnects, adjusting the edge weights in the physical chiplet graph $G$ is sufficient; the two-stage logic and fidelity-weighted heuristics extend without modification.

The hierarchical separation of stratification and elaboration, along with chiplet-aware routing, enables highly scalable and hardware-optimized compilation that can adapt to the requirements and constraints of next-generation modular quantum devices [2501.08478].

Source: https://www.emergentmind.com/topics/stratify-elaborate-quantum-compiler-seqc