Rivet Transpiler: Efficient Quantum Circuit Conversion

• Rivet Transpiler is a specialized system that converts virtual quantum circuits into device-specific instructions through incremental, segmentwise transpilation.
• It partitions circuits into a reusable 'left' segment and a modifiable 'right' segment, reducing redundant computations especially in iterative quantum machine learning and chemistry workflows.
• By minimizing swap insertions and controlling noise propagation, the system boosts transpilation speed—achieving up to 600% improvement in layerwise training efficiency.

The Rivet Transpiler is a specialized software system designed for accelerating the transformation of quantum circuits written in virtual gate sets to device-specific instructions suitable for execution on quantum hardware. By implementing incremental, segmentwise transpilation and facilitating the reuse of pre-transpiled circuit components, Rivet addresses critical bottlenecks in quantum machine learning workflows, notably where modularity and iterative modifications dominate.

1. Overview of Quantum Circuit Transpilation Challenges

Quantum circuit transpilation encompasses converting high-level quantum logic (virtual gates, arbitrary qubit connectivity) into sequences of native gates constrained by the physical qubit topology of actual devices. Two principal challenges arise: (i) mapping logical qubits ($i, j$) onto physical qubits ($p(i), p(j)$) under the device's adjacency matrix $A$; and (ii) inserting swap and basis gates to compensate for limited connectivity and native gate sets. If $A_{p(i), p(j)} \neq 1$ for a two-qubit gate $U_{ij}$, then the circuit is augmented with additional swap operations $S$:

$U_{ij} \to S \ldots U'_{ij}$

where $U'_{ij}$ is topologically executable. Optimization of circuit depth $D(U)$ and gate count $G(U)$ is further complicated by the exponential sensitivity of quantum algorithms to noise, particularly from two-qubit operations; thus, the transpilation workflow nearly always seeks to

$\min_{U'} \{ D(U') + \lambda G(U') \}$

for some balance parameter $\lambda$.

2. Rivet Transpiler Architecture and Incremental Transpilation

The central innovation of the Rivet transpiler lies in decomposing quantum circuits into a reusable "left" segment $U_{\text{left}}$ and a modifiable "right" segment $U_{\text{right}}$ (Editor's term: left–right partition). Frequently, the former encompasses state-preparation or parameterized blocks common to many evaluations, while the latter encodes measurement adaptations (e.g., basis rotations for Pauli term measurement in quantum chemistry) or incremental layers (in layerwise quantum learning). The transpiler caches $U_\text{left}$ post-transpilation and, upon modification, applies

$U' = U_\text{left} \circ R(U_\text{right})$

where $R(\cdot)$ denotes transpilation with swap-insertion and gate decomposition constrained by device topology. By focusing only on the diffusive segment, Rivet eliminates redundant compilations, markedly reducing computational overhead—especially vital when iterating over large parameter spaces or during adaptive variational quantum algorithm training.

3. Device Mapping, Coupling Constraints, and Noise Considerations

The mapping

$$T: \text{logical qubits} \to \text{physical qubits}$$

must satisfy $A_{T(i), T(j)} = 1$ for each two-qubit gate in $U_\text{right}$ post-stitching. Rivet achieves minimal swap insertions by reusing the optimized mapping of $U_\text{left}$ and restricting modifications to $U_\text{right}$. This is performed while solving

$$R^* = \arg\min_R \left[ \text{Depth}(R(U_\text{right})) + \lambda\, \text{GateCount}(R(U_\text{right})) \right]$$

subject to the coupling constraint. Significantly, this approach restricts additions of noisy two-qubit gates, directly improving execution fidelity by limiting decoherence pathways. In practice, fewer swaps translate into lower cumulative error rates—a key driver for performance in NISQ-era quantum hardware.

4. Application in Quantum Machine Learning and Iterative Algorithms

Quantum Layerwise Learning (LL) is emblematic of iterative quantum algorithm construction. Each iteration appends one or more new layers to a pre-existing circuit stack. Standard transpilation requires reprocessing the entire circuit tree, introducing computational inertia as circuit depth grows. Rivet, by segmentwise transpilation, confines this reprocessing to the appended segment. Reported empirical results include up to 600% improvements in transpilation time for LL workflows (Kaczmarek et al., 29 Aug 2025). This directly enables faster PQC (parameterized quantum circuit) training, particularly relevant when thousands of parameter updates are required in variational model optimization.

In quantum chemistry applications, expectation values over Hamiltonian terms require repeated measurement over similarly structured circuits, differing only by appended rotations to encode non-commuting Pauli bases. Rivet reuses the transpiled state-preparation block across all measurement terms, providing clear computational economy.

5. Modular Reuse and Impact on Advanced Circuit Modifications

Rivet's design enables modular transpilation workflows: only altered segments are recompiled, and static segments propagate through large batches of related jobs. This principle generalizes beyond LL and quantum chemistry to any iterative or adaptive algorithm where a major fraction of circuit structure is preserved. For algorithms requiring gradual circuit augmentation—such as quantum autoencoders, modular QML architectures, or quantum feature map updates—the incremental transpiler architecture is crucial for maintaining resource efficiency.

A plausible implication is that such modular transpilation workflows could underpin scalable quantum algorithm deployment pipelines as device sizes and experiment complexity increase, where batch processing and rapid prototyping become standard.

6. Comparative Advantages and Limitations

The Rivet transpiler yields substantial efficiency improvements for use cases characterized by repeated modifications of a stable circuit anchor. Key comparative metrics from (Kaczmarek et al., 29 Aug 2025):

• Up to 600% speedup in transpilation for layerwise training.
• Cleaner separation between device-dependent and algorithm-level logic via left–right circuit segmentation.

Limitations are primarily encountered when the underlying circuit undergoes widespread changes: as the fraction of reused structure diminishes, the advantage of partial transpilation wanes. The approach fundamentally relies on robust device coupling map management and cannot accelerate scenarios where most gates or layout mapping needs global revision.

7. Prospective Extensions and Connections

The Rivet transpiler methodology informs broader approaches for modular software design in quantum computing. Its core paradigm—segmentwise recompilation with reuse—could adapt to other transpilation domains within quantum circuit design, analysis-preserving frameworks in classical event-based systems (notably in high-energy physics contexts such as Rivet/MCgrid or CONTUR (Debbio et al., 2013, Buckley et al., 14 May 2025)), and automated reinterpretation and limit-setting tools. The continuous enrichment of data sources and statistical models in those frameworks suggests possible future integrations, where automated transpilation, modular analysis, and sophisticated data fusion coalesce to advance both simulation fidelity and experimental comparison.

In summary, the Rivet transpiler exemplifies a resource-efficient approach to quantum circuit compilation, underlined by empirical gains in quantum machine learning and quantum chemistry domains. Its segmentwise reuse paradigm is particularly suited for high-repetition, modular, or iteratively updated circuit workflows, and provides a template for scalable transpilation strategies as quantum devices and application spaces progress.