Classiq Quantum Synthesis Tools

• Classiq synthesis tools are a suite of quantum circuit synthesis technologies that convert high-level quantum algorithms into optimized circuits tailored to hardware constraints.
• They employ hybrid global-local optimization, advanced SWAP heuristics, and modular decomposition to minimize circuit depth and gate count.
• Benchmarking with standards like QUEKO, these tools address scalability and connectivity challenges to enhance quantum circuit reliability.

Classiq synthesis tools are a suite of quantum circuit synthesis technologies designed to generate, optimize, and compile high-level quantum algorithms into hardware-ready quantum circuits. These tools address the challenges posed by the scalability and physical constraints of current quantum hardware, especially in the context of mapping abstract quantum programs to concrete device topologies under strict connectivity and noise constraints. The Classiq framework incorporates high-level, modular circuit descriptions, advanced combinatorial and heuristic algorithms for layout synthesis, optimization routines minimizing depth and gate count, and support for integration with domain-specific quantum programming languages.

1. Fundamental Objectives and Context

The primary function of Classiq synthesis tools is to bridge the gap between high-level quantum algorithm specifications and executable quantum circuits tailored to hardware constraints. This synthesis process is nontrivial due to:

• Device topology constraints: Limited qubit connectivity and architecture-specific native gate sets.
• Resource minimization requirements: Minimizing circuit depth and gate count to fit within qubit coherence times.
• Scalability demands: Supporting large or modular algorithms while managing exponential increases in compilation complexity.

The layout synthesis problem at the heart of quantum compilation—the process of mapping logical qubits and gates onto a constrained hardware fabric—is provably NP-complete, i.e., there are, in general, no efficient algorithms for solving arbitrary instances optimally (Tan et al., 2020). This complexity informs both the practical limitations of synthesis tools and the research focus on heuristics, approximations, and modular or hierarchical methodologies.

2. Layout Synthesis and Optimality Gaps

A key metric for assessing quantum synthesis tools is the optimality gap: the ratio of the synthesized circuit's resource usage (typically depth or gate count) to the known optimal value for the target hardware layout. Empirical studies using QUEKO benchmarks—circuits for which the optimal depth ($T$) and gate count are known—demonstrate that existing state-of-the-art tools exhibit substantial gaps (Tan et al., 2020):

Device Type / Density	Depth Ratio Range (Synthesized/Optimal)
Rigetti Aspen-4 (sparse)	1.5× (t│ket〉) – 12×
Sycamore/Rochester (dense)	5× – 45×

For example, in the case of the greedy router in Cirq and the approach by Zulehner et al., the gap increases with device size and circuit density, ranging up to 45×, while t│ket〉 on some small/sparse circuits can reach as low as 1.5×. Classiq's tools, by implication, must address these same challenges and are tasked with closing this gap as much as practical for real-world circuits and devices.

The core formula for performance assessment is:

$\text{Depth Ratio} = \frac{T_{\text{sched}}}{T}$

where $T_{\text{sched}}$ is the achieved schedule depth and $T$ is the known optimal.

3. Techniques for Enhanced Synthesis

Given the inherent NP-completeness of depth-optimal layout synthesis (Tan et al., 2020), Classiq synthesis tools must employ hybrid strategies:

1. Hybrid global-local optimization:
   • Use global search to optimize the major dependency chains of the quantum circuit, as exemplified by analysis of QUEKO "backbone" constructions.
   • Apply local optimizations for SWAP insertion and mapping adjustments, often where most depth overhead occurs.
   • Machine learning models or lookahead strategies may be trained on benchmark data to improve these heuristics.
2. Initial placement improvements:
   • Reverse engineering the scrambling in benchmark circuits (e.g., inferring the ideal permutation $\tau^{-1}$) can eliminate the need for excess SWAP gates.
   • Graph matching and subgraph isomorphism algorithms, frequently used in VLSI and classical hardware synthesis, are adapted for qubit allocation.
3. SWAP insertion heuristics:
   • Smart cost functions, sensitive to circuit dependency structures, guide optimal SWAP placements.
   • Lookahead, multi-level planning, and dependency analysis are critical for minimizing incurred overhead.
4. Customization for hardware and problem structure:
   • Adaptive algorithms dynamically adjust routing heuristics based on device-specific parameters (e.g., connectivity, noise rates) and circuit density vectors $(d_1, d_2)$—the ratio of single-qubit to two-qubit gates.
5. Hierarchical and modular decomposition:
   • Circuits are decomposed into submodules; global optimization addresses primary dependencies, with local garnish of remaining operations.
   • Each module can be independently optimized and later composed, a strategy that leverages modular techniques analogous to those in modular system synthesis (Park et al., 2023), improving scalability.

Approach	Targeted Overhead Reduction	Method
Hybrid optimization	Depth, SWAP count	Global+local heuristics
Initial placement	SWAP gates, circuit depth	Graph matching
SWAP heuristics	Depth, gate count	Lookahead, ML-guided
Hardware customization	Overall resource usage	Adaptive algorithms
Hierarchical synthesis	Complexity, scalability	Modular decomposition

4. Integration with High-Level Design and Modular Synthesis

Classiq tools enable quantum circuit designers to specify functionality at a high level, decoupled from low-level gate details. This high-level input may employ modular design patterns:

• High-level modules (e.g., arithmetic subcircuits, QFT, error-correcting code blocks) are synthesized and verified independently, leveraging information hiding and modular contracts as suggested in modular system synthesis (Park et al., 2023).
• Each module’s implementation-agnostic specification (IAS) serves as a contract for composition, maintaining abstraction and allowing independent optimization and verification of submodules.
• Tools automatically infer algebraic specifications for modules after synthesis and use these as the interface for higher-level synthesis tasks.

This modular/hierarchical approach notably mitigates the combinatorial explosion associated with monolithic synthesis, especially as quantum algorithms grow in complexity and size.

5. Benchmarking, Evaluation, and Comparison

Classiq synthesis tools benefit from the use of open, standardized benchmarks such as QUEKO (Tan et al., 2020), allowing quantification of the optimality gap for a wide range of device sizes and circuit densities. Performance is assessed by:

• Measuring synthesized depth and gate count relative to optimal values.
• Benchmarking against state-of-the-art tools (Cirq, Qiskit, t│ket〉, Zulehner et al.'s method).
• Evaluating the impact of improvements in initial placement, modular decomposition, and advanced heuristics, with even modest reductions in the depth ratio translating to substantial increases in effective circuit reliability (i.e., longer decoherence windows).

6. Distinctive Features, Limitations, and Future Development

Distinctive aspects of Classiq synthesis tools include:

• Integration of high-level design languages (e.g., Qmod (Goldfriend et al., 29 Jul 2025)) with a sophisticated optimization backend, enabling concise circuit specification as well as automated tradeoffs between different circuit realizations.
• Automated minimization of key quantum resources such as two-qubit (CX) gate count and circuit width, as highlighted by empirical reductions of up to two orders of magnitude over rigid hand-coded baselines (Goldfriend et al., 29 Jul 2025).

However, optimal depth synthesis remains computationally infeasible for general instances due to NP-completeness (Tan et al., 2020). Future progress thus relies on improved heuristics, adaptive algorithms tailored to hardware constraints, and a rigorous modular decomposition methodology for scalable synthesis.

The development of action plans based on benchmarking, the adoption of modular/hierarchical frameworks for large circuits, and the continual refinement of heuristics, placement, and SWAP strategies are central to ongoing improvements in Classiq synthesis capability.

7. Relationship to Related Tools and Open Challenges

Compared with fully open-source and transparent tools such as the SyReC Synthesizer for reversible circuits (Adarsh et al., 2022) or open-source chemical synthesis planners such as ASKCOS (Tu et al., 3 Jan 2025), Classiq synthesis tools typically address the broader problem of end-to-end quantum circuit compilation with an emphasis on resource-constrained optimization and modularity. While proprietary restrictions are common, the trend toward benchmarking against open standards and the adoption of modular verification/synthesis architectures is shaping the future trajectory of the field.

The significant optimality gaps demonstrated in leading synthesis tools reveal a major opportunity for progress. Enhanced circuit layout synthesis, tightly integrated modular design, and hardware-aware adaptivity represent the ongoing research and engineering directions for Classiq and similar quantum synthesis frameworks.