Quantum Circuit Synthesis and Architecture Search

Quantum computing holds the promise of tackling problems beyond the reach of classical algorithms. But designing and refining quantum circuits—especially as the number of qubits increases—can be daunting. This is where quantum circuit synthesis and architecture search come in, applying automated methods such as reinforcement learning (RL), genetic algorithms, and architectural optimizations to produce circuits that balance fidelity, depth, and hardware constraints. Below, I’ll outline why this topic is so critical and highlight three of my related first-author works.

Why Circuit Synthesis Matters

In classical computing, compilers turn high-level code into optimized machine instructions. In quantum computing, we need an analogous process to map desired states or algorithmic steps onto sequences of quantum gates. Given the fragile nature of qubits and gate errors, circuit efficiency is key:

Fewer Gates: Minimizing the gate count reduces noise accumulation.
Shallower Circuits: Shorter circuit depths allow us to finish execution quickly, mitigating decoherence.
Hardware-Specific Constraints: Real quantum devices support only limited gate sets and specific connectivity patterns.

Hence, quantum circuit synthesis and architecture search aim to discover gate sequences that meet these constraints in an automated, data-driven fashion—often outperforming purely manual attempts.

A Reinforcement Learning Environment for Directed Quantum Circuit Synthesis

In our 2024 work [1], we introduced an RL environment specifically built for directed quantum circuit synthesis. Here, an RL agent iteratively chooses gates (from, say, the Clifford+T set) and applies them to qubits, inching closer to a target state.

Open-Source Environment: Standardizing how RL algorithms interface with circuit design.
Stateful Reward: The agent gauges progress based on fidelity to the target state.
Clifford+T Gate Set: A universal set widely used in theoretical fault-tolerant quantum computing.

Early tests showed the RL agent could identify surprisingly compact circuits for small-scale targets. This foundation sets the stage for more advanced RL-driven synthesis in future research.

Architectural Influence on Variational Quantum Circuits in Multi-Agent Reinforcement Learning

Although the above works focus on gate placement and sequence, circuit architecture (i.e., how gates are arranged, how qubits interact, etc.) can also make or break performance. In 2024 [2], we tackled VQC architecture in the context of multi-agent RL, but many of the insights apply equally well to single-circuit design:

Evolutionary Strategies: We used an evolutionary approach to mutate and recombine entire VQC architectures.
Parameter Efficiency: Pruning or reorganizing layers can mitigate barren plateaus and reduce trainable parameters.
Empirical Gains: We observed that certain structural “templates” consistently outperform naive, fully connected circuits in tasks requiring coordinated agent behavior.

While the scenario was multi-agent RL, the notion of “architectural influence” is universally relevant—these same architectural tweaks can help standard circuit synthesis tasks achieve shorter depths or higher fidelity.

Evaluating Mutation Techniques in Genetic Algorithm-Based Quantum Circuit Synthesis

While RL takes an iterative decision-making approach, genetic algorithms (GAs) can also navigate the enormous search space of circuit designs. In our 2025 study [3], we assessed different mutation strategies for GAs—like inserting gates, deleting gates, swapping qubits, or reorganizing gate sequences.

Circuit Population: Begin with a pool of random circuits and evaluate them by fidelity, circuit depth, or T-count.
Mutation Experiments: Tested how various perturbations influence convergence speed and final performance.
Key Finding: A combination of gate delete and swap proved most effective, balancing exploration and preservation of partially correct solutions.

Such GA-based optimizations dovetail nicely with RL approaches—each is suited to exploring different aspects of circuit design.

Looking Ahead

“Quantum circuit synthesis and architecture search” is far from solved. As hardware evolves, so will the constraints (e.g., specialized gate sets, connectivity limits, hardware noise). We anticipate the field advancing in several directions:

Hybrid Approaches: Combining RL and GA, or layering them with local gradient-based methods, to exploit each method’s strengths.
Noise-Aware Design: Integrating hardware calibration data and error models directly into the search process.
High-Level Compilers: Eventually, we want software that automatically compiles a high-level quantum algorithm into an optimized, hardware-specific circuit with minimal user intervention.

Overall, automated circuit design and architecture optimization are essential steps on the road to practical quantum advantage. The works described here offer tangible evidence that machine learning and evolutionary strategies are not just hype—they’re powerful enablers for quantum software innovation.

References

Michael Kölle, Tom Schubert, Philipp Altmann, Maximilian Zorn, Jonas Stein, Claudia Linnhoff-Popien. “A Reinforcement Learning Environment for Directed Quantum Circuit Synthesis”. Proceedings of the 16th International Conference on Agents and Artificial Intelligence - Volume 1: ICAART, pp. 83-94, 2024. DOI: 10.5220/0012383200003636 [PDF] [Code]
Michael Kölle, Tom Bintener, Maximilian Zorn, Gerhard Stenzel, Leo Sünkel, Thomas Gabor, Claudia Linnhoff-Popien. “Evaluating Mutation Techniques in Genetic Algorithm-Based Quantum Circuit Synthesis”. Proceedings of the Genetic and Evolutionary Computation Conference, pp. 907-915, 2025. DOI: 10.1145/3712256.3726402 [PDF]