Benchmarking of quantum gate decomposition frameworks

Abstract

As quantum algorithms grow in sophistication, so does the need to compile them into gate sequences that today’s quantum hardware can actually execute. This thesis explores the problem of quantum gate decomposition — the process of translating high-level unitaries into low-level gates — by benchmarking the performance of two prominent frameworks: Qiskit and Classiq. Focusing on operations central to quantum algorithms, including Multi-Controlled X (MCX) gates, Grover operators, and Haarrandom unitaries, we compare how each framework performs under varying resource constraints and optimization settings.

The results show that while Classiq often produces lower CX gate counts, particularly when ancilla qubits are not available, Qiskit demonstrates greater reliability and flexibility — especially in handling arbitrary unitaries and supporting circuit introspection. The study also examines Bernoulli-sampled Grover circuits to probe trade-offs between gate cost and target fidelity, highlighting the role of stochasticity in resourceconstrained algorithm design.

Beyond deterministic tools, this work introduces a generative approach to gate decomposition using Hidden Markov Models (HMMs). Trained on Qiskit-generated MCX decompositions, these models learned to reproduce gate sequences with structural coherence and moderate fidelity. A sweep over hidden state counts revealed interpretable trade-offs between model complexity and output quality. While simple, the HMMs demonstrate that circuit synthesis can be partially learned — suggesting future directions using more expressive sequence models.

Together, the benchmarking and generative modeling experiments provide a practical lens on decomposition strategies in the NISQ era. They also underscore the value of compiler transparency, learnability, and adaptability in shaping the future of quantum circuit design.