The standard model of quantum computation is based on quantum circuits, where the number and quality of the quantum gates composing the circuit influence the runtime and fidelity of the computation. The fidelity of the decomposition of quantum algorithms, represented as unitary matrices, to bounded depth quantum circuits depends strongly on the set of gates available for the decomposition routine. To investigate this dependence, we explore the design space of discrete quantum gate sets and present a software tool for comparative analysis of quantum processing units and control protocols based on their native gates. The evaluation is conditioned on a set of unitary transformations representing target use cases on the quantum processors. The cost function considers three key factors: (i) the statistical distribution of the decomposed circuits’ depth, (ii) the statistical distribution of process fidelities for the approximate decomposition, and (iii) the relative novelty of a gate set compared to other gate sets in terms of the aforementioned properties. The developed software, called yet another quantum quantizer (YAQQ), enables the discovery of an optimized set of quantum gates through this tunable joint cost function. To identify these gate sets, we use the novelty search algorithm, circuit decomposition techniques (like Solovay–Kitaev, Cartan, and quantum Shannon decomposition), and stochastic optimization to implement YAQQ within the Qiskit quantum simulator environment. YAQQ exploits reachability tradeoffs conceptually derived from quantum algorithmic information theory. Our results demonstrate the pragmatic application of identifying gate sets that are advantageous to popularly used quantum gate sets in representing quantum algorithms. Consequently, we demonstrate pragmatic use cases for YAQQ, including comparing transversal logical gate sets in quantum error correction codes and designing optimal quantum instruction sets for a benchmark suite of quantum algorithms. ... Read more

Quantum circuit performance on noisy intermediate-scale and early fault tolerant devices is constrained by circuit depth, two qubit gate overhead, hardware connectivity and noise. Reinforcement learning (RL) offers a framework for automating circuit design and optimization. It treats circuit construction, compilation, routing and rewriting as sequential decision-making problems. In this review, we synthesize progress in reinforcement learning-based quantum circuit optimization (RL-QCO). We cover variational ansatz search, unitary synthesis, qubit mapping, ZX-calculus simplification and fault-tolerant resource reduction. We organize the field around four Markov decision process design choices. These are state representations, reward functions, action spaces and learning agents. This perspective reveals recurring trade-offs. These include expressivity versus trainability, sparse versus shaped rewards, gate-level versus abstract actions, and general purpose versus hardware-aware policies. We also assess benchmarking practices. Key issues include reproducibility, baselines, hyperparameter sensitivity, generalization across instances and hardware-in-the-loop evaluation. Finally, we outline emerging directions. These include reusable circuit priors, amortized reward evaluation, continual hardware adaptation and integration with fault-tolerant compilation. RL-QCO is positioned as a developing design paradigm for quantum software stacks, rather than a single algorithmic recipe. ... Read more