Daniele Lizzio Bosco

Massimiliano Incudini, Daniele Lizzio Bosco, Francesco Martini et al.

Quantum computing can empower machine learning models by enabling kernel machines to leverage quantum kernels for representing similarity measures between data. Quantum kernels are able to capture relationships in the data that are not efficiently computable on classical devices. However, there is no straightforward method to engineer the optimal quantum kernel for each specific use case. We present an approach to this problem, which employs optimization techniques, similar to those used in neural architecture search and AutoML, to automatically find an optimal kernel in a heuristic manner. To this purpose we define an algorithm for constructing a quantum circuit implementing the similarity measure as a combinatorial object, which is evaluated based on a cost function and then iteratively modified using a meta-heuristic optimization technique. The cost function can encode many criteria ensuring favorable statistical properties of the candidate solution, such as the rank of the Dynamical Lie Algebra. Importantly, our approach is independent of the optimization technique employed. The results obtained by testing our approach on a high-energy physics problem demonstrate that, in the best-case scenario, we can either match or improve testing accuracy with respect to the manual design approach, showing the potential of our technique to deliver superior results with reduced effort.

Daniele Lizzio Bosco, Lukasz Cincio, Giuseppe Serra et al.

Compiling quantum circuits into Clifford+$T$ gates is a central task for fault-tolerant quantum computing using stabilizer codes. In the near term, $T$ gates will dominate the cost of fault tolerant implementations, and any reduction in the number of such expensive gates could mean the difference between being able to run a circuit or not. While exact synthesis is exponentially hard in the number of qubits, local synthesis approaches are commonly used to compile large circuits by decomposing them into substructures. However, composing local methods leads to suboptimal compilations in key metrics such as $T$-count or circuit depth, and their performance strongly depends on circuit representation. In this work, we address this challenge by proposing \textsc{Q-PreSyn}, a strategy that, given a set of local edits preserving circuit equivalence, uses a RL agent to identify effective sequences of such actions and thereby obtain circuit representations that yield a reduced $T$-count upon synthesis. Experimental results of our proposed strategy, applied on top of well-known synthesis algorithms, show up to a $20\%$ reduction in $T$-count on circuits with up to 25 qubits, without introducing any additional approximation error prior to synthesis.

Jacopo Cossio, Daniele Lizzio Bosco, Riccardo Romanello et al.

Quantum circuit optimization is a central task in Quantum Computing, as current Noisy Intermediate Scale Quantum devices suffer from error propagation that often scales with the number of operations. Among quantum operations, the CNOT gate is of fundamental importance, being the only 2-qubit gate in the universal Clifford+T set. The problem of CNOT gates minimization has been addressed by heuristic algorithms such as the well-known Patel-Markov-Hayes (PMH) for linear reversible synthesis (i.e., CNOT minimization with no topological constraints), and more recently by Reinforcement Learning (RL) based strategies in the more complex case of topology-aware synthesis, where each CNOT can act on a subset of all qubits pairs. In this work we introduce AlphaCNOT, a RL framework based on Monte Carlo Tree Search (MCTS) that address effectively the CNOT minimization problem by modeling it as a planning problem. In contrast to other RL- based solution, our method is model-based, i.e. it can leverage lookahead search to evaluate future trajectories, thus finding more efficient sequences of CNOTs. Our method achieves a reduction of up to 32% in CNOT gate count compared to PMH baseline on linear reversible synthesis, while in the constraint version we report a consistent gate count reduction on a variety of topologies with up to 8 qubits, with respect to state-of-the-art RL-based solutions. Our results suggest the combination of RL with search-based strategies can be applied to different circuit optimization tasks, such as Clifford minimization, thus fostering the transition toward the "quantum utility" era.

Daniele Lizzio Bosco, Shuteng Wang, Giuseppe Serra et al.

Recently, Quantum Visual Fields (QVFs) have shown promising improvements in model compactness and convergence speed for learning the provided 2D or 3D signals. Meanwhile, novel-view synthesis has seen major advances with Neural Radiance Fields (NeRFs), where models learn a compact representation from 2D images to render 3D scenes, albeit at the cost of larger models and intensive training. In this work, we extend the approach of QVFs by introducing QNeRF, the first hybrid quantum-classical model designed for novel-view synthesis from 2D images. QNeRF leverages parameterised quantum circuits to encode spatial and view-dependent information via quantum superposition and entanglement, resulting in more compact models compared to the classical counterpart. We present two architectural variants. Full QNeRF maximally exploits all quantum amplitudes to enhance representational capabilities. In contrast, Dual-Branch QNeRF introduces a task-informed inductive bias by branching spatial and view-dependent quantum state preparations, drastically reducing the complexity of this operation and ensuring scalability and potential hardware compatibility. Our experiments demonstrate that -- when trained on images of moderate resolution -- QNeRF matches or outperforms classical NeRF baselines while using less than half the number of parameters. These results suggest that quantum machine learning can serve as a competitive alternative for continuous signal representation in mid-level tasks in computer vision, such as 3D representation learning from 2D observations.

Riccardo Romanello, Daniele Lizzio Bosco, Jacopo Cossio et al.

CNOT gates are fundamental to quantum computing, as they facilitate entanglement, a crucial resource for quantum algorithms. Certain classes of quantum circuits are constructed exclusively from CNOT gates. Given their widespread use, it is imperative to minimise the number of CNOT gates employed. This problem, known as CNOT minimisation, remains an open challenge, with its computational complexity yet to be fully characterised. In this work, we introduce a novel reinforcement learning approach to address this task. Instead of training multiple reinforcement learning agents for different circuit sizes, we use a single agent up to a fixed size $m$. Matrices of sizes different from m are preprocessed using either embedding or Gaussian striping. To assess the efficacy of our approach, we trained an agent with m = 8, and evaluated it on matrices of size n that range from 3 to 15. The results we obtained show that our method overperforms the state-of-the-art algorithm as the value of n increases.