Quantum Monte Carlo Tree Search with Fixed Confidence

Nonstabilizerness, commonly referred to as magic, is a fundamental resource underpinning quantum advantage. In this paper, we propose a magic-informed quantum architecture search (QAS) technique that enables control over a quantum resource within the general framework of circuit design. Inspired by the AlphaGo approach, we tackle the problem with a Monte Carlo Tree Search technique equipped with a Graph Neural Network (GNN) that estimates the magic of candidate quantum circuits. The GNN model induces a magic-based bias that steers the search toward either high- or low-magic regimes, depending on the target objective. We benchmark the proposed magic-informed QAS technique on both the structured ground-state energy problem and on the more general quantum state approximation problem, spanning different sizes and target magic levels. Experimental results show that the proposed technique effectively influences the magic across the search tree and notably also on the resulting final circuit, even in regimes where the GNN operates on out-of-distribution instances. Although introducing a problem-agnostic magic bias could, in principle, constrain the search dynamics, we observe consistent improvements in solution quality across all problems tested.

Monte Carlo tree search (MCTS) enables artificial intelligence (AI) decision-making, but requires 55-300 W on conventional processors, limiting edge deployment. In-memory computing (IMC) is energy-efficient on regular workloads but has been considered incompatible with irregular multi-phase algorithms. We introduce phase-to-primitive decomposition, which reformulates each algorithmic phase as a hardware-native IMC primitive. Applied to MCTS, selection, expansion, rollout and backpropagation map to content-addressable memory, combinational logic, a resistive random-access memory (RRAM) crossbar and static random-access memory, keeping search on chip. At 22 nm with fabricated RRAM-array parameters, IMC-MCTS consumes ~60 mW for 9x9 Go, achieving 96x energy efficiency over a central processing unit (CPU) and 65x-2,059x over an H100 graphics processing unit (GPU). It reaches a European Go Federation rating within sample-size uncertainty of open-source Go engines (Pachi-UCT and Michi-C). The same substrate runs eight applications across four AI domains.

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.