Learning to Rank Tensor Network Contraction Plans for GPU-Accelerated Quantum Circuit Simulation
Authors: Alfred M. Pastor, Maribel Castillo, Jose M. Badia
Organizations: Department of Computer Science, Universitat de València, 46100 Burjassot, Spain · Department of Computer Science and Engineering, Universitat Jaume I, 12071 Castelló de la Plana, Spain
Abstract
Classical simulation remains essential for developing and validating quantum algorithms, but its cost grows rapidly with circuit size. Tensor-network contraction can reduce this cost by exploiting circuit structure, although its efficiency depends strongly on the chosen contraction plan. On GPUs, plans with similar theoretical complexity may perform very differently because execution also depends on parallelism, reduction structure, memory traffic, and contraction geometry. We present a learning-to-rank framework for selecting efficient contraction plans before executing them. Each plan is represented by structural features derived directly from its sequence of pairwise contractions, and gradient-boosted rankers are trained from GPU measurements using listwise and pairwise objectives. We evaluate the resulting models on diverse circuit families, using separate in-distribution and circuit-family-shift test sets, and compare them with random and MinFill-based baselines. The learned rankers generally identify better plans, with the listwise model providing the strongest overall decision quality. We also study backend shift by comparing empirical plan orderings on two GPU architectures and evaluating the source-trained models on the second device without retraining. The rankings remain substantially, though not perfectly, stable across GPUs, and the models retain useful decision quality. These results support Learning to Rank as a practical way to reduce contraction-plan search, while showing that performance remains partly backend dependent.
Approximate tensor-network simulators enable classical simulation of quantum circuits beyond the reach of exact methods, but selecting optimal approximation parameters -- such as bond dimension thresholds -- remains a costly trial-and-error process. We present a family-aware neural architecture that predicts both the minimum approximation threshold required to achieve target fidelity and the expected wall-clock runtime for quantum circuit simulation, given only the circuit's OpenQASM description and execution context. Our key insight is that quantum circuits from different algorithmic families (e.g., QFT, Grover, VQE) exhibit fundamentally distinct simulation cost profiles due to their differing entanglement structures. We employ family-conditioned residual corrections -- additive, family-specific adjustments atop a shared backbone, drawing on established conditional computation techniques -- enabling the model to capture both universal circuit properties and algorithmic nuances. The architecture incorporates a pretrained family classifier (97.5% accuracy) and domain-informed algorithm fingerprint features derived from gate-composition heuristics. Evaluated on circuits spanning 7--130 qubits across 10 algorithm families, our system achieves 79.5% exact threshold accuracy (91.2% within one rung) and R2=0.82 runtime correlation, with inference completing in approximately 50 ms -- replacing trial-and-error simulation runs that may take minutes to hours. Ablation studies confirm that family-aware modeling provides the single largest performance improvement (+3.2 percentage points), validating the hypothesis that algorithm family is a first-class feature for simulation cost prediction.
Tree tensor networks (TTNs) are widely used in low-rank approximation and quantum many-body simulation. In this work, we present a formal analysis of the quotient geometry underlying the TTN parameter space. Our framework allows for arbitrary horizontal distributions, and we develop efficient first- and second-order optimization algorithms that exploit this geometry. Additionally, we devise a backpropagation algorithm for training TTNs in a kernel learning setting. We validate our methods through numerical experiments on a representative digit classification task and reveal an important tradeoff between two different horizontal distributions that are available for TTNs: while one offers cleaner geometric statements, the other ultimately leads to more efficient algorithms.
Recent work suggests that relational database management systems (RDBMSs) can execute quantum circuit simulation by compiling the simulation into SQL workloads (primarily join-and-aggregate tensor contractions). While early results are promising, they largely focus on a narrow set of highly structured circuits and offer limited support for systematic database research, such as query optimization, physical design, and engine-level evaluation across a broad range of circuits. We present InferQ, a database-oriented benchmark for quantum circuit simulation. InferQ generates general, compositional circuits by assembling subcircuits from a set of circuit templates, emits each simulation task as an RDBMS-ready SQL workload, and extracts circuit and query features (static, graph, SQL, and dynamic) for workload characterization. InferQ also releases a large dataset of 202,975 circuits online, with a web-based viewer to support searching, filtering, and downloading circuits and feature records. In experiments across RDBMS engines (PostgreSQL, SQLite, DuckDB, and Umbra) and the widely used Qiskit Aer simulator, we find that RDBMSs achieve better peak memory usage than Qiskit Aer on more than 50% of the circuits generated by InferQ. Moreover, using InferQ features, lightweight machine learning models (linear and tree-based models) can accurately predict when SQL execution is preferable (with accuracy up to 95.6% for runtime and 97.4% for memory), enabling data-centric simulator selection and opening the door to principled optimization of SQL-based quantum circuit simulation.