Superconducting artificial neural networks and quantum circuits

Xiangzhen Zhou, Yuan Feng, Sanjiang Li

A quantum circuit transformation (QCT) is required when executing a quantum program in a real quantum processing unit (QPU). By inserting auxiliary SWAP gates, a QCT algorithm transforms a quantum circuit to one that satisfies the connectivity constraint imposed by the QPU. Due to the nonnegligible gate error and the limited qubit coherence time of the QPU, QCT algorithms that minimize gate number or circuit depth or maximize the fidelity of output circuits are in urgent need. Unfortunately, finding optimized transformations often involve exhaustive searches, which are extremely time consuming and not practical for most circuits. In this article, we propose a framework that uses a policy artificial neural network (ANN) trained by supervised learning on shallow circuits to help existing QCT algorithms select the most promising SWAP gate. ANNs can be trained offline in a distributed way and the trained ANN can be easily incorporated into QCT algorithms to enable them to search deeper without bringing too much overhead in time complexity. Exemplary embeddings of the trained ANNs into target QCT algorithms demonstrate that the transformation performance can be consistently improved on QPUs with various connectivity structures and random or realistic quantum circuits.

Yamamoto Tsuyoshi

M. S. Moreira, Gian Giacomo Guerreschi, Wouter Vlothuizen +14 more

Abstract Artificial neural networks are becoming an integral part of digital solutions to complex problems. However, employing neural networks on quantum processors faces challenges related to the implementation of non-linear functions using quantum circuits. In this paper, we use repeat-until-success circuits enabled by real-time control-flow feedback to realize quantum neurons with non-linear activation functions. These neurons constitute elementary building blocks that can be arranged in a variety of layouts to carry out deep learning tasks quantum coherently. As an example, we construct a minimal feedforward quantum neural network capable of learning all 2-to-1-bit Boolean functions by optimization of network activation parameters within the supervised-learning paradigm. This model is shown to perform non-linear classification and effectively learns from multiple copies of a single training state consisting of the maximal superposition of all inputs.

Solomon McKiernan, Luca Sapienza

We report on a gate-based variational quantum classifier implemented with single photons and probabilistic gates, to emulate the standard quantum circuit model framework. We evaluate the expressive power of two deployable quantum neural networks (QNNs) by computing their effective dimension, a capacity measure grounded in a proven generalization-error bound, and compare them with classical artificial neural networks (ANNs) of equivalent trainable-parameter count. Supervised binary classification tasks are used to benchmark performance across photonic and superconducting QNNs, both of which exhibit superior converged (lower) cross-entropy loss and (higher) prediction accuracy relative to matched-parameter ANNs. For a nonlinearly separable task, our photonic QNN with a single pair of trainable parameters successfully converged (loss 0.04 and accuracy 100%), whereas the equivalent ANN failed to learn the decision boundary, saturating at random-guessing performance. We simulate photonic quantum circuits, training them on the XOR problem and a two-class Iris subset using gradient-free optimization, and assess their robustness to sampling errors under realistic noise processes including photon loss and phase-shifter imperfections. Circuits with comparatively high effective dimension were deployed remotely on a six-qubit photonic quantum processor, achieving classification accuracies of up to 100% in both online and offline learning settings. Notably, even the simplest QNN deployed, with just two trainable parameters, successfully solved tasks that classically require ANNs with at least quadruple the number of parameters, suggesting an emergent algorithmic advantage. Overall, these results demonstrate a clear proof-of-principle that gate-based QNNs can be realized and trained effectively on current photonic hardware, providing proof of algorithmic advantage on a gate-based photonic QNN.

Robert J. Schoelkopf

Leszek Jaroszynski