Variational Quantum Neural Programming

Antonio Macaluso, L. Clissa, Stefano Lodi +1 more

Po‐Wei Huang, Patrick Rebentrost

Hybrid quantum-classical computing in the noisy intermediate-scale quantum (NISQ) era with variational algorithms can exhibit barren plateau issues, causing difficult convergence of gradient-based optimization techniques. In this paper, we discuss "post-variational strategies", which shift tunable parameters from the quantum computer to the classical computer, opting for ensemble strategies when optimizing quantum models. We discuss various strategies and design principles for constructing individual quantum circuits, where the resulting ensembles can be optimized with convex programming. Further, we discuss architectural designs of post-variational quantum neural networks and analyze the propagation of estimation errors throughout such neural networks. Finally, we show that empirically, post-variational quantum neural networks using our architectural designs can potentially provide better results than variational algorithms and performance comparable to that of two-layer neural networks.

Shaopeng Zhu, Shih-Han Hung, Shouvanik Chakrabarti +1 more

Variational Quantum Circuits (VQCs), or the so-called quantum neural-networks, are predicted to be one of the most important near-term quantum applications, not only because of their similar promises as classical neural-networks, but also because of their feasibility on near-term noisy intermediate-size quantum (NISQ) machines. The need for gradient information in the training procedure of VQC applications has stimulated the development of auto-differentiation techniques for quantum circuits. We propose the first formalization of this technique, not only in the context of quantum circuits but also for imperative quantum programs (e.g., with controls), inspired by the success of differentiable programming languages in classical machine learning. In particular, we overcome a few unique difficulties caused by exotic quantum features (such as quantum no-cloning) and provide a rigorous formulation of differentiation applied to bounded-loop imperative quantum programs, its code-transformation rules, as well as a sound logic to reason about their correctness. Moreover, we have implemented our code transformation in OCaml and demonstrated the resource-efficiency of our scheme both analytically and empirically. We also conduct a case study of training a VQC instance with controls, which shows the advantage of our scheme over existing auto-differentiation for quantum circuits without controls.

Syed Muhammad Abuzar Rizvi, Muhammad Shohibul Ulum, Naema Asif +1 more

Francesco Tacchino, Panagiotis Kl. Barkoutsos, Chiara Macchiavello +3 more

In the last few years, quantum computing and machine learning fostered rapid developments in their respective areas of application, introducing new perspectives on how information processing systems can be realized and programmed. The rapidly growing field of Quantum Machine Learning aims at bringing together these two ongoing revolutions. Here we first review a series of recent works describing the implementation of artificial neurons and feed-forward neural networks on quantum processors. We then present an original realization of efficient individual quantum nodes based on variational unsampling protocols. While keeping full compatibility with the overall memory-efficient feed-forward architecture, such a construction effectively reduces the quantum circuit depth required to determine the activation probability of single neurons upon input of the relevant data-encoding quantum states. This suggests a viable approach towards the use of quantum neural networks for pattern classification on near-term quantum hardware.

Bhagaban Swain, Sudipta Roy