AI for Quantum Circuits Design

This is the 11th article of Beyond Entropy, a space where the chaos of the future, the speed of emerging technologies and the explosion of opportunities are slowed down, allowing us to turn (qu)bits into our dreams.

This post is for those who want to understand how AI can contribute to quantum computing development. Building useful and efficient quantum computers and algorithms is extremely complex. On the other hand, classical machine learning algorithms have faced a huge explosion leading to today's AI revolution. It is therefore natural to ask whether AI can be a key player in improving quantum algorithms, unlocking some of the difficulties. In today's article, we will explore together a recent paper by the Variational Quantum Eigensolver (VQE) authors themselves, named the Generative Quantum Eigensolver, that shows how classical generative AI can help in the creation of effective quantum circuits.

The outline will be:

• The Generative Quantum Eigensolver: when transformer-based generative algorithms can support quantum circuit design;
• 🇪🇺 EU Digital & Tech news from EU Digital & Tech ;
• 🚀 Job & Research opportunities, talks, and events in AI.

Let’s start!

The Generative Quantum Eigensolver

Classical vs Quantum Algorithms

Classical and quantum algorithms differ fundamentally in their underlying principles, operations, and logical structure. Classical algorithms are based on Boolean logic. They use logical gates like AND, OR, NOT, XOR, etc., which operate on bits that are either 0 or 1. These operations are deterministic, meaning that given a specific input, the output is always the same. Almost all classical logic gates are irreversible. Steps are executed sequentially or in parallel, depending on the architecture. Quantum algorithms make use of quantum circuits, which are algorithms that operate on the principles of quantum mechanics, leveraging superposition, entanglement, and interference. They use quantum gates that operate on qubits, such as Hadamard Gate (creates superposition), Pauli Gates (perform rotations), CNOT (entangle qubits), etc. Quantum gates are reversible, given that they conserve information (even if they cannot copy it for the Non-cloning Theorem), and naturally exploits quantum parallelism. Quantum circuits are designed to prepare quantum states that, when measured, outputs probabilities that encode the solution to a problem.

Building Quantum Algorithms: why is difficult?

Building quantum circuits is challenging because they operates under principles that are fundamentally different from classical intuition. Among other, here are some reasons:

• Quantum gates operate on complex-valued amplitudes, requiring a deep understanding of unitary matrices and linear transformations. Even simple operations like flipping a qubit state can involve applying rotations on the Bloch sphere, which is more abstract than Boolean logic;
• Well established classical programming concepts like loops, branches, and memory do not directly translate to quantum circuits;
• Quantum computations do not yield deterministic outputs. Instead, they provide a probability distribution over possible outcomes.

• The number of qubits and gates grows exponentially with the problem size. Designing scalable circuits that remain efficient is a significant challenge;

In addition, creating a quantum circuit involves designing a sequence of operations that can evolve qubits from an initial state to a state that encodes the answer to a computational problem. Each operation has implications for subsequent operations and the number of qubits and gates grows exponentially with the problem size. Maintaining the quantum coherence necessary for the circuit to operate in quantum mode without decaying into noise is delicate. This sensitivity makes designing robust quantum algorithms inherently more complex than their classical counterparts, where operations are typically discrete and less interdependent.

Generating Quantum Circuits through AI

Deep Learning models have been shown to be able to crack complex problems. We might therefore ask whether AI can help us solving problems in the quantum realm. In particular, given the success of Generative AI in creating text, images, and videos a natural question arises:

Can classical generative models be adapted to generate meaningful quantum circuits?

In other words, being that generative models can learn to produce complex outputs by understanding underlying patterns, can they also learn to formulate quantum circuits based on training data derived from well-performing circuits. Some of the authors of the VQE algorithm (here is a review) wrote a new paper with other collaborators where they propose a solution, named Generative Quantum Eigensolver (GQE), which optimizes a classical generative model to assemble quantum operations that can improve the performance of a quantum circuit.

This method aims to significantly simplify the quantum development process, making it more accessible and efficient by reducing the need for quantum expertise in the initial phases of circuit design.

Transformer for Quantum Eigensolvers

More specifically authors built a simple GQE on top of the classical Transformer architecture, named Generative Pre-trained Transformer for Quantum Eigensolvers (GPT-QE). The goal of GPT-QE is to search for the ground state of a given Hamiltonian, which means navigating a vast state space (that grows exponentially with the number of qubits) to find the state of lowest energy. The transformer is trained on a dataset of effective quantum circuits (instead of text) with the objective of generating meaningful sequences of unitary operations (instead of words) tuned to achieve the desired ground state.

The loss function relies on the logit-mechanism, i.e. a technique that involves adjusting through backpropagation the parameters of the transformer in order to minimize the difference between the outputs of the generative model (often called logits) and the energies associated with the quantum states yielded by the circuits. By adjusting the logits so that they lead to the creation of a quantum state with energy close to the actual energy of the desired state, the model is essentially learning to generate quantum circuits that correctly model the physical system.

🇪🇺 Digital & Tech news from Europe

The European Commission will launch the AI Factories initiative in 2025, starting with seven hubs across the continent where supercomputers, data centres and tech talent will converge. These hubs promote collaboration across Europe, linking universities, startups, and industry players. The Commission’s goal is to set up AI Factories across Europe, reinforcing the EU commitment to advancing AI technology and innovation. Find the official press release with many details here or follow EU Digital & Tech .

Opportunities, talks, and events

I share some opportunities from my network that you might find interesting:

🚀 Job opportunities:

• Senior Data Engineer at mama health , an AI based healthcare startup based in Berlin and Italy (through Lorenzo Famiglini );
• Fineco Bank is looking for a Lead Machine Learning Engineer (via Fabio Fumarola ).

🔬 Research opportunities:

• Several Postdoctoral and PhD positions in Quantum Computing are available at the Jülich Supercomputing Centre (JSC) . The focus will be on hybrid quantum-classical machine learning models and optimisation algorithms for Earth Observation applications (through Gabriele Cavallaro );
• The Quantum Doctoral Programme at UCL London has several PhD positions available in Quantum Computation and Quantum Communications (via Simone Severini ).

📚 Educational opportunities:

• The Master in High-performance Computing MHPC based in Trieste has multiple full scholarships for candidates from developing countries;
• For those unfamiliar, the fellowship is a 12-week program aimed at accelerating climate careers.
• If you wish to apply to the Climatebase Fellowship programme, 12-week program aimed at accelerating climate careers, checkout their application form (via Daniel Hill ).

Thanks for reading and thanks for sharing if you found this content useful! Until the next post!