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IEEE Access

DeepQPrep: Neural Network Augmented Search for Quantum State Preparation

Patrick Selig, Niall P Murphy, David Redmond, Simon J. Caton

Published Jan 1, 2023• 13 citations
Publisher

Abstract

There is an increasing interest in the area of quantum computing but developing quantum algorithms is difficult. Neural Network augmented search algorithms have proven quite successful for general search problems (like program generation) but current approaches to quantum program generation make very restricted use of them. In this paper we present DeepQPrep, a Neural Network based approach to generate quantum circuits for state preparation; a common yet expensive task needed in many applications of quantum computing. We illustrate that Neural Network augmented search algorithms have significant promise for automated quantum program generation; DeepQPrep generated programs were able to solve 99% and 76.9% of 20000 previously unseen state prepartion tasks in a supervised machine learning context within two different application scenarios. The circuits produced by DeepQPrep are also shallower (on average) than their ground truth counterparts. We also compare DeepQPrep to IBM Qiskit’s approach to state preparation and illustrate that even when constrained, DeepQPrep generates significantly shallower circuits despite Qiskit solving more of the state preparation tasks. Based on our results, we argue that neural network augmented search approaches exhibit significant promise for generalised approaches to quantum program induction warranting further study in more complex scenarios.

DOI
10.1109/access.2023.3296802

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There is an increasing interest in the area of quantum computing but developing quantum algorithms is difficult. Neural Network augmented search algorithms have proven quite successful for general search problems (like program generation) but current approaches to quantum program generation make very restricted use of them. In this paper we present DeepQPrep, a Neural Network based approach to generate quantum circuits for state preparation; a common yet expensive task needed in many applications of quantum computing. We illustrate that Neural Network augmented search algorithms have significant promise for automated quantum program generation; DeepQPrep generated programs were able to solve 99% and 76.9% of 20000 previously unseen state prepartion tasks in a supervised machine learning context within two different application scenarios. The circuits produced by DeepQPrep are also shallower (on average) than their ground truth counterparts. We also compare DeepQPrep to IBM Qiskit’s approach to state preparation and illustrate that even when constrained, DeepQPrep generates significantly shallower circuits despite Qiskit solving more of the state preparation tasks. Based on our results, we argue that neural network augmented search approaches exhibit significant promise for generalised approaches to quantum program induction warranting further study in more complex scenarios.
There is increasing interest in the area of quantum computing, but using and developing new quantum algorithms, often represented as quantum circuits, is arduous and requires designers with a wide area of experience. The exploration of techniques for the automatic design of quantum algorithms, i.e., quantum architecture search, is therefore of high importance. This work explores the use of neural networks for quantum architecture search, since neural networks have proven quite successful in various complex search domains, and current approaches in quantum architecture search make very restricted use of them. There are many different domains in which quantum architecture search can be applied. They can be used to compile unitaries into quantum circuits, develop ansätze for variational quantum circuits, or develop new quantum algorithms by applying it to input output pairs of one task one wishes to solve. The focus in this thesis is on the task of quantum state preparation, a very important task in the field of quantum computing, as it is a subroutine in a large number of quantum algorithms like quantum machine learning and Hamiltonian simulation. This thesis approaches the task of quantum architecture search first by establishing the importance of the structure of quantum circuits. This is done with a large-scale study of the influence different circuit structure parameters, such as qubits and depth, have on the performance on variational quantum machine learning. During this research, four guidelines for designing circuits for variational quantum machine learning were established. DeepQPrep, a neural network-augmented deductive search for the automatic design of quantum circuits for quantum state preparation, was proposed. It is able to create non-parameterized quantum circuits to solve 76.9% of a restrictive set of quantum states with quantum circuits that were much shallower than the ones found in the ground-truth data. The model was trained on a dataset created in this thesis as none were available at the time. During the exploration of extensions of DeepQPrep to enable it to solve more arbitrary quantum state preparation problems without the need for labeled data, different challenges became apparent. A study on the difficulty of training neural networks to create parameterized quantum circuits using reinforcement learning found that training is hampered by the barren plateau problem of quantum computing. It shows that the variance of the gradient of the quantum circuit output with respect to its parameters goes exponentially to zero. A study showed that this problem makes the application of neural networks to encode quantum circuits highly challenging when no intermediate quantum state information is used. This culminated in DeepQPrepGrad, which combines parameterized circuits, the inductive search of DeepQPrep, and the reinforcement learning-based approach with more compact representations. By combining these parts with the gradients of quantum circuits, an approach that is able to create parameterized quantum circuits for arbitrary quantum states was obtained. The approach was evaluated on 20000 arbitrary 3-qubit quantum states without the need for any labeled data, resulting in a mean minimal similarity of 0.97 alleviated the found challenges to a large degree. This thesis explored key challenges faced when training neural networks to encode quantum circuits. These challenges are of paramount importance as they potentially affect a wide range of tasks in the field of quantum computing to which neural networks could be applied. Lastly, DeepQPrepGrad provides a significant step forward for the creation of quantum circuits using neural networks. DeepQPrepGrad makes great progress in solving the challenges highlighted above and has the potential to be applicable in a wide range of quantum architecture search tasks, such as variational eigensolver and variational quantum machine learning.
Quantum computers may solve some computing tasks more efficiently than classical computers, but to do so requires the design of appropriate quantum circuits. However, it is hard to design even simple quantum programs. Recent results have shown that deep learning augmented search has the potential to discover good circuits for a problem, but it is not yet sufficiently understood how well deep learning is able to model such a complex domain: the search space and output space grow exponentially. This work explores the ability of neural networks to encode quantum circuits for tasks that require knowledge about the unitary representation of the circuit. To this end, we trained neural networks to directly learn to predict the unitary of a circuit and applied reinforcement learning to train neural networks to solve circuit based quantum state preparation. This work finds that encoding quantum circuits is quite difficult especially with regards to the amount of entanglement applied in both application domains. The use of intermediate states and structure in quantum circuits combined with a reasonable inductive bias, where applicable, can alleviate these problems to some extent. The use of intermediate states also greatly improves the results of Deep Reinforcement Learning for quantum state preparation. Based on these results, we discuss the next set of challenges to address if we are to design neural network-based approaches for the automatic generation of quantum circuits. Add sentence on how it improves things in the end.
State preparation is currently the only means to provide input data for quantum algorithm, but finding the shortest possible sequence of gates to prepare a given state is not trivial. We approach this problem using reinforcement learning (RL), first on an agent that is trained to only prepare a single fixed quantum state. Despite the overhead of training a whole network to just produce one single data point, gradient-based backpropagation appears competitive to genetic algorithms in this scenario and single state preparation thus seems a worthwhile task. In a second case we then train a single network to prepare arbitrary quantum states to some degree of success, despite a complete lack of structure in the training data set. In both cases we find that training is severely improved by using QR decomposition to automatically map the agents' outputs to unitary operators to solve the problem of sparse rewards that usually makes this task challenging.
Designing effective quantum circuits remains a central challenge in quantum computing, as circuit structure strongly influences expressivity, trainability, and hardware feasibility. Current approaches, whether using manually designed circuit templates, fixed heuristics, or automated rules, face limitations in scalability, flexibility, and adaptability, often producing circuits that are poorly matched to the specific problem or quantum hardware. In this work, we propose the Evolutionary eXploration of Augmenting Quantum Circuits (EXAQC), an evolutionary approach to the automated design and training of parameterized quantum circuits (PQCs) which leverages and extends on strategies from neuroevolution and genetic programming. The proposed method jointly searches over gate types, qubit connectivity, parameterization, and circuit depth while respecting hardware and noise constraints. The method supports both Qiskit and Pennylane libraries, allowing the user to configure every aspect. This work highlights evolutionary search as a critical tool for advancing quantum machine learning and variational quantum algorithms, providing a principled pathway toward scalable, problem-aware, and hardware-efficient quantum circuit design. Preliminary results demonstrate that circuits evolved on classification tasks are able to achieve over 90% accuracy on most of the benchmark datasets with a limited computational budget, and are able to emulate target circuit quantum states with high fidelity scores.
Variational quantum algorithms (VQAs) are widely speculated to deliver quantum advantages for practical problems under the quantum–classical hybrid computational paradigm in the near term. Both theoretical and practical developments of VQAs share many similarities with those of deep learning. For instance, a key component of VQAs is the design of task-dependent parameterized quantum circuits (PQCs) as in the case of designing a good neural architecture in deep learning. Partly inspired by the recent success of AutoML and neural architecture search (NAS), quantum architecture search (QAS) is a collection of methods devised to engineer an optimal task-specific PQC. It has been proven that QAS-designed VQAs can outperform expert-crafted VQAs in various scenarios. In this work, we propose to use a neural network based predictor as the evaluation policy for QAS. We demonstrate a neural predictor guided QAS can discover powerful quantum circuit ansatz, yielding state-of-the-art results for various examples from quantum simulation and quantum machine learning. Notably, neural predictor guided QAS provides a better solution than that by the random-search baseline while using an order of magnitude less of circuit evaluations. Moreover, the predictor for QAS as well as the optimal ansatz found by QAS can both be transferred and generalized to address similar problems.
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.