Quantum algorithms operate on quantum states through unitary transformations in high dimensional complex Hilbert space. In this work, we propose a machine learning approach to create the quantum circuit using a single-layer complex-valued neural network. The input and ouput quantum states are provided to the network, which is trained to approximate the output state of a given quantum algorithm. To ensure that the fundamental property of unitarity is preserved throughout the training process, we employ optimization in Stiefel Manifold.
Quantum algorithms operate on quantum states through unitary transformations in high dimensional complex Hilbert space. In this work, we propose a machine learning approach to create the quantum circuit using a single-layer complex-valued neural network. The input and ouput quantum states are provided to the network, which is trained to approximate the output state of a given quantum algorithm. To ensure that the fundamental property of unitarity is preserved throughout the training process, we employ optimization in Stiefel Manifold.
This paper presents an adaptive quantum circuit design framework leveraging a neural network to automate the process of circuit creation. Traditional quantum circuit design is often a laborious and iterative process, relying heavily on expert knowledge and trial-and-error. We introduce a novel system that utilizes a trained neural network to automatically generate quantum circuits with optimized properties, aiming to significantly reduce manual effort and accelerate quantum algorithm development. The framework employs a multi-stage training process, beginning with a pre-trained model and iteratively refining it based on a defined set of performance metrics. The core mechanism centers on the neural network's ability to learn the optimal circuit parameters to maximize desired properties such as fidelity, coherence, and connectivity. This approach promises to provide a more efficient and scalable method for quantum circuit design.
The field of quantum neural networks, an emerging interdisciplinary frontier bridging quantum computing and machine learning, has recently garnered substantial attention in the scientific community. In this work, we propose a complex-valued quantum neural network in the quantum circuit framework through expanding the number domains of conventional quantum machine learning architecture from the real-valued domain to the complex-valued plane. Such an expansion can alleviate the unitary constraints in quantum feature maps and optimization blocks, and introduce enhanced nonlinear characteristics. It is proven theoretically that the expressivity can be significantly enhanced through the frequency-dependent adaptability and the exponential or hyperbolic functional distribution extension for the Fourier coefficients of quantum models' outputs. Moreover, analysis based on covering numbers indicates that our algorithm can achieve an adaptive balance between expressivity and generalization via the trainable scaling factor, while exhibiting superior parameter efficiency relative to unitary quantum learning models. The performance of the proposed algorithms is demonstrated through extensive numerical simulations in regression and classification tasks, including an experimental realization on the superconducting quantum processor. Our work advances the harnessing of imaginarity resources of quantum theory for learning tasks, achieving a theoretically grounded performance enhancement, and underscores the potential of improving quantum neural networks through structured design for future applications.
At the moment, quantum circuits are created mainly by manually placing logic elements on lines that symbolize quantum bits. The purpose of creating Quantum Circuit Synthesizer "Naginata" was due to the fact that even with a slight increase in the number of operations in a quantum algorithm, leads to the significant increase in size of the corresponding quantum circuit. This causes serious difficulties both in creating and debugging these quantum circuits. The purpose of our quantum synthesizer is enabling users an opportunity to implement quantum algorithms using higher-level commands. This is achieved by creating generic blocks for frequently used operations such as: the adder, multiplier, digital comparator (comparison operator), etc. Thus, the user could implement a quantum algorithm by using these generic blocks, and the quantum synthesizer would create a suitable circuit for this algorithm, in a format that is supported by the chosen quantum computation environment. This approach greatly simplifies the processes of development and debugging a quantum algorithm. The proposed approach for implementing quantum algorithms has a potential application in the field of machine learning, in this regard, we provided an example of creating a circuit for training a simple neural network. Neural networks have a significant impact on the technological development of the transport and road complex, and there is a potential for improving the reliability and efficiency of their learning process by utilizing quantum computation, through the introduction of quantum computing.
Abstract We show how techniques from machine learning and optimization can be used to find circuits of photonic quantum computers that perform a desired transformation between input and output states. In the simplest case of a single input state, our method discovers circuits for preparing a desired quantum state. In the more general case of several input and output relations, our method obtains circuits that reproduce the action of a target unitary transformation. We use a continuous-variable quantum neural network as the circuit architecture. The network is composed of several layers of optical gates with variable parameters that are optimized by applying automatic differentiation using the TensorFlow backend of the Strawberry Fields photonic quantum computer simulator. We demonstrate the power and versatility of our methods by learning how to use short-depth circuits to synthesize single photons, Gottesman–Kitaev–Preskill states, NOON states, cubic phase gates, random unitaries, cross-Kerr interactions, as well as several other states and gates. We routinely obtain high fidelities above 99% using short-depth circuits, typically consisting of a few hundred gates. The circuits are obtained automatically by simply specifying the target state or gate and running the optimization algorithm.
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.
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.