# Using a Deep Quantum Neural Network to Enhance the Fidelity of Quantum Convolutional Codes
## 1 Introduction  
Quantum error correction codes are used to preserve coherent states against noise. They can effectively control operational errors and decoherence. The 9-bit quantum encoding proposed by [PERSON] in 1995 can correct single-bit phase flip error or bit flip error [1]. On this basis, [PERSON], [PERSON] and [PERSON] proposed a basic quantum block code coding framework called Calderbank-Shor-Steane (CSS) code in 1996, using the idea of classical linear block error correction codes, and designed quantum error correction codes using two special classical binary error correction codes [2; 3]. In the same year, [PERSON] proposed the stabilizer code, which is a group-theoretical structure and associated subclass of quantum codes [4]. It provides a general framework which can generate several types of quantum error correcting codes instead of specific codes.  
The stabilizer formalism is very similar to the linear codes in classical error correction. Using the concept of classical error correction, it is very useful in quantum communication by preventing quantum data from encountering noise in a quantum channel. As it plays an important role in quantum error correction, it has been developed over the decades. Quantum convolutional code is a type of error correction code that combines the stabilizer formalism and the concept of traditional convolutional codes. [PERSON] proposed a type of quantum convolutional code based on classical convolutional codes in 1998 [5]. Then, based on the concept of traditional convolutional codes [6], quantum convolutional codes were constructed using the CSS code framework and methods of the stabilizer codes. [PERSON] and [PERSON] first described quantum convolutional codes in 2003 using stabilizer forms and providing an explicit encoding circuit [7]. [PERSON] proposed a tail-biting quantum convolutional code, which has a higher rate and lower decoding complexity [8; 9].  
A good circuit should have low complexity and high reliability. Fidelity is an important factor to evaluate the reliability of the output state. If the fidelity of the states afterthe decoding circuit is low, the result is not credible. Recently, a quantum neural network was proposed to enhance the fidelity of quantum states.  
In 1996, [PERSON] et al. constructed a quantum cellular neural network based on quantum metacellular automata [10] using physical nearest-neighbor connections [11]. In 1998, Dr. [PERSON] first explored quantum neural networks from a multi-universe quantum theoretical viewpoint [12], and later proposed a model for constructing superposed multi-universe quantum neural networks based on this [13], and compared to various conventional neural networks, he found that the performance of quantum neural networks is superior. Subsequently, various models and algorithms such as quantum-derived neural networks [14], quantum associative storage [15], quantum dot molecular models [16], and entangled neural networks [17] were proposed. Recent studies by [PERSON] et al. show that quantum neural networks can learn the unknown unitary operator to process the target quantum state [18]. Based on the study in [18], [PERSON] et al. proposed a quantum QNN neural network framework [19], using quantum feedforward neural networks with the trained unitary operators as quantum perceptions to assist quantum computation and enhance the fidelity of quantum states.  
Consider the case where all quantum gates are noisy. To resist the effect of noise from quantum gate operators, we use quantum neural networks to optimize the input coded states. The effect of resisting quantum gate noise is achieved by learning the unknown unitary operator and applying it to the coded quantum state, thus improving the fidelity of the coded quantum state before entering the quantum noise channel. We provide a simulation to show the effect of applying a quantum neural network on quantum convolutional codes.