Related papers: Quantitative Universal Approximation for Noisy Qua…
Universal approximation theorems are the foundations of classical neural networks, providing theoretical guarantees that the latter are able to approximate maps of interest. Recent results have shown that this can also be achieved in a…
Quantum neural networks generalize classical artificial neural networks into the quantum domain. They are formulated as parameterized quantum circuits which are optimized by measuring and minimizing a suitably chosen loss function. The core…
Quantum neural networks (QNNs) play an important role as an emerging technology in the rapidly growing field of quantum machine learning. While their empirical success is evident, the theoretical explorations of QNNs, particularly their…
The estimation of parameters characterizing dynamical processes is central to science and technology. The estimation error changes with the number N of resources employed in the experiment (which could quantify, for instance, the number of…
At its core, machine learning seeks to train models that reliably generalize beyond noisy observations; however, the theoretical vacuum in which state-of-the-art universal approximation theorems (UATs) operate isolates them from this goal,…
In the current quantum computing paradigm, significant focus is placed on the reduction or mitigation of quantum decoherence. When designing new quantum processing units, the general objective is to reduce the amount of noise qubits are…
We present a theoretical and experimental investigation of the quantization problem for artificial neural networks. We provide a mathematical definition of quantized neural networks and analyze their approximation capabilities, showing in…
The universality of a quantum neural network refers to its ability to approximate arbitrary functions and is a theoretical guarantee for its effectiveness. A non-universal neural network could fail in completing the machine learning task.…
Neural networks enjoy widespread success in both research and industry and, with the imminent advent of quantum technology, it is now a crucial challenge to design quantum neural networks for fully quantum learning tasks. Here we propose…
Quantum error mitigation, a data processing technique for recovering the statistics of target processes from their noisy version, is a crucial task for near-term quantum technologies. Most existing methods require prior knowledge of the…
Quantum kernel methods have been widely recognized as one of promising quantum machine learning algorithms that have potential to achieve quantum advantages. In this paper, we theoretically characterize the power of noisy quantum kernels…
In the race towards quantum computing, the potential benefits of quantum neural networks (QNNs) have become increasingly apparent. However, Noisy Intermediate-Scale Quantum (NISQ) processors are prone to errors, which poses a significant…
Providing non-conservative uncertainty quantification for function estimates derived from noisy observations remains a fundamental challenge in statistical machine learning, particularly for applications in safety-critical domains. In this…
Near-term quantum computers are noisy, and therefore must run algorithms with a low circuit depth and qubit count. Here we investigate how noise affects a quantum neural network (QNN) for state discrimination, applicable on near-term…
In this work, we address the question whether a sufficiently deep quantum neural network can approximate a target function as accurate as possible. We start with simple but typical physical situations that the target functions are physical…
The quantum threshold theorem shows that a noisy quantum computer can accurately and efficiently simulate any ideal quantum computation provided that noise is weakly correlated and its strength is below a critical value known as the quantum…
In this paper, we explore the impact of noise on quantum computing, particularly focusing on the challenges when sampling bit strings from noisy quantum computers as well as the implications for optimization and machine learning…
In the noisy intermediate-scale quantum (NISQ) era, one of the key questions is how to deal with the high noise level existing in physical quantum bits (qubits). Quantum error correction is promising but requires an extensive number (e.g.,…
Even though measurement results obtained in the real world are generally both noisy and continuous, quantum measurement theory tends to emphasize the ideal limit of perfect precision and quantized measurement results. In this article, a…
The quantum computing devices of today have tens to hundreds of qubits that are highly susceptible to noise due to unwanted interactions with their environment. The theory of quantum error correction provides a scheme by which the effects…