Related papers: Robust Polynomials and Quantum Algorithms
In this paper we propose a new approach to quantum neural networks. Our multi-layer architecture avoids the use of measurements that usually emulate the non-linear activation functions which are characteristic of the classical neural…
In this article we give several new results on the complexity of algorithms that learn Boolean functions from quantum queries and quantum examples. Hunziker et al. conjectured that for any class C of Boolean functions, the number of quantum…
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…
The problem of learning Boolean linear functions from quantum examples w.r.t. the uniform distribution can be solved on a quantum computer using the Bernstein-Vazirani algorithm. A similar strategy can be applied in the case of noisy…
Given their potential to demonstrate near-term quantum advantage, variational quantum algorithms (VQAs) have been extensively studied. Although numerous techniques have been developed for VQA parameter optimization, it remains a significant…
We show how to realize a general quantum circuit involving gates between arbitrary pairs of qubits by means of geometrically local quantum operations and efficient classical computation. We prove that circuit-level local stochastic noise…
We study the robustness of a fault-tolerant quantum computer subject to Gaussian non-Markovian quantum noise, and we show that scalable quantum computation is possible if the noise power spectrum satisfies an appropriate "threshold…
Spectral density functions quantify how environmental modes couple to quantum systems and govern their open dynamics. Inferring such frequency-dependent functions from time-domain measurements is an ill-conditioned inverse problem. Here, we…
We discuss quantum algorithms, based on the Bernstein-Vazirani algorithm, for finding which variables a Boolean function depends on. There are 2^n possible linear Boolean functions of n variables; given a linear Boolean function, the…
The goal in function property testing is to determine whether a black-box Boolean function has a certain property or is epsilon-far from having that property. The performance of the algorithm is judged by how many calls need to be made to…
In current noisy intermediate-scale quantum (NISQ) devices, hybrid quantum neural networks (HQNNs) offer a promising solution, combining the strengths of classical machine learning with quantum computing capabilities. However, the…
We study the sensitivity to noise of |permanent(X)|^2 for random real and complex n x n Gaussian matrices X, and show that asymptotically the correlation between the noisy and noiseless outcomes tends to zero when the noise level is…
Quantum Machine Learning (QML) has emerged as a promising field that combines the power of quantum computing with the principles of machine learning. One of the significant challenges in QML is dealing with noise in quantum systems,…
We prove two new results about the randomized query complexity of composed functions. First, we show that the randomized composition conjecture is false: there are families of partial Boolean functions $f$ and $g$ such that $R(f\circ g)\ll…
An $n$-qubit quantum circuit is said to be peaked if it has an output probability that is at least inverse-polynomially large as a function of $n$. We describe a classical algorithm with quasipolynomial runtime $n^{O(\log{n})}$ that…
Derivative Free Optimization is known to be an efficient and robust method to tackle the black-box optimization problem. When it comes to noisy functions, classical comparison-based algorithms are slower than gradient-based algorithms. For…
Recent research has demonstrated that quantum computers can solve certain types of problems substantially faster than the known classical algorithms. These problems include factoring integers and certain physics simulations. Practical…
The dynamics of quantum systems are unavoidably influenced by their environment and in turn observing a quantum system (probe) can allow one to measure its environment: Measurements and controlled manipulation of the probe such as dynamical…
Consider an unknown smooth function $f: [0,1]^d \rightarrow \mathbb{R}$, and say we are given $n$ noisy mod 1 samples of $f$, i.e., $y_i = (f(x_i) + \eta_i)\mod 1$, for $x_i \in [0,1]^d$, where $\eta_i$ denotes the noise. Given the samples…
We prove a new version of the quantum accuracy threshold theorem that applies to non-Markovian noise with algebraically decaying spatial correlations. We consider noise in a quantum computer arising from a perturbation that acts…