Related papers: Finite-size resource scaling for learning quantum …

As the size and richness of available datasets grow larger, the opportunities for solving increasingly challenging problems with algorithms learning directly from data grow at the same pace. Consequently, the capability of learning…

Hybrid quantum systems seek to combine the strength of its constituents to master the fundamental conflicting requirements of quantum technology: fast and accurate systems control together with perfect shielding from the environment,…

As quantum computing advances toward early fault-tolerant machines, testing and verification of quantum programs become urgent but costly, since each execution consumes scarce hardware resources. Unlike in classical software testing, every…

Quantum fidelity estimation is essential for benchmarking quantum states and processes on noisy quantum devices. While stabilizer operations form the foundation of fault-tolerant quantum computing, non-stabilizer resources further enable…

Quantum kernel methods promise enhanced expressivity for learning structured data, but their usefulness has been limited by kernel concentration and barren plateaus. Both effects are mathematically equivalent and suppress trainability. We…

We analyze the scaling parameter, extracted from the fidelity for two different ground states, for the one-dimensional quantum Ising model in a transverse field near the critical point. It is found that, in the thermodynamic limit, the…

Quantum kernel methods, i.e., kernel methods with quantum kernels, offer distinct advantages as a hybrid quantum-classical approach to quantum machine learning (QML), including applicability to Noisy Intermediate-Scale Quantum (NISQ)…

We establish an intriguing connection between quantum phase transitions and bifurcations in the reduced fidelity between two different reduced density matrices for quantum lattice many-body systems with symmetry-breaking orders. Our finding…

Quantum kernel methods are a promising branch of quantum machine learning, yet their effectiveness on diverse, high-dimensional, real-world data remains unverified. Current research has largely been limited to low-dimensional or synthetic…

Domain specific (dis-)similarity or proximity measures used e.g. in alignment algorithms of sequence data, are popular to analyze complex data objects and to cover domain specific data properties. Without an underlying vector space these…

Quantum hardware suffers from intrinsic device heterogeneity and environmental drift, forcing practitioners to choose between suboptimal non-adaptive controllers or costly per-device recalibration. We derive a scaling law lower bound for…

Fidelity quantum kernels have shown promise in classification tasks, particularly when a group structure in the data can be identified and exploited through a covariant feature map. In fact, there exist classification problems on which…

We train convolutional neural networks to predict whether or not a set of measurements is informationally complete to uniquely reconstruct any given quantum state with no prior information. In addition, we perform fidelity benchmarking…

High-fidelity control of quantum bits is paramount for the reliable execution of quantum algorithms and for achieving fault-tolerance, the ability to correct errors faster than they occur. The central requirement for fault-tolerance is…

Berry phases and the quantum-information theoretic notion of fidelity have been recently used to analyze quantum phase transitions from a geometrical perspective. In this paper we unify these two approaches showing that the underlying…

Fidelity approach has been widely used to detect various types of quantum phase transitions, including some that are beyond the Landau symmetry breaking theory, in condensed matter models. However, challenges remain in locating the…

Fidelity is crucial for characterizing transformations of quantum states under various quantum channels, which can be served as a fundamental tool in resource theories. Firstly, we define an $\alpha$-$z$-fidelity as a significant quantity…

Kernel method in machine learning consists of encoding input data into a vector in a Hilbert space called the feature space and modeling the target function as a linear map on the feature space. Given a cost function, computing such an…

Kernel methods are a cornerstone of classical machine learning. The idea of using quantum computers to compute kernels has recently attracted attention. Quantum embedding kernels (QEKs) constructed by embedding data into the Hilbert space…

The behavior of the ground-state fidelity susceptibility in the vicinity of a quantum critical point is investigated. We derive scaling relations describing its singular behavior in the quantum critical regime. Unlike it has been found in…