Related papers: Kernel controlled real-time Complex Langevin simul…
Quantum simulation is known to be capable of simulating certain dynamical systems in continuous time -- Schrodinger's equations being the most direct and well-known -- more efficiently than classical simulation. Any linear dynamical system…
The Complex Langevin (CL) method to simulate `complex probabilities', ideally produces expectation values for the observables that converge to a limit equal to the expectation values obtained with the original complex `probability' measure.…
Quantum machine learning is a growing research field that aims to perform machine learning tasks assisted by a quantum computer. Kernel-based quantum machine learning models are paradigmatic examples where the kernel involves quantum…
Current quantum devices execute specific tasks that are hard for classical computers and have the potential to solve problems such as quantum simulation of material science and chemistry, even without error correction. For practical…
Quantum kernels quantify similarity between data points by measuring the inner product between quantum states, computed through quantum circuit measurements. By embedding data into quantum systems, quantum kernel feature maps, that may be…
Kernel means are frequently used to represent probability distributions in machine learning problems. In particular, the well known kernel density estimator and the kernel mean embedding both have the form of a kernel mean. Unfortunately,…
Quantum kernel methods (QKMs) offer an appealing framework for machine learning on near-term quantum computers. However, QKMs generically suffer from exponential concentration, requiring an exponential number of measurements to resolve the…
Discrete translational symmetry plays a fundamental role in condensed matter physics and lattice gauge theories, enabling the analysis of systems that would otherwise be intractable. Despite this, many open problems remain. Quantum…
The kernel polynomial method allows to sample overall spectral properties of a quantum system, while sparse diagonalization provides accurate information about a few important states. We present a method combining these two approaches…
Kernel methods are of current interest in quantum machine learning due to similarities with quantum computing in how they process information in high-dimensional feature (Hilbert) spaces. Kernels are believed to offer particular advantages…
Linear combination of Hamiltonian simulation (LCHS) connects the general linear non-unitary dynamics with unitary operators and serves as the mathematical backbone of designing near-optimal quantum linear differential equation algorithms.…
Quantum computing gives direct access to the study of real-time dynamics of quantum many-body systems. In principle, it is possible to directly calculate non-equal-time correlation functions, from which one can detect interesting phenomena,…
Quantum machine learning is a rapidly evolving field of research that could facilitate important applications for quantum computing and also significantly impact data-driven sciences. In our work, based on various arguments from complexity…
We study the utility of a complex Langevin (CL) equation as an alternative for the Monte Carlo (MC) procedure in the evaluation of expectation values occurring in fermionic many-body problems. We find that a CL approach is natural in cases…
Quantum kernel methods leverage a kernel function computed by embedding input information into the Hilbert space of a quantum system. However, large Hilbert spaces can hinder generalization capability, and the scalability of quantum kernels…
Dynamical quantum phase transition is a critical phenomenon involving out-of-equilibrium states and broken symmetries without classical analogy. However, when finite-sized systems are analyzed, dynamical singularities of the rate function…
In the landscape of approaches toward the simulation of Lattice Models with complex action the Complex Langevin (CL) appears as a straightforward method with a simple, well defined setup. Its applicability, however, is controlled by certain…
Quantum entanglement is a key ingredient for quantum information processing with capabilities beyond that of classical computation. We study the generation and role of entanglement in the dynamics of spin-1/2 models, both for the design of…
Kernel-based learning algorithms are widely used in machine learning for problems that make use of the similarity between object pairs. Such algorithms first embed all data points into an alternative space, where the inner product between…
Kernel approximation is widely used to scale up kernel SVM training and prediction. However, the memory and computation costs of kernel approximation models are still too high if we want to deploy them on memory-limited devices such as…