Related papers: Neural Network Solution of Non-Markovian Quantum S…
A Markov assumption considers a physical system memoryless to simplify its dynamics. Whereas memory effect or the non-Markovian phenomenon is more general in nature. In the quantum regime, it is challenging to define or quantify the…
Numerical simulation of individual open quantum systems has proven advantages over density operator computations. Quantum state diffusion with a moving basis (MQSD) provides a practical numerical simulation method which takes full advantage…
Quantum Diffusion Models (QDMs) are an emerging paradigm in Generative AI that aims to use quantum properties to improve the performances of their classical counterparts. However, existing algorithms are not easily scalable due to the…
In this paper we present a quantum algorithm that uses noise as a resource. The goal of our quantum algorithm is the calculation of operator averages of an open quantum system evolving in time. Selected low-noise system qubits and noisy…
Understanding how to characterise and mitigate errors is a key challenge in developing reliable quantum architecture for near-term applications. Recent work (arXiv:2103.17243) provides an efficient set of algorithms for analysing unknown…
Flow models are a cornerstone of modern machine learning. They are generative models that progressively transform probability distributions according to learned dynamics. Specifically, they learn a continuous-time Markov process that…
A central task in the field of quantum computing is to find applications where quantum computer could provide exponential speedup over any classical computer. Machine learning represents an important field with broad applications where…
We consider the problem of modeling heterogeneous materials where micro-scale dynamics and interactions affect global behavior. In the presence of heterogeneities in material microstructure it is often impractical, if not impossible, to…
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…
Quantum estimation theory is a reformulation of random statistical theory with the modern language of quantum mechanics. In fact, the density operator plays a role similar to that of probability distribution functions in classical…
Stochastic models of biochemical reaction networks are widely used to capture intrinsic noise in cellular systems. The typical formulation of these models are based on Markov processes for which there is extensive research on efficient…
Drawing from the theory of stochastic differential equations, we introduce a novel sampling method for known distributions and a new algorithm for diffusion generative models with unknown distributions. Our approach is inspired by the…
This work presents a formulation to express and optimize stochastic neural networks as quantum circuits in gate-based quantum computing. Motivated by a classical perceptron, stochastic neurons are introduced and combined into a quantum…
Characterising optical quantum states is essential for the development of quantum technologies. While traditional approaches to perform full quantum state tomography are often experimentally demanding, neuromorphic architectures may provide…
A general quantum search algorithm aims to evolve a quantum system from a known source state $|s\rangle$ to an unknown target state $|t\rangle$. It uses a diffusion operator $D_{s}$ having source state as one of its eigenstates and $I_{t}$,…
We present a quantum algorithm for computational fluid dynamics based on the Lattice-Boltzmann method. Our approach involves a novel encoding strategy and a modified collision operator, assuming full relaxation to the local equilibrium…
We find the conditions under which a quantum regression theorem can be assumed valid for non-Markovian master equations consisting in Lindblad superoperators with memory kernels. Our considerations are based on a generalized Born-Markov…
Quantum information technologies provide promising applications in communication and computation, while machine learning has become a powerful technique for extracting meaningful structures in 'big data'. A crossover between quantum…
One long-standing difficult problem in quantum dissipative dynamics is to solve the spin-boson model in a non-Markovian regime where a tractable systematic master equation does not exist. The spin-boson model is particularly important due…
The presence of noise is currently one of the main obstacles to achieving large-scale quantum computation. Strategies to characterise and understand noise processes in quantum hardware are a critical part of mitigating it, especially as the…