Related papers: Diffusion-based Quantum Error Mitigation using Sto…
We present a novel generative modeling method called diffusion normalizing flow based on stochastic differential equations (SDEs). The algorithm consists of two neural SDEs: a forward SDE that gradually adds noise to the data to transform…
Error mitigation has been one of the recently sought after methods to reduce the effects of noise when computation is performed on a noisy near-term quantum computer. Interest in simulating stochastic processes with quantum models gained…
Quantum systems can be used to measure various quantities in their environment with high precision. Often, however, their sensitivity is limited by the decohering effects of this same environment. Dynamical decoupling schemes are widely…
One of the major challenges for erroneous quantum computers is undoubtedly the control over the effect of noise. Considering the rapid growth of available quantum resources that are not fully fault-tolerant, it is crucial to develop…
This is a pedagogical review of the possible connection between the stochastic quantization in physics and the diffusion models in machine learning. For machine-learning applications, the denoising diffusion model has been established as a…
Generative models for quantum data pose significant challenges but hold immense potential in fields such as chemoinformatics and quantum physics. Quantum denoising diffusion probabilistic models (QuDDPMs) enable efficient learning of…
Stochastic methods are ubiquitous to a variety of fields, ranging from Physics to Economy and Mathematics. In many cases, in the investigation of natural processes, stochasticity arises every time one considers the dynamics of a system in…
Diffusion models have emerged as a dominant framework for generative modeling, but their mathematical foundations are often presented separately through diffusion probabilistic models, score-based modeling, stochastic differential…
Digital quantum computers are potentially an ideal platform for simulating open quantum many-body systems beyond the digital classical computers. Many studies have focused on obtaining the ground state by simulating time dynamics or…
Generic open quantum systems are notoriously difficult to simulate unless one looks at specific regimes. In contrast, classical dissipative systems can often be effectively described by stochastic processes, which are generally less…
Parameterized Quantum Circuits (PQCs) have been acknowledged as a leading strategy to utilize near-term quantum advantages in multiple problems, including machine learning and combinatorial optimization. When applied to specific tasks, the…
Reaction diffusion systems describe the behaviour of dynamic, interacting, particulate systems. Quantum stochastic processes generalise Brownian motion and Poisson processes, having operator valued It\^{o} calculus machinery. Here it is…
Score-based diffusion models learn to reverse a stochastic differential equation that maps data to noise. However, for complex tasks, numerical error can compound and result in highly unnatural samples. Previous work mitigates this drift…
We develop numerical methods for reaction-diffusion systems based on the equations of fluctuating hydrodynamics (FHD). While the FHD formulation is formally described by stochastic partial differential equations (SPDEs), it becomes similar…
Open quantum systems are a topic of intense theoretical research. The use of master equations to model a system's evolution subject to an interaction with an external environment is one of the most successful theoretical paradigms. General…
Quantum systems of interest are typically coupled to several quantum channels (more generally environments). In this paper, we develop an exact stochastic Schr\"{o}dinger equation for an open quantum system coupled to a hybrid environment…
Large-scale quantum systems require optical coherence between distant quantum devices, necessitating spectral indistinguishability. Scalable solid-state platforms offer promising routes to this goal. However, environmental disorders,…
Quantum computing allows for the manipulation of highly correlated states whose properties quickly go beyond the capacity of any classical method to calculate. Thus one natural problem which could lend itself to quantum advantage is the…
We present a quantum open-system approach to analyze the nonunitary dynamics of a superconducting qubit when it evolves under the influence of external noise. We consider the presence of longitudinal and transverse environmental…
Quantum error correction protects quantum information against environmental noise. When using qubits, a measure of quality of a code is the maximum number of errors that it is able to correct. We show that a suitable notion of ``number of…