Related papers: The continuum limit of a tensor network: a path in…
A comprehensive study is performed of general massive, tensor, two-loop Feynman diagrams with two and three external legs. Reduction to generalized scalar functions is discussed. Integral representations, supporting the same class of…
Complex (semi-)classical paths, or instantons, form an integral part of our understanding of quantum physics. Whereas real classical paths describe classically allowed transitions in the real-time Feynman path integral, classically…
Tensor network decompositions of path integrals for simulating open quantum systems have recently been proven to be useful. However, these methods scale exponentially with the system size. This makes it challenging to simulate the…
We show that the formalism of tensor-network states, such as the matrix product states (MPS), can be used as a basis for variational quantum Monte Carlo simulations. Using a stochastic optimization method, we demonstrate the potential of…
Modern approaches to generative modeling of continuous data using tensor networks incorporate compression layers to capture the most meaningful features of high-dimensional inputs. These methods, however, rely on traditional Matrix Product…
We introduce SeeMPS, a Python library dedicated to implementing tensor network algorithms based on the well-known Matrix Product States (MPS) and Quantized Tensor Train (QTT) formalisms. SeeMPS is implemented as a complete finite precision…
We introduce a change of perspective on tensor network states that is defined by the computational graph of the contraction of an amplitude. The resulting class of states, which we refer to as tensor network functions, inherit the…
Understanding the equilibrium properties and out of equilibrium dynamics of quantum field theories are key aspects of fundamental problems in theoretical particle physics and cosmology. However, their classical simulation is highly…
We propose a natural, parameter-free, discrete-variable formulation of Feynman path integrals. We show that for discrete-variable quantum systems, Feynman path integrals take the form of walks on the graph whose weighted adjacency matrix is…
We present a quantum algorithm that additively approximates the value of a tensor network to a certain scale. When combined with existing results, this provides a complete problem for quantum computation. The result is a simple new way of…
The evolution of complex correlated quantum systems such as random circuit networks is governed by the dynamical buildup of both entanglement and entropy. We here introduce a real-time field theory approach -- essentially a fusion of the $G…
Standard quantum mechanics is viewed as a limit of a cut system with artificially restricted dimension of a Hilbert space. Exact spectrum of cut momentum and coordinate operators is derived and the limiting transition to the infinite…
Tensor networks permit computational and entanglement resources to be concentrated in interesting regions of Hilbert space. Implemented on NISQ machines they allow simulation of quantum systems that are much larger than the computational…
In this paper we construct the continuous Matrix Product State (MPS) representation of the vacuum of the field theory corresponding to the continuous limit of an Ising model. We do this by exploiting the observation made by Hastings and…
The signature of a path is a sequence of tensors whose entries are iterated integrals, playing a key role in stochastic analysis and applications. The set of all signature tensors at a particular level gives rise to the universal signature…
A continuously measured quantum system may be described by restricted path integrals (RPI) or equivalently by non-Hermitian Hamiltonians. The measured system is then considered as an open system, the influence of the environment being taken…
Continuous-time Bayesian networks is a natural structured representation language for multicomponent stochastic processes that evolve continuously over time. Despite the compact representation, inference in such models is intractable even…
The quantum $5$-state Potts model is known to possess a perturbative description using complex conformal field theory (CCFT), the analytic continuation of ``theory space" to a complex plane. To study the corresponding complex fixed point on…
Coherent states can be used for diverse applications in quantum physics including the construction of coherent state path integrals. Most definitions make use of a lattice regularization; however, recent definitions employ a continuous-time…
Quantum combs are powerful conceptual tools for capturing multi-time processes in quantum information theory, constituting the most general quantum mechanical process. But, despite their causal nature, they lack a meaningful physical…