Related papers: Splitting the local Hilbert space: MPS-based appro…
Many-body approaches to open quantum systems have recently become powerful tools for investigating the detailed role of dissipative environments in diverse non-equilibrium molecular and condensed matter processes. Here, we report the…
Quantum machine learning (QML) is a rapidly expanding field that merges the principles of quantum computing with the techniques of machine learning. One of the powerful mathematical frameworks in this domain is tensor networks. These…
Motivated by a real failure dataset in a two-dimensional context, this paper presents an extension of the Markov modulated Poisson process (MMPP) to two dimensions. The one-dimensional MMPP has been proposed for the modeling of dependent…
Faithfully simulating the dynamics of open quantum systems requires efficiently addressing the challenge of an infinite Hilbert space. Inspired by the shifted boson operator technique used in ground-state studies of the spin-boson model…
We extend random matrix theory to consider randomly interacting spin systems with spatial locality. We develop several methods by which arbitrary correlators may be systematically evaluated in a limit where the local Hilbert space dimension…
We report on experimental measurement of the Hilbert-Schmidt distance between two two-qubit states by many-particle interference. We demonstrate that our three-step method for measuring distances in Hilbert space is far less complex than…
The advancement of quantum simulators motivates the development of a theoretical framework to assist with efficient state preparation in quantum many-body systems. Generally, preparing a target entangled state via unitary evolution with…
I introduce a modification of continuous matrix product states (CMPS) that makes them adapted to relativistic quantum field theories (QFT). These relativistic CMPS can be used to solve genuine 1+1 dimensional QFT without UV cutoff and…
We present a variational matrix product state (vMPS) for the ground state of the spin-1/2 Heisenberg model. The MPS effectively organizes the various dimer configurations, in faithful reflection of the resonating valence bond (RVB) picture…
We present a method for solving implicit (factored) Markov decision processes (MDPs) with very large state spaces. We introduce a property of state space partitions which we call epsilon-homogeneity. Intuitively, an epsilon-homogeneous…
Based on the MPS formalism, we introduce an ansatz for capturing excited states in finite systems with open boundary conditions, providing a very efficient method for computing, e.g., the spectral gap of quantum spin chains. This method can…
Identifying quantum phases and phase transitions is key to understand complex phenomena in statistical physics. In this work, we propose an unconventional strategy to access quantum phases and phase transitions by visualization based on the…
Quantum turbulence spans length scales from the system size $L$ to the healing length $\xi$, making direct numerical simulations (DNS) of the Gross-Pitaevskii (GP) equation computationally expensive when $L \gg \xi$. We present a matrix…
In this study, we introduce a novel family of tensor networks, termed constrained matrix product states (MPS), designed to incorporate exactly arbitrary discrete linear constraints, including inequalities, into sparse block structures.…
This work presents a comparative study of new and existing optimization and diagonalization methods for solving time-independent partial differential equations (PDEs) using matrix product states (MPS) in the quantized tensor-train formalism…
Stochastic partition models divide a multi-dimensional space into a number of rectangular regions, such that the data within each region exhibit certain types of homogeneity. Due to the nature of their partition strategy, existing partition…
We reformulate the full quantum dynamics of spin systems using a phase space representation based on SU(2) coherent states which generates an exact mapping of the dynamics of any spin system onto a set of stochastic differential equations.…
Tensor networks establish an adaptable framework for the emulation of quantum circuits. By partitioning exponentially large registers and gates into smaller tensors, this unlocks fast transformations through tensor algebra, and grants fine…
To compute approximate solutions for combinatorial optimization problems, we describe variational methods based on the product state (PS) and matrix product state (MPS) ansatzes. We perform variational energy minimization with respect to a…
In this note, we describe a method for reconstructing matrix product states from a small number of efficiently-implementable measurements. Our method is exponentially faster than standard tomography, and it can also be used to certify that…