Related papers: Splitting the local Hilbert space: MPS-based appro…
Solving quantum many-body systems is one of the most significant regimes where quantum computing applies. Currently, as a hardware-friendly computational paradigms, variational algorithms are often used for finding the ground energy of…
Matrix Product States (MPS), also known as Tensor Train (TT) decomposition in mathematics, has been proposed originally for describing an (especially one-dimensional) quantum system, and recently has found applications in various…
We develop a means of simulating the evolution and measurement of a multipartite quantum state under discrete or continuous evolution using another quantum system with states and operators lying in a real Hilbert space. This extends…
We introduce a functional matrix product state (FMPS) based method for simulating the real-space representation of continuous-variable (CV) quantum computation. This approach efficiently simulates non-Gaussian CV systems by leveraging their…
The matrix product state (MPS) belongs to the most important mathematical models in, for example, condensed matter physics and quantum information sciences. However, to realize an $N$-qubit MPS with large $N$ and large entanglement on a…
We derive an exact formula for a matrix product state (MPS) representation (or a PEPS in higher number of dimensions) of the ground state of translationally invariant bosonic lattice systems in terms of a single one-dimensional Euclidean…
Recent contributions in the field of quantum state tomography have shown that, despite the exponential growth of Hilbert space with the number of subsystems, tomography of one-dimensional quantum systems may still be performed efficiently…
Finance, especially option pricing, is a promising industrial field that might benefit from quantum computing. While quantum algorithms for option pricing have been proposed, it is desired to devise more efficient implementations of costly…
The simulation of quantum systems is a task for which quantum computers are believed to give an exponential speedup as compared to classical ones. While ground states of one-dimensional systems can be efficiently approximated using Matrix…
We consider the manifold of all quantum many-body states that can be generated by arbitrary time-dependent local Hamiltonians in a time that scales polynomially in the system size, and show that it occupies an exponentially small volume in…
This paper introduces matrix product state (MPS) decomposition as a new and systematic method to compress multidimensional data represented by higher-order tensors. It solves two major bottlenecks in tensor compression: computation and…
Numerical methods for obtaining exact dynamics of non-Markovian open quantum systems are mostly limited to either small systems or to short-time evolution only. Here, we propose a new algorithm for computing process tensors--matrix product…
Tensor network states, especially Matrix Product States (MPS), are crucial tools for studying how particles in large quantum systems are entangled with each other. MPS are particularly effective for modeling systems in one-dimensional…
This work gives a detailed investigation of matrix product state (MPS) representations for pure multipartite quantum states. We determine the freedom in representations with and without translation symmetry, derive respective canonical…
This paper introduces matrix product state (MPS) decomposition as a computational tool for extracting features of multidimensional data represented by higher-order tensors. Regardless of tensor order, MPS extracts its relevant features to…
We present a novel mapping for studying 2D many-body quantum systems by solving an effective, one-dimensional long-range model in place of the original two-dimensional short-range one. In particular, we address the problem of choosing an…
Recent experiments in quantum simulators have provided evidence for the Many-Body Localized (MBL) phase in 1D and 2D bosonic quantum matter. The theoretical study of such bosonic MBL, however, is a daunting task due to the unbounded nature…
The modified Born series (MBS) is a fast and accurate method for simulating wave propagation in complex structures. In the current implementation of the MBS, the simulation size is limited by the working memory of a single computer or…
We study quantum states generated by a sequence of nearest neighbor bipartite entangling operations along a one-dimensional chain of spin qubits. After a single sweep of such a set of operations, the system is effectively described by a…
This article presents general procedures for constructing, estimating, and testing Hilbert space multi-dimensional (HSM) models, which are based on quantum probability theory. HSM models can be applied to collections of K different…