Related papers: Numerically efficient unitary evolution for Hamilt…
Compactly representing and efficently applying linear operators are fundamental ingredients in tensor network methods for simulating quantum many-body problems and solving high-dimensional problems in scientific computing. In this work, we…
Bosonic Gaussian states are ubiquitous in quantum optics and condensed matter physics. While they are efficiently handled within the Gaussian formalism, sampling requires calculating amplitudes in the boson occupation basis. This step,…
We study a restricted class of correlator product states (CPS) for a spin-half chain in which each spin is contained in just two overlapping plaquettes. This class is also a restriction upon matrix product states (MPS) with local dimension…
We introduce a novel method of efficiently simulating the non-equilibrium steady state of large many-body open quantum systems with highly non-local interactions, based on a variational Monte Carlo optimization of a matrix product operator…
Efficient sampling from ensembles of Hamiltonian cycles is critical for predicting the thermodynamic properties of compact polymers, with applications including modeling protein and RNA folding and designing soft materials. Although…
We present an algorithmic construction scheme for matrix-product-operator (MPO) representations of arbitrary $U(1)$-invariant operators whenever there is an expression of the local structure in terms of a finite-states machine (FSM). Given…
Encoding classical data in a quantum state is a key prerequisite of many quantum algorithms. Recently matrix product state (MPS) methods emerged as the most promising approach for constructing shallow quantum circuits approximating input…
We propose and implement a novel hybrid meta-heuristic optimization algorithm for the identification of non-collinear global ground-states in magnetic systems. The inputs to this optimization scheme are directly from non-collinear density…
We propose a framework to design concurrently a frustration-free quantum many-body Hamiltonian and its numerically exact ground states on a sufficiently large finite-size cluster in one and two dimensions using an elementary matrix product…
Matrix exponentiation (ME) is widely used in various fields of science and engineering. For example, the unitary dynamics of quantum systems is described by exponentiation of Hamiltonian operators. However, despite a significant attention,…
A key feature of ground states of gapped local 1D Hamiltonians is their relatively low entanglement --- they are well approximated by matrix product states (MPS) with bond dimension scaling polynomially in the length $N$ of the chain, while…
Simulation of quantum systems is challenging due to the exponential size of the state space. Tensor networks provide a systematically improvable approximation for quantum states. 2D tensor networks such as Projected Entangled Pair States…
A generic method to investigate many-body continuous-variable systems is pedagogically presented. It is based on the notion of matrix product states (so-called MPS) and the algorithms thereof. The method is quite versatile and can be…
In quantum many-body systems, complex dynamics delocalize the physical degrees of freedom. This spreading of information throughout the system has been extensively studied in relation to quantum thermalization, scrambling, and chaos.…
In this work we propose an approach for implementing time-evolution of a quantum system using product formulas. The quantum algorithms we develop have provably better scaling (in terms of gate complexity and circuit depth) than a naive…
We propose a modification technique for discrete time systems for exponentially fast convergence to compact sets. The extension technique allows us to use tools defined on Euclidean spaces to systems evolving on manifolds by modifying the…
We significantly enhance the simulation accuracy of initial Trotter circuits for Hamiltonian simulation of quantum systems by integrating first-order Riemannian optimization with tensor network methods. Unlike previous approaches, our…
Quantum state tomography (QST) is the gold standard technique for obtaining an estimate for the state of small quantum systems in the laboratory. Its application to systems with more than a few constituents (e.g. particles) soon becomes…
The construction of good effective models is an essential part of understanding and simulating complex systems in many areas of science. It is a particular challenge for correlated many body quantum systems displaying emergent physics. We…
We investigate the relation between the scaling of block entropies and the efficient simulability by Matrix Product States (MPS), and clarify the connection both for von Neumann and Renyi entropies (see Table I). Most notably, even states…