相关论文: A General Automatic Method for Optimal Constructio…

A zero-site density matrix renormalization algorithm (DMRG0) is proposed to minimize the energy of matrix product states (MPS). Instead of the site tensors themselves, we propose to optimize sequentially the "message" tensors between…

Maximum bipartite matching (MBM) is a fundamental problem in combinatorial optimization with a long and rich history. A classic result of Hopcroft and Karp (1973) provides an $O(m \sqrt{n})$-time algorithm for the problem, where $n$ and $m$…

We present a method to apply the well-known matrix product state (MPS) formalism to partially separable states in solid state systems. The computational effort of our method is equal to the effort of the standard density matrix…

In the ordinal Matroid Secretary Problem (MSP), elements from a weighted matroid are presented in random order to an algorithm that must incrementally select a large weight independent set. However, the algorithm can only compare pairs of…

Minimum Cost Polygon Overlay (MCPO) is a unique two-dimensional optimization problem that involves the task of covering a polygon shaped area with a series of rectangular shaped panels. This has a number of applications in the construction…

We introduce an efficient method to calculate the ground state of one-dimensional lattice models with periodic boundary conditions. The method works in the representation of Matrix Product States (MPS), related to the Density Matrix…

We present an implementation of the relativistic quantum-chemical density matrix renormalization group (DMRG) approach based on a matrix-product formalism. Our approach allows us to optimize matrix product state (MPS) wave functions…

Matrix product states (MPSs) and matrix product operators (MPOs) are fundamental tools in the study of quantum many-body systems, particularly in the context of tensor network methods such as Time-Evolving Block Decimation (TEBD). However,…

We study the classical compilation of quantum circuits for the preparation of matrix product states (MPS), which are quantum states of low entanglement with an efficient classical description. Our algorithm represents a near-term…

We introduce a new paradigm for solving regularized variational problems. These are typically formulated to address ill-posed inverse problems encountered in signal and image processing. The objective function is traditionally defined by…

Matrix product density operator (MPDO) provides an efficient tensor network representation of mixed states on one-dimensional quantum many-body systems. We study a real-space renormalization group transformation of MPDOs represented by a…

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…

Port-Hamiltonian system theory is a well-known framework for the control of complex physical systems. The majority of port-Hamiltonian control design methods base on an explicit input-state-output port-Hamiltonian model for the system under…

Non-commutative polynomial optimization (NPO) problems seek to minimize the state average of a polynomial of some operator variables, subject to polynomial constraints, over all states and operators, as well as the Hilbert spaces where…

The well-conditioned multi-product formula (MPF), proposed by [Low, Kliuchnikov, and Wiebe, 2019], is a simple high-order time-independent Hamiltonian simulation algorithm that implements a linear combination of standard product formulas of…

The maximum bipartite matching problem is among the most fundamental and well-studied problems in combinatorial optimization. A beautiful and celebrated combinatorial algorithm of Hopcroft and Karp (1973) shows that maximum bipartite…

We discuss a few simple modifications to time-dependent density matrix renormalization group (DMRG) algorithms which allow to access larger time scales. We specifically aim at beginners and present practical aspects of how to implement…

We show how to construct relevant families of matrix product operators in one and higher dimensions. Those form the building blocks for the numerical simulation methods based on matrix product states and projected entangled pair states. In…

Tensor networks, which are originally developed for characterizing complex quantum many-body systems, have recently emerged as a powerful framework for capturing high-dimensional probability distributions with strong physical…

A major challenge in robotics is to design robust policies which enable complex and agile behaviors in the real world. On one end of the spectrum, we have model-free reinforcement learning (MFRL), which is incredibly flexible and general…