相关论文: Spin chain simulations with a meron cluster algori…
The simulation of spin models close to critical points of continuous phase transitions is heavily impeded by the occurrence of critical slowing down. A number of cluster algorithms, usually based on the Fortuin-Kasteleyn representation of…
We show how to combine the light-cone and matrix product algorithms to simulate quantum systems far from equilibrium for long times. For the case of the XXZ spin chain at $\Delta=0.5$, we simulate to a time of $\approx 22.5$. While part of…
An order parameter, termed the maximal row correlation, is proposed for classical spin systems. Monte Carlo simulations on various Potts models suggest that this order parameter is applicable to a broad range of spin systems, including…
The physics of interacting integer-spin chains has been a topic of intense theoretical interest, particularly in the context of symmetry-protected topological phases. However, there has not been a controllable model system to study this…
Quantum spin systems with strong geometric restrictions give rise to rich quantum phases such as valence bond solids and spin liquid states. However, the geometric restrictions often hamper the application of sophisticated numerical…
Numerical simulations of strongly correlated electron systems suffer from the notorious fermion sign problem which has prevented progress in understanding if systems like the Hubbard model display high-temperature superconductivity. Here we…
Classical simulation of quantum computation is necessary for studying the numerical behavior of quantum algorithms, as there does not yet exist a large viable quantum computer on which to perform numerical tests. Tensor network (TN)…
In recent years, a better understanding of the Monte Carlo method has provided us with many new techniques in different areas of statistical physics. Of particular interest are so called cluster methods, which exploit the considerable…
The spin network simulator model represents a bridge between (generalized) circuit schemes for standard quantum computation and approaches based on notions from Topological Quantum Field Theories (TQFT). More precisely, when working with…
The sign problem in quantum Monte Carlo calculations is analyzed using the meron-cluster solution. The concept of merons can be used to solve the sign problem for a limited class of models. Here we show that the method can be used to…
An efficient Monte Carlo algorithm for the simulation of spin models with long-range interactions is discussed. Its central feature is that the number of operations required to flip a spin is independent of the number of interactions…
Using Suzuki-Trotter decompositions of exponential operators we describe new algorithms for the numerical integration of the equations of motion for classical spin systems. These techniques conserve spin length exactly and, in special…
We describe methods to construct digital quantum simulation algorithms for quantum spin systems on a regular lattice with local interactions. In addition to tools such as the Trotter-Suzuki expansion and graph coloring, we also discuss the…
Quantum simulation is a foundational application for quantum computers, projected to offer insights into complex quantum systems beyond the reach of classical computation. However, with the exception of Trotter-based methods, which suffer…
We demonstrate how correlation functions for non-diagonal operators can be measured with the loop-cluster algorithm for quantum spin models. We introduce the U(1) quantum link model and present the construction of a cluster algorithm for…
We study the real-time simulation of open quantum systems, where the system is modeled by a spin chain, with each spin associated with its own harmonic bath. Our method couples the inchworm method for the spin-boson model and the modular…
We discuss the sign problem arising in Monte Carlo simulations of frustrated quantum spin systems. We show that for a class of ``semi-frustrated'' systems (Heisenberg models with ferromagnetic couplings $J_z(r) < 0$ along the $z$-axis and…
A brief review is given of the physical implementation of quantum computation within spin systems or other two-state quantum systems. The importance of the controlled-NOT or quantum XOR gate as the fundamental primitive operation of quantum…
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…
Hamiltonian simulation is a promising application for quantum computers to achieve a quantum advantage. We present classical algorithms based on tensor network methods to optimize quantum circuits for this task. We show that, compared to…