Related papers: Efficient Algorithms for Weakly-Interacting Quantu…
We establish an efficient approximation algorithm for the partition functions of a class of quantum spin systems at low temperature, which can be viewed as stable quantum perturbations of classical spin systems. Our algorithm is based on…
We establish a polynomial-time approximation algorithm for partition functions of quantum spin models at high temperature. Our algorithm is based on the quantum cluster expansion of Neto\v{c}n\'y and Redig and the cluster expansion approach…
Long-range quantum systems, in which the interactions decay as $1/r^{\alpha}$, are of increasing interest due to the variety of experimental set-ups in which they naturally appear. Motivated by this, we study fundamental properties of…
We consider a family of quantum spin systems which includes as special cases the ferromagnetic XY model and ferromagnetic Ising model on any graph, with or without a transverse magnetic field. We prove that the partition function of any…
We establish a general framework for developing approximation algorithms for a class of counting problems. Our framework is based on the cluster expansion of abstract polymer models formalism of Koteck\'y and Preiss. We apply our framework…
The problem of simulating the thermal behavior of quantum systems remains a central open challenge in quantum computing. Unlike well-established quantum algorithms for unitary dynamics, \emph{provably efficient} algorithms for preparing…
In this work, we present a compact analytical approximation for the quantum partition function of systems composed of quantum oscillators. The proposed formula is general and applicable to an arbitrary number of oscillators described by a…
A new scheme is proposed which will permit electron spin resonance pulse techniques to be used to realize a quantum computer with a 100 qbits, or more. The computation is performed on effective pure states which correspond to off-diagonal…
The numerical simulation of dynamical phenomena in interacting quantum systems is a notoriously hard problem. Although a number of promising numerical methods exist, they often have limited applicability due to the growth of entanglement or…
We propose and analyze a setup based on (solid-state) qubits coupled to a common multi-mode transmission line, which allows for coherent spin-spin interactions over macroscopic on-chip distances, without any ground-state cooling…
We describe an efficient numerical method for simulating the dynamics and steady states of collective spin systems in the presence of dephasing and decay. The method is based on the Schwinger boson representation of spin operators and uses…
The computational cost of exact methods for quantum simulation using classical computers grows exponentially with system size. As a consequence, these techniques can only be applied to small systems. By contrast, we demonstrate that quantum…
A theoretical spin-based scheme for performing a variety of quantum computations is presented. It makes use of an array of multiple identical computer vectors of phosphorus-doped silicon where the nuclei serve as logical qubits and the…
We present a perfect marginal sampler of the unique Gibbs measure of a spin system on $\mathbb Z^2$. The algorithm is an adaptation of a previous `lazy depth-first' approach by the authors, but relaxes the requirement of strong spatial…
We present an efficient algorithm for twirling a multi-qudit quantum state. The algorithm can be used for approximating the twirling operation in an ensemble of physical systems in which the systems cannot be individually accessed. It can…
We have developed an efficient Monte Carlo algorithm, which accelerates slow Monte Carlo dynamics in quasi-one-dimensional Ising spin systems. The loop algorithm of the quantum Monte Carlo method is applied to the classical spin models with…
We describe an efficient numerical method for simulating the dynamics of interacting spin ensembles in the presence of dephasing and decay. The method builds on the discrete truncated Wigner approximation for isolated systems, which…
For a transverse-field Ising chain with weak long-range interactions we develop a perturbative scheme, based on quantum kinetic equations, around the integrable nearest-neighbour model. We introduce, discuss, and benchmark several…
Kohn-Sham spin-density functional theory provides an efficient and accurate model to study electron-electron interaction effects in quantum dots, but its application to large systems is a challenge. An efficient algorithm for the…
For $d \ge 2$ and all $q\geq q_{0}(d)$ we give an efficient algorithm to approximately sample from the $q$-state ferromagnetic Potts and random cluster models on finite tori $(\mathbb Z / n \mathbb Z )^d$ for any inverse temperature…