# Quantum algorithms for spin models and simulable gate sets for quantum computation

@article{Nest2009QuantumAF, title={Quantum algorithms for spin models and simulable gate sets for quantum computation}, author={Maarten Van den Nest and Wolfgang Dur and Robert Raussendorf and Hans J. Briegel}, journal={Physical Review A}, year={2009}, volume={80}, pages={052334} }

We present simple mappings between classical lattice models and quantum circuits, which provide a systematic formalism to obtain quantum algorithms to approximate partition functions of lattice models in certain complex-parameter regimes. We, e.g., present an efficient quantum algorithm for the six-vertex model as well as a two-dimensional Ising-type model. We show that classically simulating these (complex-parameter) spin models is as hard as simulating universal quantum computation, i.e., BQP…

## 34 Citations

Quantum algorithms for classical lattice models

- Physics, Mathematics
- 2011

We give efficient quantum algorithms to estimate the partition function of (i) the six-vertex model on a two-dimensional (2D) square lattice, (ii) the Ising model with magnetic fields on a planar…

A quantum information approach to statistical mechanics

- Physics
- 2013

We review some connections between quantum information and statistical mechanics. We focus on three sets of results for classical spin models. First, we show that the partition function of all…

Normalizer Circuits and Quantum Computation

- Physics, Computer ScienceArXiv
- 2016

An efficient formalism for simulating families of quantum circuits, that are non-universal but comprise important quantum gates such as QFT or CNOT, is developed and used to design new algorithms that provide quantum speedups.

Commuting quantum circuits and complexity of Ising partition functions

- MathematicsArXiv
- 2013

Instantaneous quantum polynomial-time (IQP) computation is a class of quantum computation consisting only of commuting two-qubit gates and is not universal. Nevertheless, it has been shown that if…

Computing partition functions in the one-clean-qubit model

- Computer Science, Mathematics
- 2021

It is proved that a version of the partition function estimation problem within additive error is complete for the so-called DQC1 complexity class, suggesting that the method provides a super-polynomial speedup for certain parameter values.

Solving search problems by strongly simulating quantum circuits

- Computer ScienceScientific reports
- 2013

This article shows that strong simulation algorithms perform another fundamental task: solving search problems, and enhances the utility of strong simulation methods and extends the class of search problems known to be efficiently simulable.

Measuring complex-partition-function zeros of Ising models in quantum simulators

- PhysicsPhysical Review A
- 2019

Studying the zeros of partition functions in the space of complex control parameters allows one to understand formally how critical behavior of a many-body system can arise in the thermodynamic limit…

Title Commuting quantum circuits and complexity of Ising partitionfunctions

- Mathematics
- 2018

Instantaneous quantumpolynomial-time (IQP) computation is a class of quantum computation consisting only of commuting two-qubit gates and is not universal. Nevertheless, it has been shown that if…

Quantum circuits and low-degree polynomials over F2

- Computer Science, Mathematics
- 2016

This work explores a correspondence between quantum circuits and low-degree polynomials over the finite field F2 and gives proofs of classical hardness results based on quantum circuit concepts and finds efficient classical simulation algorithms for certain classes of quantum circuits based on efficient algorithms for classes of polynomers.

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