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Related Experiment Video

Updated: Jul 7, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

Variational quantum Monte Carlo simulations with tensor-network states.

A W Sandvik¹, G Vidal

¹Department of Physics, Boston University, 590 Commonwealth Avenue, Boston, Massachusetts 02215, USA.

Physical Review Letters

|February 1, 2008

Summary

This summary is machine-generated.

Tensor-network states, like matrix-product states (MPS), offer a new basis for variational quantum Monte Carlo simulations. This approach shows potential for complex quantum systems, improving computational efficiency.

Related Experiment Videos

Last Updated: Jul 7, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

Area of Science:

Quantum physics
Computational condensed matter physics
Quantum many-body systems

Background:

Tensor-network states, particularly matrix-product states (MPS), are powerful tools for describing quantum many-body systems.
Variational quantum Monte Carlo (VQMC) methods are widely used for studying ground-state properties of quantum systems.
Efficient numerical methods are crucial for tackling the complexity of quantum critical phenomena.

Purpose of the Study:

To introduce and validate the use of tensor-network states as a variational basis for quantum Monte Carlo simulations.
To assess the computational efficiency and scalability of this novel approach.
To apply the method to a relevant physical model, the transverse Ising chain at criticality.

Main Methods:

Formulation of VQMC simulations using tensor-network states (MPS) as the variational ansatz.
Implementation of a stochastic optimization technique for parameter optimization.
Performance evaluation on the transverse Ising chain model with periodic boundary conditions, up to 256 spins and bond dimension D=48.

Main Results:

Demonstrated the feasibility of employing MPS as a variational basis within VQMC.
Achieved a formal computational scaling of O(ND^3) for the proposed scheme.
This scaling is significantly more favorable than standard MPS (O(ND^5)) and density matrix renormalization group (O(ND^6)) methods for periodic systems.

Conclusions:

The proposed VQMC approach with tensor-network states offers a computationally advantageous alternative for studying quantum many-body systems.
This method holds promise for enabling simulations of larger and more complex quantum systems at criticality.
The improved scaling could unlock new possibilities in quantum simulation research.