Quantum Computing Method Developed for Nonperturbative Shear Viscosity Calculation

A study by researchers from the InQubator for Quantum Simulation at the University of Washington and the Lawrence Berkeley National Laboratory has developed a quantum computing method to perform a nonperturbative calculation of the shear viscosity for a 2+1 dimensional SU2 gauge theory. The method, which uses the lattice Hamiltonian formulation, could be significant for future research in quantum physics. The team’s findings on the ratio of the shear viscosity and the entropy density align with a well-known holographic result, contributing to the understanding of quantum physics and the study of relativistic heavy ion collisions.

What is the Purpose of the Study on Shear Viscosity in Quantum Computing?

The study, conducted by Francesco Turro, Anthony Ciavarella, and Xiaojun Yao from the InQubator for Quantum Simulation at the University of Washington and the Lawrence Berkeley National Laboratory, aims to perform a nonperturbative calculation of the shear viscosity for a 2+1 dimensional SU2 gauge theory. This is achieved by using the lattice Hamiltonian formulation. The researchers used the exact diagonalization of the lattice Hamiltonian with a local Hilbert space truncation to calculate the retarded Green’s function of the stress-energy tensor. The shear viscosity was then obtained via the Kubo formula.

The researchers accounted for the renormalization group flow of the coupling when taking the continuum limit, but no additional operator renormalization was performed. The ratio of the shear viscosity and the entropy density was found to be consistent with a well-known holographic result at several temperatures on a 4×4 honeycomb lattice with the local electric representation truncated at jmax=1/2.

What are the Findings of the Study?

The researchers also found that the ratio of the spectral function and frequency exhibits a peak structure when the frequency is small. Both the exact diagonalization method and simple matrix product state classical simulation method beyond jmax=1/2 on bigger lattices require exponentially growing resources. Therefore, the researchers developed a quantum computing method to calculate the retarded Green’s function and analyze various systematics of the calculation, including jmax truncation and finite size effects, Trotter errors, and the thermal state preparation efficiency.

The thermal state preparation method still requires resources that grow exponentially with the lattice size, but with a very small prefactor at high temperature. The researchers tested their quantum circuit on both the Quantinuum emulator and the IBM simulator for a small lattice and obtained results consistent with the classical computing ones.

How is the Study Relevant to Quantum Computing?

The study is relevant to quantum computing as it develops a quantum computing method to calculate the retarded Green’s function. This method is used to analyze various systematics of the calculation, including jmax truncation and finite size effects, Trotter errors, and the thermal state preparation efficiency. The researchers’ thermal state preparation method still requires resources that grow exponentially with the lattice size, but with a very small prefactor at high temperature.

What is the Significance of the Study in the Field of Quantum Physics?

The study is significant in the field of quantum physics as it performs a nonperturbative calculation of the shear viscosity for a 2+1 dimensional SU2 gauge theory using the lattice Hamiltonian formulation. The researchers’ findings on the ratio of the shear viscosity and the entropy density being consistent with a well-known holographic result at several temperatures on a 4×4 honeycomb lattice with the local electric representation truncated at jmax=1/2 contribute to the understanding of quantum physics.

What are the Implications of the Study for Future Research?

The implications of the study for future research are significant. The researchers’ development of a quantum computing method to calculate the retarded Green’s function and analyze various systematics of the calculation could be used in future research. The findings on the ratio of the shear viscosity and the entropy density being consistent with a well-known holographic result at several temperatures on a 4×4 honeycomb lattice with the local electric representation truncated at jmax=1/2 could also be explored further in future studies.

What is the Context of the Study in Relation to Relativistic Heavy Ion Collisions?

The scientific goal of relativistic heavy ion collisions is to study the deconfined phase of nuclear matter at finite temperature and/or density, known as the quark-gluon plasma (QGP). The most striking property of the QGP created in current heavy ion collision experiments is its small shear viscosity, as shown by the good agreement between the experimental data on various particles yields and azimuthal distributions and a description that is mainly based on relativistic hydrodynamics. The study’s findings contribute to the understanding of this phenomenon.