arXiv subjects

Anthony Ciavarella

Publications and source records attributed to Anthony Ciavarella.

5 recordsLinked to original sources

arXiv2024

Classical and Quantum Computing of Shear Viscosity for $2+1D$ SU(2) Gauge Theory

We perform a nonperturbative calculation of the shear viscosity for $(2+1)$-dimensional SU(2) gauge theory by using the lattice Hamiltonian formulation. The retarded Green's function of the stress-energy tensor is calculated from real time evolution via exact diagonalization of the lattice Hamiltonian with a local Hilbert space truncation, and the shear viscosity is obtained via the Kubo formula. When taking the continuum limit, we account for the renormalization group flow of the coupling but no additional operator renormalization. We find the ratio of the shear viscosity and the entropy density $\frac{\eta}{s}$ is consistent with a well-known holographic result $\frac{1}{4\pi}$ at several temperatures on a $4\times4$ honeycomb lattice with the local electric representation truncated at $j_{\rm max}=\frac{1}{2}$. We also find the ratio of the spectral function and frequency $\frac{\rho^{xy}(\omega)}{\omega}$ exhibits a peak structure when the frequency is small. Both the exact diagonalization method and simple matrix product state classical simulation method beyond $j_{\rm max}=\frac{1}{2}$ on bigger lattices require exponentially growing resources. So we develop a quantum computing method to calculate the retarded Green's function and analyze various systematics of the calculation including $j_{\rm max}$ truncation and finite size effects, Trotter errors and the thermal state preparation efficiency. Our thermal state preparation method still requires resources that grow exponentially with the lattice size, but with a very small prefactor at high temperature. We test our quantum circuit on both the Quantinuum emulator and the IBM simulator for a small lattice and obtain results consistent with the classical computing ones.

hep-lat↗

arXiv2022

Some Conceptual Aspects of Operator Design for Quantum Simulations of Non-Abelian Lattice Gauge Theories

In the Kogut-Susskind formulation of lattice gauge theories, a set of quantum numbers resides at the ends of each link to characterize the vertex-local gauge field. We discuss the role of these quantum numbers in propagating correlations and supporting entanglement that ensures each vertex remains gauge invariant, despite time evolution induced by operators with (only) partial access to each vertex Hilbert space. Applied to recent proposals for eliminating vertex-local Hilbert spaces in quantum simulation, we describe how the required entanglement is generated via delocalization of the time evolution operator with nearest-neighbor controls. These hybridizations, organized with qudits or qubits, exchange classical operator preprocessing for reductions in quantum resource requirements that extend throughout the lattice volume.

quant-ph↗

arXiv2022

Simulating Effective QED on Quantum Computers

In recent years simulations of chemistry and condensed materials has emerged as one of the preeminent applications of quantum computing, offering an exponential speedup for the solution of the electronic structure for certain strongly correlated electronic systems. To date, most treatments have ignored the question of whether relativistic effects, which are described most generally by quantum electrodynamics (QED), can also be simulated on a quantum computer in polynomial time. Here we show that effective QED, which is equivalent to QED to second order in perturbation theory, can be simulated in polynomial time under reasonable assumptions while properly treating all four components of the wavefunction of the fermionic field. In particular, we provide a detailed analysis of such simulations in position and momentum basis using Trotter-Suzuki formulas. We find that the number of $T$-gates needed to perform such simulations on a $3D$ lattice of $n_s$ sites scales at worst as $O(n_s^3/ε)^{1+o(1)}$ in the thermodynamic limit for position basis simulations and $O(n_s^{4+2/3}/ε)^{1+o(1)}$ in momentum basis. We also find that qubitization scales slightly better with a worst case scaling of $\widetilde{O}(n_s^{2+2/3}/ε)$ for lattice eQED and complications in the prepare circuit leads to a slightly worse scaling in momentum basis of $\widetilde{O}(n_s^{5+2/3}/ε)$. We further provide concrete gate counts for simulating a relativistic version of the uniform electron gas that show challenging problems can be simulated using fewer than $10^{13}$ non-Clifford operations and also provide a detailed discussion of how to prepare multi-reference configuration interaction states in effective QED which can provide a reasonable initial guess for the ground state. Finally, we estimate the planewave cutoffs needed to accurately simulate heavy elements such as gold.

quant-ph↗

arXiv2021

A Trailhead for Quantum Simulation of SU(3) Yang-Mills Lattice Gauge Theory in the Local Multiplet Basis

Maintaining local interactions in the quantum simulation of gauge field theories relegates most states in the Hilbert space to be unphysical -- theoretically benign, but experimentally difficult to avoid. Reformulations of the gauge fields can modify the ratio of physical to gauge-variant states often through classically preprocessing the Hilbert space and modifying the representation of the field on qubit degrees of freedom. This paper considers the implications of representing SU(3) Yang-Mills gauge theory on a lattice of irreducible representations in both a global basis of projected global quantum numbers and a local basis in which controlled-plaquette operators support efficient time evolution. Classically integrating over the internal gauge space at each vertex (e.g., color isospin and color hypercharge) significantly reduces both the qubit requirements and the dimensionality of the unphysical Hilbert space. Initiating tuning procedures that may inform future calculations at scale, the time evolution of one- and two-plaquettes are implemented on one of IBM's superconducting quantum devices, and early benchmark quantities are identified. The potential advantages of qudit environments, with either constrained 2D hexagonal or 1D nearest-neighbor internal state connectivity, are discussed for future large-scale calculations.

quant-ph↗

arXiv2020

An Algorithm for Quantum Computation of Particle Decays

A quantum algorithm is developed to calculate decay rates and cross sections using quantum resources that scale polynomially in the system size assuming similar scaling for state preparation and time evolution. This is done by computing finite-volume one- and two-particle Green's functions on the quantum hardware. Particle decay rates and two particle scattering cross sections are extracted from the imaginary parts of the Green's function. A $0+1$ dimensional implementation of this method is demonstrated on IBM's superconducting quantum hardware for the decay of a heavy scalar particle to a pair of light scalars.

hep-th↗