We present numerically exact solutions to the full-dimensional Schrodinger Equation for the few-electron gas (few-EG) model of electronic structure theory. Our core methodology uses a Sum-of-Products (SOP) representation of singular potentials to make the fully correlated multi-particle quantum mechanical problem computationally tractable. With full access to periodic wave-functions, we analyze the exchange/correlation, spin symmetry, and thermodynamic ( $T = 0$ K) phases for few-EG systems with up to four explicit electrons per unit cell. We also present pure-spin exchange/correlation functionals for the same few-EG solutions. Finally, we consider the family of few-EG calculations in juxtaposition with the closely related uniform electron gas (UEG) system, for which previous calculations have been performed using density functional theory and quantum Monte Carlo methods. The exact few-EG solutions all display a similar oscillatory behavior at lower densities, which is not predicted by previous UEG simulations.We present numerically exact solutions to the full-dimensional Schrodinger Equation for the few-electron gas (few-EG) model of electronic structure theory. Our core methodology uses a Sum-of-Products (SOP) representation of singular potentials to make the fully correlated multi-particle quantum mechanical problem computationally tractable. With full access to periodic wave-functions, we analyze the exchange/correlation, spin symmetry, and thermodynamic ($T = 0$K) phases for few-EG systems with up to four explicit electrons per unit cell. We also present pure-spin exchange/correlation functionals for the same few-EG solutions. Finally, we consider the family of few-EG calculations in juxtaposition with the closely related uniform electron gas (UEG) system, for which previous calculations have been performed using density functional theory and quantum Monte Carlo methods. The exact few-EG solutions all display a similar oscillatory behavior at lower densities, which is not predicted by previous UEG simulations.

arXiv:1809.07363Sep 19, 20180 citations

Electron-Based Quantum Computing

Chuck Easttom

Springer eBooksJan 1, 20240 citations

Spin-Based Lattice-Gas Quantum Computers in Solids Using Optical Addressing

Marlan O. Scully, Olga A. Kocharovskaya, George R. Welch +3 more

The purpose of this project was to develop quantum computing hardware suitable for implementing quantum lattice-gas algorithms, with eventual application to turbulent flow simulations. A number of quantum systems were investigated, including rare-earth dopants in oxide crystals and in II-VI semiconductors. However, in the option year it was decided to concentrate exclusively on nitrogen-vacancy (NV) color centers in diamond. Surprising, it was found that NV diamond exhibited the key elements needed to develop few-qubit room-temperature solid-state quantum processing nodes. This included the ability to optically initialize and readout the NV electron spin state, fractional millisecond lifetimes for electron spins, and few-nanosecond electron spin Rabi flops. We also demonstrated the relatively long distance (few nanometer) coupling of a single NV spin to the electron spin of a single substitutional nitrogen (N). To achieve long range optical interconnections and entanglement between nodes, cryogenic cooling will likely still be required to sufficiently narrow the optical absorption lines. To this end we located diamond samples with unusually high purity, and found NV centers in these crystals that exhibited exceptionally narrowband and stable optical lines. We also demonstrated electric field tuning of the optical transition frequency as required for controlling atom-atom and atom-cavity coupling.The purpose of this project was to develop quantum computing hardware suitable for implementing quantum lattice-gas algorithms, with eventual application to turbulent flow simulations. A number of quantum systems were investigated, including rare-earth dopants in oxide crystals and in II-VI semiconductors. However, in the option year it was decided to concentrate exclusively on nitrogen-vacancy (NV) color centers in diamond. Surprising, it was found that NV diamond exhibited the key elements needed to develop few-qubit room-temperature solid-state quantum processing nodes. This included the ability to optically initialize and readout the NV electron spin state, fractional millisecond lifetimes for electron spins, and few-nanosecond electron spin Rabi flops. We also demonstrated the relatively long distance (few nanometer) coupling of a single NV spin to the electron spin of a single substitutional nitrogen (N). To achieve long range optical interconnections and entanglement between nodes, cryogenic cooling will likely still be required to sufficiently narrow the optical absorption lines. To this end we located diamond samples with unusually high purity, and found NV centers in these crystals that exhibited exceptionally narrowband and stable optical lines. We also demonstrated electric field tuning of the optical transition frequency as required for controlling atom-atom and atom-cavity coupling.

Apr 30, 20070 citations

Quantum melting on a lattice and a delocalization transition

E. V. Tsiper, F. G. Pikus, Alexei L. Efros

We consider 2d gas of spinless fermions with the Coulomb interaction on a lattice at T=0 and at different values of the hopping amplitude J. At small J electrons form a periodic structure. At filling factor ν=1/6 this structure melts at J as low as 0.02--0.03 in units of the nearest-neighbor Coulomb energy. We argue that this transition is connected to the dielectric-metal and dielectric-superconductor transitions. To demonstrate this point we perform computer modeling of the systems 6x6 with 6 and 7 electrons and 6x12 with 12 electrons. By sweeping J we compute simultaneously persistent current and structural characteristics of the electron distribution.We consider 2d gas of spinless fermions with the Coulomb interaction on a lattice at T=0 and at different values of the hopping amplitude J. At small J electrons form a periodic structure. At filling factor ν=1/6 this structure melts at J as low as 0.02--0.03 in units of the nearest-neighbor Coulomb energy. We argue that this transition is connected to the dielectric-metal and dielectric-superconductor transitions. To demonstrate this point we perform computer modeling of the systems 6x6 with 6 and 7 electrons and 6x12 with 12 electrons. By sweeping J we compute simultaneously persistent current and structural characteristics of the electron distribution.

arXiv:cond-mat/9512150Dec 22, 19950 citations

Quantum Computing and Lattice QCD

Martin J. Savage A

Bulletin of the American Physical SocietyOct 29, 20200 citations

T = 0

K) phases for few-EG systems with up to four explicit electrons per unit cell. We also present pure-spin exchange/correlation functionals for the same few-EG solutions. Finally, we consider the family of few-EG calculations in juxtaposition with the closely related uniform electron gas (UEG) system, for which previous calculations have been performed using density functional theory and quantum Monte Carlo methods. The exact few-EG solutions all display a similar oscillatory behavior at lower densities, which is not predicted by previous UEG simulations.