393 research outputs found
Comparison of one-dimensional and quasi-one-dimensional Hubbard models from the variational two-electron reduced-density-matrix method
Minimizing the energy of an -electron system as a functional of a
two-electron reduced density matrix (2-RDM), constrained by necessary
-representability conditions (conditions for the 2-RDM to represent an
ensemble -electron quantum system), yields a rigorous lower bound to the
ground-state energy in contrast to variational wavefunction methods. We
characterize the performance of two sets of approximate constraints,
(2,2)-positivity (DQG) and approximate (2,3)-positivity (DQGT) conditions, at
capturing correlation in one-dimensional and quasi-one-dimensional (ladder)
Hubbard models. We find that, while both the DQG and DQGT conditions capture
both the weak and strong correlation limits, the more stringent DQGT conditions
improve the ground-state energies, the natural occupation numbers, the pair
correlation function, the effective hopping, and the connected (cumulant) part
of the 2-RDM. We observe that the DQGT conditions are effective at capturing
strong electron correlation effects in both one- and quasi-one-dimensional
lattices for both half filling and less-than-half filling
Increasing the representation accuracy of quantum simulations of chemistry without extra quantum resources
Proposals for near-term experiments in quantum chemistry on quantum computers
leverage the ability to target a subset of degrees of freedom containing the
essential quantum behavior, sometimes called the active space. This
approximation allows one to treat more difficult problems using fewer qubits
and lower gate depths than would otherwise be possible. However, while this
approximation captures many important qualitative features, it may leave the
results wanting in terms of absolute accuracy (basis error) of the
representation. In traditional approaches, increasing this accuracy requires
increasing the number of qubits and an appropriate increase in circuit depth as
well. Here we introduce a technique requiring no additional qubits or circuit
depth that is able to remove much of this approximation in favor of additional
measurements. The technique is constructed and analyzed theoretically, and some
numerical proof of concept calculations are shown. As an example, we show how
to achieve the accuracy of a 20 qubit representation using only 4 qubits and a
modest number of additional measurements for a simple hydrogen molecule. We
close with an outlook on the impact this technique may have on both near-term
and fault-tolerant quantum simulations
Apobec1 complementation factor (A1CF) and RBM47 interact in tissue-specific regulation of C to U RNA editing in mouse intestine and liver
Zero and Finite Temperature Quantum Simulations Powered by Quantum Magic
We present a comprehensive approach to quantum simulations at both zero and
finite temperatures, employing a quantum information theoretic perspective and
utilizing the Clifford + Rz transformations. We introduce the "quantum magic
ladder", a natural hierarchy formed by systematically augmenting Clifford
transformations with the addition of Rz gates. These classically simulable
similarity transformations allow us to reduce the quantumness of our system,
conserving vital quantum resources. This reduction in quantumness is essential,
as it simplifies the Hamiltonian and shortens physical circuit-depth,
overcoming constraints imposed by limited error correction. We improve the
performance of both digital and analog quantum computers on ground state and
finite temperature molecular simulations, not only outperforming the
Hartree-Fock solution, but also achieving consistent improvements as we ascend
the quantum magic ladder. By facilitating more efficient quantum simulations,
our approach enables near-term and early fault-tolerant quantum computers to
address novel challenges in quantum chemistry.Comment: 12 pages, 9 figure
The Fermionic Quantum Emulator
The fermionic quantum emulator (FQE) is a collection of protocols for emulating quantum dynamics of fermions efficiently taking advantage of common symmetries present in chemical, materials, and condensed-matter systems. The library is fully integrated with the OpenFermion software package and serves as the simulation backend. The FQE reduces memory footprint by exploiting number and spin symmetry along with custom evolution routines for sparse and dense Hamiltonians, allowing us to study significantly larger quantum circuits at modest computational cost when compared against qubit state vector simulators. This release paper outlines the technical details of the simulation methods and key technical advantages
- …