140 research outputs found
Quantum time dynamics of 1D-Heisenberg models employing the Yang-Baxter equation for circuit compression
Quantum time dynamics (QTD) is considered a promising problem for quantum
supremacy on near-term quantum computers. However, QTD quantum circuits grow
with increasing time simulations. This study focuses on simulating the time
dynamics of 1-D integrable spin chains with nearest neighbor interactions. We
show how the quantum Yang-Baxter equation can be exploited to compress and
produce a shallow quantum circuit. With this compression scheme, the depth of
the quantum circuit becomes independent of step size and only depends on the
number of spins. We show that the compressed circuit scales quadratically with
system size, which allows for the simulations of time dynamics of very large
1-D spin chains. We derive the compressed circuit representations for different
special cases of the Heisenberg Hamiltonian. We compare and demonstrate the
effectiveness of this approach by performing simulations on quantum computers
Exploring Parameter Redundancy in the Unitary Coupled-Cluster Ansatze for Hybrid Variational Quantum Computing
One of the commonly used chemical-inspired approaches in variational quantum
computing is the unitary coupled-cluster (UCC) ansatze. Despite being a
systematic way of approaching the exact limit, the number of parameters in the
standard UCC ansatze exhibits unfavorable scaling with respect to the system
size, hindering its practical use on near-term quantum devices. Efforts have
been taken to propose some variants of UCC ansatze with better scaling. In this
paper we explore the parameter redundancy in the preparation of unitary
coupled-cluster singles and doubles (UCCSD) ansatze employing spin-adapted
formulation, small amplitude filtration, and entropy-based orbital selection
approaches. Numerical results of using our approach on some small molecules
have exhibited a significant cost reduction in the number of parameters to be
optimized and in the time to convergence compared with conventional UCCSD-VQE
simulations. We also discuss the potential application of some machine learning
techniques in further exploring the parameter redundancy, providing a possible
direction for future studies
Ionization Potentials of First-Row Transition Metal Aqua Ions
We report computations of the vertical ionization potentials within the
approximation of the near-complete series of first-row transition metal (V-Cu)
aqua ions in their most common oxidation states, i.e. V, Cr,
Cr, Mn, Fe, Fe, Co, Ni, and
Cu. The -orbital occupancy of these systems spans a broad range from
to . All the structures were first optimized at the density
functional theory level using a large cluster of explicit water molecules that
are embedded in a continuum solvation model. Vertical ionization potentials
were computed with the one-shot approach on a range of transition
metal ion clusters (6, 18, 40, and 60 explicit water molecules) wherein the
convergence with respect to the basis set size was evaluated using the systems
with 40 water molecules. We assess the results using three different density
functional approximations as starting points for the vertical ionization
potential calculations, namely @PBE, @PBE0, and
@rSCAN. While the predicted ground-state structures are similar
with all three exchange-correlation functionals, the vertical ionization
potentials were in closer agreement with the experiment when using the
@PBE0 and @rSCAN approaches, with the r2SCAN based
calculations being significantly less expensive. Computed bond distances and
vertical ionization potentials for all structures were compared with available
experimental data and are in good agreement
Hybrid algorithm for the time-dependent Hartree-Fock method using the Yang-Baxter equation on quantum computers
The time-dependent Hartree-Fock (TDHF) method is an approach to simulate the
mean field dynamics of electrons within the assumption that the electrons move
independently in their self-consistent average field and within the space of
single Slater determinants. One of the major advantages of performing time
dynamics within Hartree-Fock theory is the free fermionic nature of the
problem, which makes TDHF classically simulatable in polynomial time. Here, we
present a hybrid TDHF implementation for quantum computers. This quantum
circuit grows with time; but with our recent work on circuit compression via
the Yang-Baxter equation (YBE), the resulting circuit is constant depth. This
study provides a new way to simulate TDHF with the aid of a quantum device as
well as provides a new direction for the application of YBE symmetry in quantum
chemistry simulations.Comment: arXiv admin note: text overlap with arXiv:2112.0169
Orbital-free kinetic-energy density functionals with a densitydependent kernel
We report linear-response kinetic-energy density functionals, which show significant improvement over the Wang-Teter, Perrot, Smargiassi-Madden, Wang-Govind-Carter functionals, yet still maintain O(N ln N) scaling. Numerical tests show that these functionals, which contain a double-density-dependent kernel, can reproduce the Kohn-Sham results almost exactly for several aluminum bulk phases. We further show that with a sensible choice of the uniform background density, energies of formation for the low-index aluminum surfaces, where the density variations are very large, can be reproduced to within reasonable accuracy
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