Abstract We find a lower bound on the computational complexity of Grover’s quantum search algorithms in low-dimensional networks using the renormalization group (RG). It highlights the competition between Grover’s abstract algorithm, i.e., a rotation in Hilbert space, and quantum transport in an actual geometry. It can be characterized in terms of the quantum walk dimension <?CDATA ${d}_{w}^{Q}$ ?> d w Q and the spatial (fractal) dimension df or, alternatively, the spectral dimension of the network, ds , even when translational invariance is broken.Abstract We find a lower bound on the computational complexity of Grover’s quantum search algorithms in low-dimensional networks using the renormalization group (RG). It highlights the competition between Grover’s abstract algorithm, i.e., a rotation in Hilbert space, and quantum transport in an actual geometry. It can be characterized in terms of the quantum walk dimension <?CDATA ${d}_{w}^{Q}$?> d w Q and the spatial (fractal) dimension df or, alternatively, the spectral dimension of the network, ds , even when translational invariance is broken.

Journal of Physics Conference SeriesJun 1, 20190 citations

Efficient quantum search algorithms on a bulk quantum computation model

誠也大久保

Jan 1, 20050 citations

SpinGlassPEPS.jl: Tensor-network package for Ising-like optimization on quasi-two-dimensional graphs

Tomasz Śmierzchalski, Anna M. Dziubyna, Konrad Jałowiecki +4 more

This work introduces SpinGlassPEPS $.$ jl, a software package implemented in Julia, designed to find low-energy configurations of generalized Potts models, including Ising and QUBO problems, utilizing heuristic tensor network contraction algorithms on quasi-2D geometries. In particular, the package employs the Projected Entangled-Pairs States to approximate the Boltzmann distribution corresponding to the model's cost function. This enables an efficient branch-and-bound search (within the probability space) that exploits the locality of the underlying problem's topology. As a result, our software enables the discovery of low-energy configurations for problems on quasi-2D graphs, particularly those relevant to modern quantum annealing devices. The modular architecture of SpinGlassPEPS $.$ jl supports various contraction schemes and hardware acceleration.This work introduces SpinGlassPEPS$.$jl, a software package implemented in Julia, designed to find low-energy configurations of generalized Potts models, including Ising and QUBO problems, utilizing heuristic tensor network contraction algorithms on quasi-2D geometries. In particular, the package employs the Projected Entangled-Pairs States to approximate the Boltzmann distribution corresponding to the model's cost function. This enables an efficient branch-and-bound search (within the probability space) that exploits the locality of the underlying problem's topology. As a result, our software enables the discovery of low-energy configurations for problems on quasi-2D graphs, particularly those relevant to modern quantum annealing devices. The modular architecture of SpinGlassPEPS$.$jl supports various contraction schemes and hardware acceleration.

arXiv:2502.02317Feb 4, 20250 citations

Novel optimization of quantum search algorithm to minimize complexity

Tarun Kumar, Dilip Kumar, Gurmohan Singh

Chinese Journal of PhysicsMar 9, 20237 citations

On the efficiency of Hamiltonian–based quantum computation for low–rank matrices

Zhenwei Cao, Alexander Elgart

We present an extension of Adiabatic Quantum Computing (AQC) algorithm for the unstructured search to the case when the number of marked items is unknown. The algorithm maintains the optimal Grover speedup and includes a small counting subroutine. Our other results include a lower bound on the amount of time needed to perform a general Hamiltonian-based quantum search, a lower bound on the evolution time needed to perform a search that is valid in the presence of control error and a generic upper bound on the minimum eigenvalue gap for evolutions. In particular, we demonstrate that quantum speedup for the unstructured search using AQC type algorithms may only be achieved under very rigid control precision requirements.We present an extension of Adiabatic Quantum Computing (AQC) algorithm for the unstructured search to the case when the number of marked items is unknown. The algorithm maintains the optimal Grover speedup and includes a small counting subroutine. Our other results include a lower bound on the amount of time needed to perform a general Hamiltonian-based quantum search, a lower bound on the evolution time needed to perform a search that is valid in the presence of control error and a generic upper bound on the minimum eigenvalue gap for evolutions. In particular, we demonstrate that quantum speedup for the unstructured search using AQC type algorithms may only be achieved under very rigid control precision requirements.

Jan 1, 20126 citations

{d}_{w}^{Q}

?> d w Q and the spatial (fractal) dimension df or, alternatively, the spectral dimension of the network, ds , even when translational invariance is broken.

This work introduces SpinGlassPEPS

.

jl, a software package implemented in Julia, designed to find low-energy configurations of generalized Potts models, including Ising and QUBO problems, utilizing heuristic tensor network contraction algorithms on quasi-2D geometries. In particular, the package employs the Projected Entangled-Pairs States to approximate the Boltzmann distribution corresponding to the model's cost function. This enables an efficient branch-and-bound search (within the probability space) that exploits the locality of the underlying problem's topology. As a result, our software enables the discovery of low-energy configurations for problems on quasi-2D graphs, particularly those relevant to modern quantum annealing devices. The modular architecture of SpinGlassPEPS

.

jl supports various contraction schemes and hardware acceleration.