Faster randomized partial trace estimation
- URL: http://arxiv.org/abs/2310.12364v1
- Date: Wed, 18 Oct 2023 22:20:09 GMT
- Title: Faster randomized partial trace estimation
- Authors: Tyler Chen, Robert Chen, Kevin Li, Skai Nzeuton, Yilu Pan, Yixin Wang
- Abstract summary: We develop randomized matrix-free algorithms for estimating partial traces.
We apply our algorithm to study the thermodynamics of several Heisenberg spin systems.
- Score: 17.697674095200284
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: We develop randomized matrix-free algorithms for estimating partial traces.
Our algorithm improves on the typicality-based approach used in [T. Chen and
Y-C. Cheng, Numerical computation of the equilibrium-reduced density matrix for
strongly coupled open quantum systems, J. Chem. Phys. 157, 064106 (2022)] by
deflating important subspaces (e.g. corresponding to the low-energy
eigenstates) explicitly. This results in a significant variance reduction for
matrices with quickly decaying singular values. We then apply our algorithm to
study the thermodynamics of several Heisenberg spin systems, particularly the
entanglement spectrum and ergotropy.
Related papers
- Simulating NMR Spectra with a Quantum Computer [49.1574468325115]
This paper provides a formalization of the complete procedure of the simulation of a spin system's NMR spectrum.
We also explain how to diagonalize the Hamiltonian matrix with a quantum computer, thus enhancing the overall process's performance.
arXiv Detail & Related papers (2024-10-28T08:43:40Z) - Eigenstate Correlations in Dual-Unitary Quantum Circuits: Partial Spectral Form Factor [0.0]
Analytic insights into eigenstate correlations can be obtained by the recently introduced partial spectral form factor.
We study the partial spectral form factor in chaotic dual-unitary quantum circuits in the thermodynamic limit.
arXiv Detail & Related papers (2024-07-29T12:02:24Z) - Quantum tomography of helicity states for general scattering processes [55.2480439325792]
Quantum tomography has become an indispensable tool in order to compute the density matrix $rho$ of quantum systems in Physics.
We present the theoretical framework for reconstructing the helicity quantum initial state of a general scattering process.
arXiv Detail & Related papers (2023-10-16T21:23:42Z) - A hybrid quantum-classical algorithm for multichannel quantum scattering
of atoms and molecules [62.997667081978825]
We propose a hybrid quantum-classical algorithm for solving the Schr"odinger equation for atomic and molecular collisions.
The algorithm is based on the $S$-matrix version of the Kohn variational principle, which computes the fundamental scattering $S$-matrix.
We show how the algorithm could be scaled up to simulate collisions of large polyatomic molecules.
arXiv Detail & Related papers (2023-04-12T18:10:47Z) - A Sublinear-Time Quantum Algorithm for Approximating Partition Functions [0.0]
We present a novel quantum algorithm for estimating Gibbs partition functions in sublinear time.
This is the first speed-up of this type to be obtained over the seminal nearly-linear time of vStefankovivc, Vempala and Vigoda.
arXiv Detail & Related papers (2022-07-18T14:41:48Z) - Numerical computation of the equilibrium-reduced density matrix for
strongly coupled open quantum systems [2.538209532048867]
We describe a numerical algorithm for approximating the equilibrium-reduced density matrix and the effective (mean force) Hamiltonian for a set of system spins coupled strongly to a set of bath spins when the total system is held in canonical thermal equilibrium by weak coupling with a "super-bath"
Further numerical experiments demonstrate the potential of our approach for applications including the study of quantum phase transitions and entanglement entropy for long-range interaction systems.
arXiv Detail & Related papers (2022-04-18T03:25:58Z) - Exact analytical relation between the entropies and the dominant
eigenvalue of random reduced density matrices [0.0]
In this paper, we show how the entropy (including the von Neumann entropy) obtained by tracing across various sizes of subsystems is related to their dominant eigenvalue.
The correlation between our study and entanglement generated by quantum computing is provided with various examples.
arXiv Detail & Related papers (2022-04-04T18:00:05Z) - Spectral clustering under degree heterogeneity: a case for the random
walk Laplacian [83.79286663107845]
This paper shows that graph spectral embedding using the random walk Laplacian produces vector representations which are completely corrected for node degree.
In the special case of a degree-corrected block model, the embedding concentrates about K distinct points, representing communities.
arXiv Detail & Related papers (2021-05-03T16:36:27Z) - Determination of the critical exponents in dissipative phase
transitions: Coherent anomaly approach [51.819912248960804]
We propose a generalization of the coherent anomaly method to extract the critical exponents of a phase transition occurring in the steady-state of an open quantum many-body system.
arXiv Detail & Related papers (2021-03-12T13:16:18Z) - Spectral Analysis of Product Formulas for Quantum Simulation [0.0]
We show that the Trotter step size needed to estimate an energy eigenvalue within precision can be improved in scaling from $epsilon$ to $epsilon1/2$ for a large class of systems.
Results partially generalize to diabatic processes, which remain in a narrow energy band separated from the rest of the spectrum by a gap.
arXiv Detail & Related papers (2021-02-25T03:17:25Z) - Optimal Randomized First-Order Methods for Least-Squares Problems [56.05635751529922]
This class of algorithms encompasses several randomized methods among the fastest solvers for least-squares problems.
We focus on two classical embeddings, namely, Gaussian projections and subsampled Hadamard transforms.
Our resulting algorithm yields the best complexity known for solving least-squares problems with no condition number dependence.
arXiv Detail & Related papers (2020-02-21T17:45:32Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.