Zobrazeno 1 - 10
of 16 412
pro vyhledávání: '"Trotter, A. P."'
Autor:
Okajima, Koki, Kabashima, Yoshiyuki
We analyze the quantum Hopfield model in which an extensive number of patterns are embedded in the presence of a uniform transverse field. This analysis employs the replica method under the replica symmetric ansatz on the Suzuki-Trotter representatio
Externí odkaz:
http://arxiv.org/abs/2411.02012
In analog and digital simulations of practically relevant quantum systems, the target dynamics can only be implemented approximately. The Trotter product formula is the most common approximation scheme as it is a generic method which allows tuning ac
Externí odkaz:
http://arxiv.org/abs/2410.03059
Autor:
Jing, Yifan, Zou, Tingxiang
We establish a group-action version of the Szemer\'edi-Trotter theorem over any field, extending Bourgain's result for the group $\mathrm{SL}_2(k)$. As an Elekes-Szab\'o-type application, we obtain quantitative bounds on the number of collinear tripl
Externí odkaz:
http://arxiv.org/abs/2411.13084
Autor:
Chen, Yi-Hsiang
Suppressing the Trotter error in dynamical quantum simulation typically requires running deeper circuits, posing a great challenge for noisy near-term quantum devices. Studies have shown that the empirical error is usually much smaller than the one s
Externí odkaz:
http://arxiv.org/abs/2409.16634
Autor:
Watson, James D., Watkins, Jacob
Product formulae are a popular class of digital quantum simulation algorithms due to their conceptual simplicity, low overhead, and performance which often exceeds theoretical expectations. Recently, Richardson extrapolation and polynomial interpolat
Externí odkaz:
http://arxiv.org/abs/2408.14385
Autor:
Ando, Chihiro
For an elliptic curve $E$ over $\mathbb{Q}$ without complex multiplication, Lang and Trotter conjecture \[ \# \{ p0$ is a co
Externí odkaz:
http://arxiv.org/abs/2408.13695
Autor:
Li, Langyu
Hamiltonian simulation is one of the most promising applications of quantum computers, and the product formula is one of the most important methods for this purpose. Previous related work has mainly focused on the worst$-$case or average$-$case scena
Externí odkaz:
http://arxiv.org/abs/2408.03891
We study convergence rates of the Trotter-Kato splitting $e^{A+L} = \lim_{n \to \infty} (e^{L/n} e^{A/n})^n$ in the strong operator topology. In the first part, we use complex interpolation theory to treat generators $L$ and $A$ of contraction semigr
Externí odkaz:
http://arxiv.org/abs/2407.04045
Autor:
Akahoshi, Yutaro, Toshio, Riki, Fujisaki, Jun, Oshima, Hirotaka, Sato, Shintaro, Fujii, Keisuke
Achieving practical quantum speedup with limited resources is a crucial challenge in both academic and industrial communities. To address this, a partially fault-tolerant quantum computing architecture called ``space-time efficient analog rotation qu
Externí odkaz:
http://arxiv.org/abs/2408.14929
Autor:
Sugisaki, Kenji
Publikováno v:
AIP Advances 14, 095021 (2024)
Electronic structure calculations of atoms and molecules are considered to be a promising application for quantum computers. Two key algorithms, the quantum phase estimation (QPE) and the variational quantum eigensolver (VQE), have been extensively s
Externí odkaz:
http://arxiv.org/abs/2406.09830