We develop a master equation formalism to describe the evolution of the average density matrix of a closed quantum system driven by a stochastic Hamiltonian. The average over random processes generally results in decoherence effects in closed system dynamics, in addition to the usual unitary evolution. We then show that, for an important class of problems in which the Hamiltonian is proportional to a Gaussian random process, the 2nd-order master equation yields exact dynamics. The general formalism is applied to study the examples of a two-level system, two atoms in a stochastic magnetic field and the heating of a trapped ion.
Simulation of quantum chemistry is expected to be a principal application of quantum computing. In quantum simulation, a complicated Hamiltonian describing the dynamics of a quantum system is decomposed into its constituent terms, where the effect of each term during time-evolution is individually computed. For many physical systems, the Hamiltonian has a large number of terms, constraining the scalability of established simulation methods. To address this limitation we introduce a new scheme that approximates the actual Hamiltonian with a sparser Hamiltonian containing fewer terms. By stochas…
对于许多哈密顿量，人们可以很自然地将其与一个|Psi| ^2分布马尔可夫过程联系起来。对于非相对论性的量子力学，这个过程实际上是决定性的，被称为玻姆力学。对于量子场论的哈密顿量，它是一个典型的变量粒子位形空间上的跳跃过程。我们为正则化的量子场论定义了这些过程，从而推广了John S. Bell [Phys.Rep.137，49（1986）]和我们自己[J.Phys.A：Math.Gen.36，4143（2003）]。我们引入了一个用相互作用哈密顿量表示跳跃率的公式，并建立了跳跃率有限的条件。
Synthesizing Arbitrary Non-Hermitian Hamiltonian with Stochastic Floquet Engineering
College of Science, NUDT（国防科技大学理学院）；Center for Joint Quantum Studies and Department of Physics, School of Science, Tianjin University（天津大学理学院量子联合研究中心与物理系）；Department of Physics, Hunan Normal University（湖南师范大学物理系）
We propose a class of randomized quantum Krylov diagonalization (rQKD) algorithms capable of solving the eigenstate estimation problem with modest quantum resource requirements. Compared to previous real-time evolution quantum Krylov subspace methods, our approach expresses the time evolution operator, $e^{-i\hat{H} τ}$, as a linear combination of unitaries and subsequently uses a stochastic sampling procedure to reduce circuit depth requirements. While our methodology applies to any Hamiltonian with fast-forwardable subcomponents, we focus on its application to the explicitly double-factorize…
