On the truncation of the harmonic oscillator wavepacket

基于哈密顿截断的量子计算机实时散射模拟

Real-Time Scattering on Quantum Computers via Hamiltonian Truncation

本文提出基于哈密顿截断的量子计算框架，用于模拟$(1+1)$维标量$\phi^4$理论的实时散射，并在IonQ离子阱设备上验证了波包态制备及碰撞后粒子产生等关键现象，展示了其在量子比特效率上优于格点方法的潜力。

Comment on: "On the influence of a Coulomb-like potential induced by the Lorentz symmetry breaking effects on the harmonic oscillator''. Eur. Phys. J. Plus (2012) \textbf{127}: 102

We analyze the calculation of bound states for a nonrelativistic spin-half neutral particle under the influence of a Coulomb-like potential induced by Lorentz symmetry breaking effects. We show that the truncation condition proposed by the authors only provides one energy eigenvalue for a particular model potential and misses all the other bound-state energies. The dependence of the cyclotron frequency on the quantum numbers is a mere artifact of the truncation condition that is by no means necessary for the existence of bound states.

Comment on: "On the Dirac oscillator subject to a Coulomb-type central potential induced by the Lorentz symmetry violation"

We analyze recent results on a Dirac oscillator. We show that the truncation of the Frobenius series does not yield all the eigenvalues and eigenfunctions of the radial equation. For this reason the eigenvalues reported by the authors are useless and the prediction of allowed oscillator frequencies meaningless.

在耦合量子比特-振子系统中创建多组分薛定谔猫态

Creating multicomponent Schrödinger cat states in a coupled qubit-oscillator system

通过耦合 semiclassical 振子与量子比特系统，研究如何制备各种薛定谔猫态的变种，利用量子淬火和自旋测量实现振子的相干叠加态。

The rotating harmonic oscillator revisited

We analyze the distribution of the eigenvalues of the quantum-mechanical rotating harmonic oscillator by means of the Frobenius method. A suitable ansatz leads to a three-term recurrence relation for the expansion coefficients. Truncation of the series yields some particular eigenvalues and eigenfunctions in exact analytical form. The former can be organized in such a way that one obtains suitable information about the whole spectrum of the model.

波包叠加的非线性动力学

Nonlinear dynamics of superpostion of wavepackets

本文研究克尔介质、莫尔斯振子和玻色约瑟夫森结中波包叠加的非线性动力学，利用首次回归时间分布、递归图和Lyapunov指数等方法，揭示叠加态对周期、准周期、遍历及混沌动力学的显著影响。

Time-extended measurement of the position of a driven harmonic oscillator

The von Neumann interaction between a particle and an apparatus, both of arbitrary mass, has been considered in the measurement of the position of a simple harmonic oscillator acted on by an external force. When the measurement has finite duration, both the motion of the pointer and the oscillator influence the result of the measurement. Provided that the oscillator is in an eigenstate of its position at the start of the measurement, the pointer will indicate the arithmetic average between the initial and final position of the particle with an added term which depends on the duration of the me…

Testing Quantum Coherence in Stochastic Electrodynamics with Squeezed Schrödinger Cat States

The interference pattern in electron double-slit diffraction is a hallmark of quantum mechanics. A long standing question for stochastic electrodynamics (SED) is whether or not it is capable of reproducing such effects, as interference is a manifestation of quantum coherence. In this study, we use excited harmonic oscillators to directly test this quantum feature in SED. We use two counter-propagating dichromatic laser pulses to promote a ground-state harmonic oscillator to a squeezed Schrödinger cat state. Upon recombination of the two well-separated wavepackets, an interference pattern emerg…

Truncated channel representations for coupled harmonic oscillators

Coupled quantum harmonic oscillators, studied by many authors using many different techniques over the decades, are frequently used toy-models to study open quantum systems. In this manuscript, we explicitly study the simplest oscillator model -- a pair of initially decoupled quantum harmonic oscillators interacting with a spring-like coupling, where the bath oscillator is initially in a thermal-like state. In particular, we treat the completely positive and trace preserving map on the system as a quantum channel, and study the truncation of the channel by truncating its Kraus set and its outp…

标量场论量子模拟的坐标空间表示

Coordinate space representation for quantum simulation of scalar field theory

该研究提出基于坐标空间简谐振子基的φ⁴模型表述，其单体态矩阵和相互作用张量呈有效带对角结构，可降低量子模拟资源，经数值验证其低能谱与动量空间表述一致。