M. T. Thomaz
The geometric phase acquired by the vector states under an adiabatic evolution along a noncyclic path can be calculated correctly in any instantaneous basis of a Hamiltonian that varies in time due to a time-dependent classical field.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
继续探索
We show that a noncyclic phase of geometric origin has to be included in the approximate adiabatic wave function. The adiabatic noncyclic geometric phase for systems exhibiting a conical intersection as well as for an Aharonov-Bohm situation is worked out in detail. A spin-1/2 experiment to measure the adiabatic noncyclic geometric phase is discussed. We also analyze some misconceptions in the literature and textbooks concerning noncyclic geometric phases.
We show that the difference of adiabatic phases, that are basis-dependent, in noncyclic evolution of non-degenerate quantum systems have to be taken into account to give the correct interference result in the calculation of physical quantities in states that are a superposition of instantaneous eigenstates of energy. To verify the contribution of those adiabatic phases in the interference phenomena, we consider the spin-1/2 model coupled to a precessing external magnetic field. In the model, the adiabatic phase increases in time up to reach the difference of the Berry's phases of the model whe…
We use the theory of dynamical invariants to yield a simple derivation of noncyclic analogues of the Abelian and non-Abelian geometric phases. This derivation relies only on the principle of gauge invariance and elucidates the existing definitions of the Abelian noncyclic geometric phase. We also discuss the adiabatic limit of the noncyclic geometric phase and compute the adiabatic non-Abelian noncyclic geometric phase for a spin 1 magnetic (or electric) quadrupole interacting with a precessing magnetic (electric) field.
Genuinely noncyclic geometric gates in two-pulse schemes
本文提出一种真正非循环几何门方案，通过测地线段开放路径演化计算基，并确保时间演化算符本征态不积累动力学相位，从而消除传统非循环几何门的几何性质模糊性。
Single-modulated-pulse two-qubit gates for Rydberg atoms with noncyclic geometric control
针对量子计算中高鲁棒性高保真双量子比特门的实现需求，提出基于里德堡阻塞的单调制脉冲非循环几何控制方案，可提升抗系统误差能力、缩短门控时间，为任意双量子比特门提供解析波形。
We show that neutrino spin and spin-flavor transitions involve nonvanishing geometric phases. The geometric character of neutrino spin rotation is explored by studying the neutrino spin trajectory in the projective Hilbert space representation and its relation to the geometric phase. Analytical expressions are derived for noncyclic geometric phases. Several calculations are performed for different cases of rotating and nonrotating magnetic fields in the context of solar neutrinos and neutrinos produced inside neutron stars. Also the effects of adiabaticity, critical magnetic fields and cross b…
In [Phys. Rev. Lett. 95, 080502 (2005)], Zheng proposed a scheme for implementing a conditional phase shift via adiabatic passages. The author claims that the gate is "neither of dynamical nor geometric origin" on the grounds that the Hamiltonian does not follow a cyclic change. He further argues that "in comparison with the adiabatic geometric gates, the nontrivial cyclic loop is unnecessary, and thus the errors in obtaining the required solid angle are avoided, which makes this new kind of phase gates superior to the geometric gates." In this Comment, we point out that geometric operations, …
In this paperwe propose two theoretical schemes for implementation of quantum phase gates by engineering the phase-sensitive dark state of two atoms subjected to Rydberg-Rydberg interaction. Combining the conventional adiabatic techniques and currently developed approaches of phase control, a feasible proposal for implementation of a geometric phase gate is presented, where the conditional phase shift (Berry phase) is achieved by adiabatically and cyclically changing the parameters of the driving fields. Here we find that the geometric phase acquired is related to the way how the relative phas…
If a quantum system evolves in a noncyclic fashion the corresponding geometric phase or holonomy may not be fully defined. Off-diagonal geometric phases have been developed to deal with such cases. Here, we generalize these phases to the non-Abelian case, by introducing off-diagonal holonomies that involve evolution of more than one subspace of the underlying Hilbert space. Physical realizations of the off-diagonal holonomies in adiabatic evolution and interferometry are put forward.
We introduce an alternative way to derive the generalized form of the master equation recently presented by J. P. Pekola et al. [Phys. Rev. Lett. 105, 030401 (2010)] for an adiabatically steered two-level quantum system interacting with a Markovian environment. The original derivation employed the effective Hamiltonian in the adiabatic basis with the standard interaction picture approach but without the usual secular approximation. Our approach is based on utilizing a master equation for a non-steered system in the first super-adiabatic basis. It is potentially efficient in obtaining higher-or…
Using a kinematic approach we show that the non-adiabatic, non-cyclic, geometric phase corresponding to the radiation emitted by a three level cascade system provides a sensitive diagnostic tool for determining the entanglement properties of the two modes of radiation. The nonunitary, noncyclic path in the state space may be realized through the same control parameters which control the purity/mixedness and entanglement. We show analytically that the geometric phase is related to concurrence in certain region of the parameter space. We further show that the rate of change of the geometric phas…
Based only on the parallel transport condition, we present a general method to compute Abelian or non-Abelian geometric phases acquired by the basis states of pure or mixed density operators, which also holds for nonadiabatic and noncyclic evolution. Two interesting features of the non-Abelian geometric phase obtained by our method stand out: i) it is a generalization of Wilczek and Zee's non-Abelian holonomy, in that it describes nonadiabatic evolution where the basis states are parallelly transported between distinct degenerate subspaces, and ii) the non-Abelian character of our geometric ph…
Improving adiabatic quantum factorization via chopped random-basis optimization
本文应用截断随机基（CRAB）优化改进绝热量子因子分解，在分解21至2479的整数时显著提升目标态保真度，且对退相干噪声具有韧性，为推进绝热量子算法提供了有力工具。
Adiabatic quantum computation starts from embedding a computational problem into a Hamiltonian whose ground state encodes the solution to the problem. This problem Hamiltonian, $H_{\rm p}$, is normally chosen to be diagonal in the computational basis, that is a product basis for qubits. We point out that $H_{\rm p}$ can be chosen to be non-diagonal in the computational basis. To be more precise, we show how to construct $H_{\rm p}$ in such a way that all its excited states are entangled with respect to the qubit tensor product structure, while the ground state is still of the product form and …
We extend the concept of locality to enclose a situation where a tensor-product structure for the Hilbert space is not \textit {a priori} assumed; rather, this locality is related to a given matrix representation of the Hamiltonian associated to the system. As a result, we formulate a Lieb-Robinson-like bound for Hamiltonians local in a given basis. In particular, we employ this bound to obtain alternatively the adiabatic condition, where adiabaticity is naturally ensued from a locality in energy basis and a relatively small Lieb-Robinson bound.
Let $H(t)=(1-t/T)H_0 + (t/T)H_1$, $t\in [0,T]$, be the Hamiltonian governing an adiabatic quantum algorithm, where $H_0$ is diagonal in the Hadamard basis and $H_1$ is diagonal in the computational basis. We prove that $H_0$ and $H_1$ must each have at least two large mutually-orthogonal eigenspaces if the algorithm's running time is to be subexponential in the number of qubits. We also reproduce the optimality proof of Farhi and Gutmann's search algorithm in the context of this adiabatic scheme; because we only consider initial Hamiltonians that are diagonal in the Hadamard basis, our result …
The analysis of geometric phases associated with level crossing is reduced to the familiar diagonalization of the Hamiltonian in the second quantized formulation. A hidden local gauge symmetry, which is associated with the arbitrariness of the phase choice of a complete orthonormal basis set, becomes explicit in this formulation (in particular, in the adiabatic approximation) and specifies physical observables. The choice of a basis set which specifies the coordinate in the functional space is arbitrary in the second quantization, and a sub-class of coordinate transformations, which keeps the …
The unitary operator corresponding to the classical canonical transformation that connects a general closed system to an open system under adiabatic conditions is found. The quantum invariant operator of the adiabatic open system is derived from the unitary transformation of the quantum Hamiltonian of the closed system. On the basis of these results, we investigate the evolution of the general quantum adiabatic system and construct a revised adiabatic theorem. The adiabatic theorem developed here exactly reduces to the well-known Berry adiabatic theorem when the control parameter
Relying only on first principles, we derive a master equation of Lindblad form generally applicable for adiabatically time dependent systems. Our analysis shows that the much debated secular approximation can be valid for slowly time dependent Hamiltonians when performed in an appropriate basis. We apply our approach to the well known Landau-Zener problem where we find that adiabaticity is improved by coupling to a low temperature environment.
I describe one quantum approach to solving 3-satisfiability (3-SAT), the well known problem in computer science. The approach is based on repeatedly measuring the truth value of the clauses forming the 3-SAT proposition using a non-orthogonal basis. If the basis slowly evolves then there is a strong analogy to adiabatic quantum computing, although the approach is entirely circuit-based. To solve a 3-SAT problem of n variables requires a quantum register of $n$ qubits, or more precisely rebits i.e. qubits whose phase need only be real. For cases of up to n=26 qubits numerical simulations indica…
The problem of photoionization of atomic hydrogen in a white-dwarf-strength magnetic field is revisited to understand the existing discrepancies in the positive-energy spectra obtained by a variety of theoretical approaches reported in the literature. Oscillator strengths for photoionization are calculated with the adiabatic-basis-expansion method developed by Mota-Furtado and O'Mahony [Phys. Rev. A {\bf 76}, 053405 (2007)]. A comparative study is performed between the adiabatic-basis-expansion method and our previously developed coupled-channel theory [Phys. Rev. A {\bf 94}, 033422 (2016)]. A…
We propose a novel method to describe realistically ionization processes with absorbing boundary conditions in basis expansion within the formalism of the so-called Non-Adiabatic Quantum Molecular Dynamics. This theory couples self-consistently a classical description of the nuclei with a quantum mechanical treatment of the electrons in atomic many-body systems. In this paper we extend the formalism by introducing absorbing boundary conditions via an imaginary potential. It is shown how this potential can be constructed in time-dependent density functional theory in basis expansion. The approa…
Direct dynamics methods using Gaussian wavepackets have to rely only on local properties, such as gradients and hessians at the center of the wavepacket, so as to be compatible with the usual quantum chemistry methods. Matrix elements of the potential energy surfaces between wavepackets therefore usually have to be approximated. It is shown, that if a modified form of valence bond theory is used instead of the usual MO-based theories, the matrix elements can be obtained exactly. This is so because the molecular Hamiltonian only contains the Coulomb potential, for which matrix elements between …
A controlled-phase gate was demonstrated in superconducting Xmon transmon qubits with fidelity reaching 99.4%, relying on the adiabatic interaction between the |11> and |02> states. Here we explain the theoretical concepts behind this protocol that achieves fast gate times with only $σ_z$ control of the Hamiltonian, based on a theory of non-linear mapping of state errors to a power spectral density and use of optimal window functions. With a solution given in the Fourier basis, optimization is shown to be straightforward for practical cases of an arbitrary state change and finite bandwidth of …
A quantum system will stay near its instantaneous ground state if the Hamiltonian that governs its evolution varies slowly enough. This quantum adiabatic behavior is the basis of a new class of algorithms for quantum computing. We test one such algorithm by applying it to randomly generated, hard, instances of an NP-complete problem. For the small examples that we can simulate, the quantum adiabatic algorithm works well, and provides evidence that quantum computers (if large ones can be built) may be able to outperform ordinary computers on hard sets of instances of NP-complete problems.
Grover's algorithm is one of the most important quantum algorithms, which performs the task of searching an unsorted database without a priori probability. Recently the adiabatic evolution has been used to design and reproduce quantum algorithms, including Grover's algorithm. In this paper, we show that quantum search algorithm by adiabatic evolution has two properties that conventional quantum search algorithm doesn't have. Firstly, we show that in the initial state of the algorithm only the amplitude of the basis state corresponding to the solution affects the running time of the algorithm, …
We investigate the effects of systematic errors of the control parameters on single-qubit gates based on non-adiabatic non-Abelian geometric holonomies and those relying on purely dynamical evolution. It is explicitly shown that the systematic error in the Rabi frequency of the control fields affects these two kinds of gates in different ways. In the presence of this systematic error, the transformation produced by the non-adiabatic non-Abelian geometric gate is not unitary in the computational space, and the resulting gate infidelity is larger than that with the dynamical method. Our results …
Digital adiabatic evolution is universally accurate
本研究证明数字绝热演化对模拟误差具有内在鲁棒性且误差不随时间累积，通过分析Trotterization和广义量子信号处理方法，结合数值模拟证实其效率远超预期，为量子平台上的准确高效实现奠定基础。
Adiabatic Quantum Phase Estimation
本文提出了一种简单的绝热协议，用于量子相位估计，实现了最优的海森堡极限缩放，同时在精度和失败概率上具有鲁棒性。
Hardness-dependent quantum adiabatic schedules for the maximum-independent-set problem
针对最大独立集问题与中性原子量子计算平台，提出一种依赖问题难度而非规模的高效绝热调度数值方法，性能优于基准且易硬件实现，已在256量子比特Aquila计算机上验证，扩展至混合算法有望用现有技术求解更难实例。
We consider the dynamics of a two-level system (qubit) driven by strong and short resonant pulses in the framework of Floquet theory. First we derive analytical expressions for the quasienergies and Floquet states of the driven system. If the pulse amplitude varies very slowly, the system adiabatically follows the instantaneous Floquet states, which acquire dynamical phases that depend on the evolution of the quasienergies over time. The difference between the phases acquired by the two Floquet states corresponds to a qubit state rotation, generalizing the notion of Rabi oscillations to the ca…
For a particular case of three-body scattering in two dimensions, and matching analytical expressions at a transition point, we obtain accurate solutions for the hyperspherical adiabatic basis and potential. We find analytical expressions for the respective, asymptotic, inverse logarithmic and inverse power potential behaviors, that arise as functions of the radial coordinate. The model that we consider is that of two particles interacting with a repulsive step potential, a third particle acting as a spectator. The model is simple but gives insight, as the 2-body interaction is long ranged in …
The adiabatic theorem provides the basis for the adiabatic model of quantum computation. Recently the conditions required for the adiabatic theorem to hold have become a subject of some controversy. Here we show that the reported violations of the adiabatic theorem all arise from resonant transitions between energy levels. In the absence of fast driven oscillations the traditional adiabatic theorem holds. Implications for adiabatic quantum computation is discussed.
We consider the time evolution of the adiabatic particle number in both time-dependent electric fields and in de Sitter spaces, and define a super-adiabatic particle number in which the (divergent) adiabatic expansion is truncated at optimal order. In this super-adiabatic basis, the particle number evolves smoothly in time, according to Berry's universal adiabatic smoothing of the Stokes phenomenon. This super-adiabatic basis also illustrates clearly the quantum interference effects associated with particle production, in particular for sequences of time-dependent electric field pulses, and in…
Dicke State Generation and Extreme Spin Squeezing via Rapid Adiabatic Passage
本文提出在Dicke态基上利用快速绝热通道生成具有最大量子Fisher信息的纠缠态，突破相位灵敏度经典极限，且方案对驱动场变化鲁棒、时间标度优越。
Fast and robust quantum gates is the cornerstone of fault-tolerance quantum computation. In this paper, we propose to achieve quantum gates based on non-cyclic geometric evolution. Dynamical phase during the evolution is cancelled by spin-echo process and the adiabatic control can be sped up through shortcut to adiabatic manner. Different from geometric gates based on cyclic evolution, the superiority of non-cyclic scheme is that the operation time is proportional to the rotation angle (but not the geometric phase) of quantum state. Therefore, the non-cyclic scheme becomes fairly fast in the c…
Quasi-holonomy in non-adiabatic quantum evolution
研究非绝热量子时间演化中沿复格拉斯曼流形回路子空间的准全纯性，通过分解薛定谔演化，获依赖动力学传播子的有效几何生成元，探讨多种分解方式及相关问题。
Fermi's golden rule rate expression for transitions due to nonadiabatic derivative couplings in the adiabatic basis
本文推导了在绝热基矢中非绝热跃迁的费米黄金规则速率表达式，考虑了非Condon效应及振动位移耦合，适用于核振动模型的闭合形式速率表达式。
This paper presents analytic formulas for various transition times in the Landau-Zener model. Considerable differences are found between the transition times in the diabatic and adiabatic bases, and between the jump time (the time for which the transition probability rises to the region of its asymptotic value) and the relaxation time (the characteristic damping time of the oscillations which appear in the transition probability after the crossing). These transition times have been calculated by using the exact values of the transition probabilities and their derivatives at the crossing point …
A measure for adiabatic contributions to quantum transitions
本文提出一种度量量子跃迁中绝热贡献的方法，可区分由本征态绝热变化与多本征态拍频引起的跃迁，并适用于含时密度泛函理论模拟以量化绝热性及核运动的相对重要性。
We present a system composed of two flux qubits and a transmission-line resonator. Instead of using the rotating wave approximation (RWA), we analyse the system by the adiabatical approximation methods under two opposite extreme conditions. Basic properties of the system are calculated and compared under these two different conditions. Energy-level spectrum of the system in the adiabatical displaced oscillator basis is shown, and the theoretical result is compared with the numerical solution.
Nonadiabatic conical intersection dynamics in the local diabatic representation with Strang splitting and Fourier basis
开发了一种精确的锥形交叉非绝热波包动力学方法，结合局部绝热表示、Strang 分裂和 Fourier 基，能捕获所有非绝热效应并无奇点，可直接利用标准电子结构计算的绝热态进行精确建模。
We present a quantum algorithm for implementing $ϕ^4$ lattice scalar field theory on qubit computers. The field is represented in the discretized field amplitude basis. The number of qubits and elementary gates required by the implementation of the evolution operator is proportional to the lattice size. The algorithm allows efficient $ϕ^4$ state preparation for a large range of input parameters in both the normal and broken-symmetry phases. The states are prepared using a combination of variational and adiabatic evolution methods. First, the ground state of a local Hamiltonian, which includes …
Coherent states in the time-energy plane provide a natural basis to study adiabatic scattering. We relate the (diagonal) matrix elements of the scattering matrix in this basis with the frozen on-shell scattering data. We describe an exactly solvable model, and show that the error in the frozen data cannot be estimated by the Wigner time delay alone. We introduce the notion of energy shift, a conjugate of Wigner time delay, and show that for incoming state $ρ(H_0)$ the energy shift determines the outgoing state.
Geometry-Enabled Radiation from Structured Paraxial Electrons
本文提出了一种基于几何框架的结构化电子辐射机制，通过结合Foldy-Wouthuysen变换与Lewis-Ermakov不变量，揭示了非循环几何演化与光子辐射之间的直接联系。
\textit{Ab Initio} Adiabatic Potential Energy Surfaces and Non-adiabatic Couplings for O$_3$: Construction of Four State Diabatic Hamiltonian
本文通过从头计算方法构建了臭氧四个电子态的绝热势能面及非绝热耦合，准确重现了臭氧和氧气的解离能，并分析了非绝热耦合项在四态子希尔伯特空间中的表现。
The Constrained Adiabatic Trajectory Method (CATM) allows us to compute solutions of the time-dependent Schrödinger equation using the Floquet formalism and Fourier decomposition, using matrix manipulation within a non-orthogonal basis set, provided that suitable constraints can be applied to the initial conditions for the Floquet eigenstate. A general form is derived for the inherent absorbing potential, which can reproduce any dispersed boundary conditions. This new artificial potential acting over an additional time interval transforms any wavefunction into a desired state, with an error in…
Preferred Basis in Coupled Electron-Nuclear Dynamics
本文借鉴退相干理论中的指针态和偏好态概念，为强耦合电子-核系统提出一种自然高效的动力学基，并据此重新审视混合量子-经典方法，阐明其成功条件与改进路径。
Geometric-phase control of Krylov complexity in adiabatic dynamics
本文在缓慢演化自旋系统的瞬时本征态基下，研究了量子绝热动力学中Krylov复杂度与Berry相位的关联，发现初始Krylov基为叠加态时Krylov复杂度非零，单量子比特系统中其振荡频率与外场强度和Berry相位相关。
Adiabatically driven dissipative many-body quantum spin systems
本文研究了缓慢横向场驱动的耗散量子Ising自旋链，解析计算了慢动力学生成元与非绝热相干性，发现特定脉冲下系统仅经历经典基态跃迁，并揭示了其与Rydberg原子系综等当前多体研究热点的直接联系。
Adiabatic following has been an widely-employed technique for achieving near-complete population transfer in a `two-level' quantum mechanical system. The theoretical basis, however, could be generalized to a broad class of systems exhibiting SU(2) symmetry. In the present work, we present an analogy of population transfer dynamics of two level atomic system with that of light propagation in a classical `one-dimensional' photonic crystal, commonly known as distributed-Bragg-reflector (DBR). This formalism facilitates in adapting the idea of adiabatic following, more precisely the rapid adiabati…
Does the oscillatory behavior of the Momentum Spectrum depend on the basis in the Post-Transient Stage?
本研究在标量QED中，通过Bogoliubov变换分析两个绝热基下的粒子对产生，发现振荡动量谱在时间标度后重叠，并揭示多光子区域的多模态结构。
We investigate a simple and robust scheme for choosing the phases of adiabatic electronic states smoothly (as a function of geometry) so as to maximize the performance of ab initio non-adiabatic dynamics methods. Our approach is based upon consideration of the overlap matrix ($\mathbf{U}$) between basis functions at successive points in time and selecting the phases so as to minimize the matrix norm of $\log(\mathbf{U})$. In so doing, one can extend the concept of parallel transport to cases with sharp curve crossings. We demonstrate that this algorithm performs well under extreme situations w…
We introduce a self-consistent framework for the analysis of both Abelian and non-Abelian geometric phases associated with open quantum systems, undergoing cyclic adiabatic evolution. We derive a general expression for geometric phases, based on an adiabatic approximation developed within an inherently open-systems approach. This expression provides a natural generalization of the analogous one for closed quantum systems, and we prove that it satisfies all the properties one might expect of a good definition of a geometric phase, including gauge invariance. A striking consequence is the emerge…
Recent experiments with increasingly larger numbers of qubits have sparked renewed interest in adiabatic quantum computation, and in particular quantum annealing. A central question that is repeatedly asked is whether quantum features of the evolution can survive over the long time-scales used for quantum annealing relative to standard measures of the decoherence time. We reconsider the role of decoherence in adiabatic quantum computation and quantum annealing using the adiabatic quantum master equation formalism. We restrict ourselves to the weak-coupling and singular-coupling limits, which c…
Time dependent Vibrational Electronic Coupled Cluster (VECC) theory for non-adiabatic nuclear dynamics
提出含时振动电子耦合簇（VECC）方法，无需基组且多项式标度，可准确模拟非绝热振动电子模型的光电子/紫外-可见吸收光谱，并成功应用于含14个电子态和63个简正模式的六螺烯模型。
We examine the adiabatic preparation of spatially-ordered Rydberg excitations of atoms in finite one-dimensional lattices by frequency-chirped laser pulses, as realized in a number of recent experiments simulating quantum Ising model. Our aims are to unravel the microscopic mechanism of the phase transition from the unexcited state of atoms to the antiferromagnetic-like state of Rydberg excitations by traversing an extended gapless phase, and to estimate the preparation fidelity of the target state in a moderately sized system amenable to detailed numerical analysis. We find that, in the basis…
Non-Abelian holonomic transformations in digitally coupled acoustic waveguides guided by the global adiabatic criterion
研究利用声学平台实现由全局绝热准则引导的非阿贝尔完整变换，通过数字耦合四波导结构及相关模块实现两阶段相位拼接完整演化，相比高斯包络有优势，还支持单向声学模式转换，验证了声学NHTs用于紧凑波控制等作用。
The ground-state potential and dipole moment of carbon monoxide: contributions from electronic correlation, relativistic effects, QED, adiabatic, and non-adiabatic corrections
本文采用相对论耦合簇方法（CCSDT）结合有限场方法，重新计算了CO分子基态的势能曲线和偶极矩曲线，考虑了相对论、QED及绝热修正，结果与半经验数据合理一致。
On-the-fly quantum nonadiabatic dynamics for large systems greatly benefits from the adiabatic representation readily available from the electronic structure programs. However, frequently occurring in this representation conical intersections introduce non-trivial geometric or Berry phases which require a special treatment for adequate modelling of the nuclear dynamics. We analyze two approaches for nonadiabatic dynamics using the time-dependent variational principle and the adiabatic representation. The first approach employs adiabatic electronic functions with global parametric dependence on…
扫码添加微信好友，提出您的宝贵建议 👇
💡 备注请填写：网站反馈
发表机构由 AI 从论文文本抽取，如发现错误，欢迎反馈修正建议。