Anandan-Aharonov测不准关系与智能态

Non-Stoquastic Interactions in Quantum Annealing via the Aharonov-Anandan Phase

We argue that a complete description of quantum annealing (QA) implemented with continuous variables must take into account the non-adiabatic Aharonov-Anandan geometric phase that arises when the system Hamiltonian changes during the anneal. We show that this geometric effect leads to the appearance of non-stoquastic terms in the effective quantum Ising Hamiltonians that are typically used to describe QA with flux-qubits. We explicitly demonstrate the effect of these geometric interactions when QA is performed with a system of one and two coupled flux-qubits. The realization of non-stoquastic …

使用塞曼和海森堡哈密顿量的量子计算实现中的几何门与动力门

Geometric vs. Dynamical Gates in Quantum Computing Implementations Using Zeeman and Heisenberg Hamiltonians

量子计算在几何相位方面，即Berry或Aharonov-Anandan相位，在一定程度上是容错的。我们研究其实现的基础上塞曼耦合旋转场和各向同性海森堡相互作用，描述NMR，也可以实现在量子点和冷原子。利用量子比特基态的一种新的物理表示，我们构造了基于Berry相位和Aharonov-Anandan相位的$π/8$和Hadamard门。对于旋转场中的两个相互作用的量子比特，我们发现，当两个量子比特的旋磁比相等时，基于Berry相位或基于Aharonov-Anandan相位的两个量子比特门总是不可能构造的。在实现量子门的通用集合时，可以组合几何$π/8$和Hadamard门以及动态$\sqrt{\rm SWAP}$门。

Phases of the electronic two-level model under the rotating wave approximation

We present the time evolution of the electronic two-level model in the rotating wave approximation (RWA). We calculate the Aharonov-Anandan phase of the vector states with cyclic evolution either within the period of an external monochromatic electric field or the period corresponding to Rabi's frequency. The Aharonov-Anandan phase is shown to be dependent on the initial vector state, unless the system evolves in the adiabatic regime; in the latter case, the Aharonov-Anandan phase recovers Berry's phase. Our results are also discussed in the quasi-resonant regime.

通过Aharanov-Anandan相移的NMR C-NOT门

NMR C-NOT gate through Aharanov-Anandan's phase shift

最近，提出了利用NMR通过Berry相位（绝热循环几何相位）移位进行量子计算（Jones等人，Nature，403，869（2000））。这种几何量子门由于Berry相位的几何性质，有望对某些类型的错误具有容错性。本文给出了一种在动态无相位演化环上利用Aharonov-Anandan相移（非绝热循环相移）实现NMR C-NOT门的方案。在我们的方案中，门是非相干运行的，因此它受退相干的影响较小。并且，在该方案中，我们在获得几何相移时选择了零动态相位时间演化环，不需要采取任何额外的操作来消除动态相位。

Atomic interferometer measurements of Berry's and Aharonov-Anandan's phases for isolated spins S > 1/2 non-linearly coupled to external fields

The aim of the present paper is to propose experiments for observing the significant features of Berry's phases for S>1, generated by spin-Hamiltonians endowed with two couplings, a magnetic dipole and an electric quadrupole one with external B and E fields, as theoretically studied in our previous work. The fields are assumed orthogonal, this mild restriction leading to geometric and algebraic simplifications. Alkali atoms appear as good candidates for interferometric measurements but there are challenges to be overcome. The only practical way to generate a suitable E-field is to use the ac S…

Geometric and Majorana phases in neutrino oscillations

Geometric (Aharonov--Anandan) phases in neutrino oscillations have been claimed [Phys. Lett. B 780 (2018) 216] to be sensitive to the Majorana phases in neutrino mixing. More recently, however, it has been pointed out [Phys. Lett. B 818 (2021) 136376] that the proposed phases are not gauge invariant. Using both kinematic and geometric approaches, we show that all gauge-invariant Aharonov--Anandan phases (including the off-diagonal geometric phases associated with flavor transitions) are independent of the Majorana phases. This finding, which generalizes the well-known fact that conventional os…

非对易坐标系中的偶极子动力学和量子相位

Dynamics of Dipoles and Quantum Phases in Noncommutative Coordinates

在非对易坐标系中，研究了具有电、磁偶极矩的自旋为1/2的中性粒子与外电场、外磁场相互作用的动力学。空间的非对易性被插入到半经典约束哈密顿系统中。研究了粒子与电磁场相互作用所获得的量子相位与作用在系统上的（半）经典力之间的关系，并将其推广到非对易坐标系中建立量子相位的公式。一般形式主义是适用于物理系统产生的Aharonov-Bohm，Aharonov-Casher，他-McKellar-Wilkens和Anandan阶段在非交换坐标。的非交换性参数θ的界限推导出变形相的Aharonov-Bohm和Aharonov-Casher相的实验数据进行比较。

绝热几何相是否有一个规定的参数空间？

Is there a prescribed parameter's space for the adiabatic geometric phase?

确定了非相对论性带电无自旋粒子在Penning阱和旋转磁场叠加场作用下的周期运动的Aharonov-Anandan和Berry相。讨论了参数空间的选取以及束缚势对称性与Berry相的关系。

Quantum geometric phase in Majorana's stellar representation: Mapping onto a many-body Aharonov-Bohm phase

The (Berry-Aharonov-Anandan) geometric phase acquired during a cyclic quantum evolution of finite-dimensional quantum systems is studied. It is shown that a pure quantum state in a (2J+1)-dimensional Hilbert space (or, equivalently, of a spin-J system) can be mapped onto the partition function of a gas of independent Dirac strings moving on a sphere and subject to the Coulomb repulsion of 2J fixed test charges (the Majorana stars) characterizing the quantum state. The geometric phase may be viewed as the Aharonov-Bohm phase acquired by the Majorana stars as they move through the gas of Dirac s…

Geometric aspects of analog quantum search evolutions

We use geometric concepts originally proposed by Anandan and Aharonov to show that the Farhi-Gutmann time optimal analog quantum search evolution between two orthogonal quantum states is characterized by unit efficiency dynamical trajectories traced on a projective Hilbert space. In particular, we prove that these optimal dynamical trajectories are the shortest geodesic paths joining the initial and the final states of the quantum evolution. In addition, we verify they describe minimum uncertainty evolutions specified by an uncertainty inequality that is tighter than the ordinary time-energy u…

光子量子计算机上的贝里相位

Berry's phase on photonic quantum computers

该研究提出了一种连续变量量子计算算法，用于在光子量子计算机上模拟带电粒子的贝里相位，并通过实验观测到几何相位现象。